Buffer solution ( ).pdf

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____________________WORLD TECHNOLOGIES____________________
Table of Contents
Chapter 1 - Solution
Chapter 2 - Solubility
Chapter 3 - Solubility Equilibrium
Chapter 4 - Solvation and Solvation Shell
Chapter 5 - Ideal Solution
Chapter 6 - Aqueous Solution, Solid Solution and Buffer Solution
Chapter 7 - Mixture and Suspension
Chapter 8 - Colloid
Chapter 9 - Total Dissolved Solids
Chapter 10 - Henry's Law
Chapter 11 - Solvent
Chapter 12 - Acetic Acid
Chapter 13 - gamma–Butyrolactone
Chapter 14 - Dimethyl Sulfoxide
Chapter 15 - Formic Acid
Chapter 16 - Methylsulfonylmethane and Paraldehyde
Chapter 17 - Polyethylene Glycol
Chapter 18 - Acetonitrile and Sulfolane

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Chapter 1
Solution
Making a saline water solution by dissolving table salt (NaCl) in water. The salt is the
solute and the water the solvent.

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In chemistry, a solution is a homogeneous mixture composed of two substances. In such
a mixture, a solute is dissolved in another substance, known as a solvent. The solvent
does the dissolving.
Types of solutions
Solutions are homogenous mixtures consisting of one solvent and one or more solutes.
Homogenous means that the components and properties of the mixture are uniform
throughout its entire volume. Usually, the substance present in the greatest amount is
considered the solvent. Solvents can be gases, liquids, or solids. One or more components
present in the solution other than the solvent are called solutes. The solution has the same
physical state as the solvent.
Gas
If the solvent is a gas, only gases are dissolved under any given set of conditions. An
example of a gaseous solution is air (oxygen and other gases dissolved in nitrogen). Since
interactions between molecules play almost no role, dilute gases form rather trivial
solutions. In part of the literature, they are not even classified as solutions, but addressed
as mixtures.
Liquid
If the solvent is a liquid, then gases, liquids, and solids can be dissolved. Examples are:
• Gas in liquid:
o Oxygen in water.
o Carbon dioxide in water is a less simple example, because the solution is
accompanied by a chemical reaction (formation of ions). Note also that the
visible bubbles in carbonated water are not the dissolved gas, but only an
effervescence; the dissolved gas itself is not visible since it is dissolved on
a molecular level.
• Liquid in liquid:
o The mixing of two or more substances of the same chemistry but different
concentrations to form a constant.(Homogenization of solutions)
o Alcoholic beverages are basically solutions of ethanol in water.
• Solid in liquid:
o Sucrose (table sugar) in water
o Sodium chloride or any other salt in water forms an electrolyte: When
dissolving, salt dissociates into ions.
Counterexamples are provided by liquid mixtures that are not homogeneous: colloids,
suspensions, emulsions are not considered solutions.
Body fluids are examples for complex liquid solutions, containing many different solutes.
They are electrolytes since they contain solute ions (e.g. potassium and sodium).

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Furthermore, they contain solute molecules like sugar and urea. Oxygen and carbon
dioxide are also essential components of blood chemistry, where significant changes in
their concentrations can be a sign of illness or injury.
Solid
If the solvent is a solid, then gases, liquids, and solids can be dissolved.
• Gas in solid:
o Hydrogen dissolves rather well in metals, especially in palladium; this is
studied as a means of hydrogen storage.
• Liquid in solid:
o mercury in gold, forming an amalgam
o Hexane in paraffin wax
• Solid in solid:
o Steel, basically a solution of carbon atoms in a crystalline matrix of iron
atoms.
o Alloys like bronze and many others.
o Polymers containing plasticizers.
Solubility
The ability of one compound to dissolve in another compound is called solubility. When
a liquid is able to completely dissolve in another liquid the two liquids are miscible. Two
substances that can never mix to form a solution are called immiscible.
All solutions have a positive entropy of mixing. The interactions between different
molecules or ions may be energetically favored or not. If interactions are unfavorable,
then the free energy decreases with increasing solute concentration. At some point the
energy loss outweighs the entropy gain, and no more solute particles can be dissolved;
the solution is said to be saturated. However, the point at which a solution can become
saturated can change significantly with different environmental factors, such as
temperature, pressure, and contamination. For some solute-solvent combinations a
supersaturated solution can be prepared by raising the solubility (for example by
increasing the temperature) to dissolve more solute, and then lowering it (for example by
cooling).
Usually, the greater the temperature of the solvent, the more of a given solid solute it can
dissolve. However, most gases and some compounds exhibit solubilities that decrease
with increased temperature. Such behavior is a result of an exothermic enthalpy of
solution. Some surfactants exhibit this behaviour. The solubility of liquids in liquids is
generally less temperature-sensitive than that of solids or gases.

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Properties
The physical properties of compounds such as melting point and boiling point change
when other compounds are added. Together they are called colligative properties. There
are several ways to quantify the amount of one compound dissolved in the other
compounds collectively called concentration. Examples include molarity, mole fraction,
and parts per million (PPM).
The properties of ideal solutions can be calculated by the linear combination of the
properties of its components. If both solute and solvent exist in equal quantities (such as
in a 50% ethanol, 50% water solution), the concepts of "solute" and "solvent" become
less relevant, but the substance that is more often used as a solvent is normally designated
as the solvent (in this example, water).
Liquid solutions
In principle, all types of liquids can behave as solvents: liquid noble gases, molten
metals, molten salts, molten covalent networks, and molecular liquids. In the practice of
chemistry and biochemistry, most solvents are molecular liquids. They can be classified
into polar and non-polar, according to whether their molecules possess a permanent
electric dipole moment. Another distinction is whether their molecules are able to form
hydrogen bonds (protic and aprotic solvents). Water, the most commonly used solvent, is
both polar and sustains hydrogen bonds.
Water is a good solvent because the molecules are polar and capable of forming hydrogen
bonds.

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Salts dissolve in polar solvents, forming positive and negative ions that are attracted to
the negative and positive ends of the solvent molecule, respectively. If the solvent is
water, hydration occurs when the charged solute ions become surrounded by water
molecules. A standard example is aqueous saltwater. Such solutions are called
electrolytes.
For non-ionic solutes, the general rule is: like dissolves like.
Polar solutes dissolve in polar solvents, forming polar bonds or hydrogen bonds. As an
example, all alcoholic beverages are aqueous solutions of ethanol. On the other hand,
non-polar solutes dissolve better in non-polar solvents. Examples are hydrocarbons such
as oil and grease that easily mix with each other, while being incompatible with water.
An example for the immiscibility of oil and water is a leak of petroleum from a damaged
tanker, that does not dissolve in the ocean water but rather floats on the surface.

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Chapter 2
Solubility
Solubility is the property of a solid, liquid, or gaseous chemical substance called solute to
dissolve in a liquid solvent to form a homogeneous solution of the solute in the solvent.
The solubility of a substance fundamentally depends on the used solvent as well as on
temperature and pressure. The extent of the solubility of a substance in a specific solvent
is measured as the saturation concentration where adding more solute does not increase
the concentration of the solution.
The solvent is generally a liquid, which can be a pure substance or a mixture. One also
speaks of solid solution, but rarely of solution in a gas.
The extent of solubility ranges widely, from infinitely soluble (fully miscible) such as
ethanol in water, to poorly soluble, such as silver chloride in water. The term insoluble is
often applied to poorly or very poorly soluble compounds.
Under certain conditions the equilibrium solubility can be exceeded to give a so-called
supersaturated solution, which is metastable.
Solubility is not to be confused with the ability to dissolve or liquefy a substance, because
they might occur not only because of dissolution but also because of a chemical reaction.
For example, zinc is insoluble in hydrochloric acid, but does dissolve in it by chemical
reaction into zinc chloride and hydrogen, where zinc chloride is then soluble in
hydrochloric acid. Solubility does not also depend on particle size or other kinetic factors;
given enough time, even large particles will eventually dissolve.
Molecular view
Solubility occurs under dynamic equilibrium, which means that solubility results from the
simultaneous and opposing processes of dissolution and phase joining (e.g. precipitation
of solids). The solubility equilibrium occurs when the two processes proceed at a constant
rate.
The term solubility is also used in some fields where the solute is altered by solvolysis.
For example, many metals and their oxides are said to be "soluble in hydrochloric acid,"
whereas the aqueous acid degrades the solid to irreversibly give soluble products. It is
also true that most ionic solids are degraded by polar solvents, but such processes are

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reversible. In those cases where the solute is not recovered upon evaporation of the
solvent the process is referred to as solvolysis. The thermodynamic concept of solubility
does not apply straightforwardly to solvolysis.
When a solute dissolves, it may form several species in the solution. For example, an
aqueous suspension of ferrous hydroxide, Fe(OH)2, will contain the series
[Fe(H2O)6 − x(OH)x](2 − x)+
as well as other oligomeric species. Furthermore, the solubility
of ferrous hydroxide and the composition of its soluble components depends on pH. In
general, solubility in the solvent phase can be given only for a specific solute which is
thermodynamically stable, and the value of the solubility will include all the species in
the solution (in the example above, all the iron-containing complexes).
Factors affecting solubility
Solubility is defined for specific phases. For example, the solubility of aragonite and
calcite in water are expected to differ, even though they are both polymorphs of calcium
carbonate and have the same chemical formula.
The solubility of one substance in another is determined by the balance of intermolecular
forces between the solvent and solute, and the entropy change that accompanies the
solvation. Factors such as temperature and pressure will alter this balance, thus changing
the solubility.
Solubility may also strongly depend on the presence of other species dissolved in the
solvent, for example, complex-forming anions (ligands) in liquids. Solubility will also
depend on the excess or deficiency of a common ion in the solution, a phenomenon
known as the common-ion effect. To a lesser extent, solubility will depend on the ionic
strength of solutions. The last two effects can be quantified using the equation for
solubility equilibrium.
For a solid that dissolves in a redox reaction, solubility is expected to depend on the
potential (within the range of potentials under which the solid remains the
thermodynamically stable phase). For example, solubility of gold in high-temperature
water is observed to be almost an order of magnitude higher when the redox potential is
controlled using a highly-oxidizing Fe3O4-Fe2O3 redox buffer than with a moderately-
oxidizing Ni-NiO buffer.

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Solubility (metastable) also depends on the physical size of the crystal or droplet of solute
(or, strictly speaking, on the specific or molar surface area of the solute). For highly
defective crystals, solubility may increase with the increasing degree of disorder. Both of
these effects occur because of the dependence of solubility constant on the Gibbs energy
of the crystal. The last two effects, although often difficult to measure, are of practical
importance. For example, they provide the driving force for precipitate aging (the crystal
size spontaneously increasing with time).
Temperature
The solubility of a given solute in a given solvent typically depends on temperature. For
many solids dissolved in liquid water, the solubility increases with temperature up to 100
°C. In liquid water at high temperatures, (e.g., that approaching the critical temperature),
the solubility of ionic solutes tends to decrease due to the change of properties and
structure of liquid water; the lower dielectric constant results in a less polar solvent.
Gaseous solutes exhibit more complex behavior with temperature. As the temperature is
raised, gases usually become less soluble in water (to minimum which is below 120 °C
for most permanent gases), but more soluble in organic solvents.

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The chart shows solubility curves for some typical solid inorganic salts (temperature is in
degrees Celsius). Many salts behave like barium nitrate and disodium hydrogen arsenate,
and show a large increase in solubility with temperature. Some solutes (e.g. NaCl in
water) exhibit solubility which is fairly independent of temperature. A few, such as
cerium(III) sulfate, become less soluble in water as temperature increases. This
temperature dependence is sometimes referred to as "retrograde" or "inverse" solubility.
Occasionally, a more complex pattern is observed, as with sodium sulfate, where the less
soluble decahydrate crystal loses water of crystallization at 32 °C to form a more soluble
anhydrous phase.
The solubility of organic compounds nearly always increases with temperature. The
technique of recrystallization, used for purification of solids, depends on a solute's
different solubilities in hot and cold solvent. A few exceptions exist, such as certain
cyclodextrins.
Pressure
For condensed phases (solids and liquids), the pressure dependence of solubility is
typically weak and usually neglected in practice. Assuming an ideal solution, the
dependence can be quantified as:

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where the index i iterates the components, Ni is the mole fraction of the ith
component in
the solution, P is the pressure, the index T refers to constant temperature, Vi,aq is the
partial molar volume of the ith
component in the solution, Vi,cr is the partial molar volume
of the ith
component in the dissolving solid, and R is the universal gas constant.
The pressure dependence of solubility does occasionally have practical significance. For
example, precipitation fouling of oil fields and wells by calcium sulfate (which decreases
its solubility with decreasing pressure) can result in decreased productivity with time.
Solubility of gases
Henry's law is used to quantify the solubility of gases in solvents. The solubility of a gas
in a solvent is directly proportional to the partial pressure of that gas above the solvent.
This relationship is written as:
where kH is a temperature-dependent constant (for example, 769.2 L•atm/mol for
dioxygen (O2) in water at 298 K), p is the partial pressure (atm), and c is the
concentration of the dissolved gas in the liquid (mol/L).
The solubility of gases is sometimes also quantified using Bunsen solubility coefficient.
In the presence of small bubbles, the solubility of the gas does not depend on the bubble
radius in any other way than through the effect of the radius on pressure (i.e., the
solubility of gas in the liquid in contact with small bubbles is increased due to pressure
increase by Δp = 2γ/r).
Polarity
A popular aphorism used for predicting solubility is "like dissolves like". This statement
indicates that a solute will dissolve best in a solvent that has a similar chemical structure
to itself. This view is simplistic, but it is a useful rule of thumb. The overall solvation
capacity of a solvent depends primarily on its polarity. For example, a very polar
(hydrophilic) solute such as urea is very soluble in highly polar water, less soluble in
fairly polar methanol, and practically insoluble in non-polar solvents such as benzene. In
contrast, a non-polar or lipophilic solute such as naphthalene is insoluble in water, fairly
soluble in methanol, and highly soluble in non-polar benzene.
The solubility is favored by entropy of mixing and depends on enthalpy of dissolution
and the hydrophobic effect.
Synthetic chemists often exploit differences in solubilities to separate and purify
compounds from reaction mixtures, using the technique of liquid-liquid extraction.

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Rate of dissolution
Dissolution is not always an instantaneous process. It is fast when salt and sugar dissolve
in water but much slower for a tablet of aspirin or a large crystal of hydrated copper(II)
sulfate. These observations are the consequence of two factors: the rate of solubilization
is related to the solubility product and the surface area of the material. The speed at
which a solid dissolves may depend on its crystallinity or lack thereof in the case of
amorphous solids and the surface area (crystallite size) and the presence of
polymorphism. Many practical systems illustrate this effect, for example in designing
methods for controlled drug delivery. Critically, the dissolution rate depends on the
presence of mixing and other factors that determine the degree of undersaturation in the
liquid solvent film immediately adjacent to the solid solute crystal. In some cases,
solubility equilibria can take a long time to establish (hours, days, months, or many years;
depending on the nature of the solute and other factors). In practice, it means that the
amount of solute in a solution is not always determined by its thermodynamic solubility,
but may depend on kinetics of dissolution (or precipitation).
The rate of dissolution and solubility should not be confused as they are different
concepts, kinetic and thermodynamic, respectively. The solubilization kinetics, as well as
apparent solubility can be improved after complexation of an active ingredient with
cyclodextrin. This can be used in the case of drug with poor solubility.
Quantification of solubility
Solubility is commonly expressed as a concentration, either by mass (g of solute per kg of
solvent, g per dL (100 mL) of solvent), mass concentration, molarity, molality, mole
fraction or other similar descriptions of concentration. The maximum equilibrium amount
of solute that can dissolve per amount of solvent is the solubility of that solute in that
solvent under the specified conditions. The advantage of expressing solubility in this
manner is its simplicity, while the disadvantage is that it can strongly depend on the
presence of other species in the solvent (for example, the common ion effect).
Solubility constants are used to describe saturated solutions of ionic compounds of
relatively low solubility. The solubility constant is a special case of an equilibrium
constant. It describes the balance between dissolved ions from the salt and undissolved
salt. The solubility constant is also "applicable" (i.e. useful) to precipitation, the reverse
of the dissolving reaction. As with other equilibrium constants, temperature can affect the
numerical value of solubility constant. The solubility constant is not as simple as
solubility, however the value of this constant is generally independent of the presence of
other species in the solvent.
The Flory-Huggins solution theory is a theoretical model describing the solubility of
polymers. The Hansen Solubility Parameters and the Hildebrand solubility parameters are
empirical methods for the prediction of solubility. It is also possible to predict solubility
from other physical constants such as the enthalpy of fusion.

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The partition coefficient (Log P) is a measure of differential solubility of a compound in
a hydrophobic solvent (octanol) and a hydrophilic solvent (water). The logarithm of these
two values enables compounds to be ranked in terms of hydrophilicity (or
hydrophobicity).
Applications
Solubility is of fundamental importance in a large number of scientific disciplines and
practical applications, ranging from ore processing, to the use of medicines, and the
transport of pollutants.
Solubility is often said to be one of the "characteristic properties of a substance," which
means that solubility is commonly used to describe the substance, to indicate a
substance's polarity, to help to distinguish it from other substances, and as a guide to
applications of the substance. For example, indigo is described as "insoluble in water,
alcohol, or ether but soluble in chloroform, nitrobenzene, or concentrated sulfuric acid".
Solubility of a substance is useful when separating mixtures. For example, a mixture of
salt (sodium chloride) and silica may be separated by dissolving the salt in water, and
filtering off the undissolved silica. The synthesis of chemical compounds, by the
milligram in a laboratory, or by the ton in industry, both make use of the relative
solubilities of the desired product, as well as unreacted starting materials, byproducts, and
side products to achieve separation.
Another example of this is the synthesis of benzoic acid from phenylmagnesium bromide
and dry ice. Benzoic acid is more soluble in an organic solvent such as dichloromethane
or diethyl ether, and when shaken with this organic solvent in a separatory funnel, will
preferentially dissolve in the organic layer. The other reaction products, including the
magnesium bromide, will remain in the aqueous layer, clearly showing that separation
based on solubility is achieved. This process, known as liquid-liquid extraction, is an
important technique in synthetic chemistry.
Solubility of ionic compounds in water
Some ionic compounds (salts) dissolve in water, which arises because of the attraction
between positive and negative charges. For example, the salt's positive ions (e.g. Ag+
)
attract the partially-negative oxygens in H2O. Likewise, the salt's negative ions (e.g. Cl−
)
attract the partially-positive hydrogens in H2O. Note: oxygen is partially-negative
because it is more electronegative than hydrogen, and vice-versa.
AgCl(s) Ag+
(aq) + Cl−
(aq)
However, there is a limit to how much salt can be dissolved in a given volume of water.
This amount is given by the solubility product, Ksp. This value depends on the type of salt
(AgCl vs. NaCl, for example), temperature, and the common ion effect.

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One can calculate the amount of AgCl that will dissolve in 1 liter of water, some algebra
is required.
Ksp = [Ag+
] × [Cl−
] (definition of solubility product)
Ksp = 1.8 × 10−10
(from a table of solubility products)
[Ag+
] = [Cl−
], in the absence of other silver or chloride salts,
[Ag+
]2
= 1.8 × 10−10
[Ag+
] = 1.34 × 10−5
The result: 1 liter of water can dissolve 1.34 × 10−5
moles of AgCl(s) at room temperature.
Compared with other types of salts, AgCl is poorly soluble in water. In contrast, table salt
(NaCl) has a higher Ksp and is, therefore, more soluble.
Soluble Insoluble
Group I and NH4
+
compounds
Carbonates (Except Group I, NH4
+
and
uranyl compounds)
Nitrates
Sulfites (Except Group I and NH4
+
compounds)
Acetates (Ethanoates) (Except Ag+
compounds)
Phosphates (Except Group I and NH4
+
compounds)
Chlorides, bromides and iodides (Except
Ag+
, Pb2+
, Cu+
and Hg2
2+
)
Hydroxides and oxides (Except Group I,
NH4
+
, Ba2+
, Sr2+
and Tl+
)
Sulfates (Except Ag+
, Pb2+
, Ba2+
, Sr2+
and
Ca2+
)
Sulfides (Except Group I, Group II and
NH4
+
compounds)
Solubility of organic compounds
The principle outlined above under polarity, that like dissolves like, is the usual guide to
solubility with organic systems. For example, petroleum jelly will dissolve in gasoline
because both petroleum jelly and gasoline are hydrocarbons. It will not, on the other
hand, dissolve in alcohol or water, since the polarity of these solvents is too high. Sugar
will not dissolve in gasoline, since sugar is too polar in comparison with gasoline. A
mixture of gasoline and sugar can therefore be separated by filtration, or extraction with
water.
Solubility in non-aqueous solvents
Most publicly available solubility values are those for solubility in water. The reference
also lists some for non-aqueous solvents. Solubility data for non-aqueous solvents is
currently being collected via an open notebook science crowdsourcing project.

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Solid solution
This term is often used in the field of metallurgy to refer to the extent that an alloying
element will dissolve into the base metal without forming a separate phase. The solubility
line (or curve) is the line (or lines) on a phase diagram which give the limits of solute
addition. That is, the lines show the maximum amount of a component that can be added
to another component and still be in solid solution. In the solid's crystalline structure, the
'solute' element can either take the place of the matrix within the lattice (a substitutional
position, for example: chromium in iron) or can take a place in a space between the
lattice points (an interstitial position, for example: carbon in iron).
In microelectronic fabrication, solid solubility refers to the maximum concentration of
impurities one can place into the substrate.
Incongruent dissolution
Many substances dissolve congruently, i.e., the composition of the solid and the dissolved
solute stoichiometrically match. However, some substances may dissolve incongruently,
whereby the composition of the solute in solution does not match that of the solid. This
solubilization is accompanied by alteration of the "primary solid" and possibly formation
of a secondary solid phase. However, generally, some primary solid also remains and a
complex solubility equilibrium establishes. For example, dissolution of albite may result
in formation of gibbsite.
NaAlSi3O8(s) + H+
+ 7H2O = Na+
+ Al(OH)3(s) + 3H4SiO4.
In this case, the solubility of albite is expected to depend on the solid-to-solvent ratio.
This kind of solubility is of great importance in geology, where it results in formation of
metamorphic rocks.

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Chapter 3
Solubility Equilibrium
Solubility equilibrium is a type of dynamic equilibrium. It exists when a chemical
compound in the solid state is in chemical equilibrium with a solution of that compound.
The solid may dissolve unchanged, with dissociation or with chemical reaction with
another constituent of the solvent, such as acid or alkali. Each type of equilibrium is
characterized by a temperature-dependent equilibrium constant. Solubility equilibria are
important in pharmaceutical, environmental and many other scenarios.
Definitions
A solubility equilibrium exists when a chemical compound in the solid state is in
chemical equilibrium with a solution of that compound. The equilibrium is an example of
dynamic equilibrium in that some individual molecules migrate between the solid and
solution phases such that the rates of dissolution and precipitation are equal to one
another. When equilibrium is established, the solution is said to be saturated. The
concentration of the solute in a saturated solution is known as the solubility. Units of
solubility may be molar (mol dm−3
) or expressed as mass per unit volume, such as μg
ml−1
. Solubility is temperature dependent. A solution containing a higher concentration of
solute than the solubility is said to be supersaturated. A supersaturated solution may be
induced to come to equilibrium by the addition of a "seed" which may be a tiny crystal of
the solute, or a tiny solid particle, which initiates precipitation.
There are three main types of solubility equilibria.
1. Simple dissolution.
2. Dissolution with dissociation. This is characteristic of salts. The equilibrium
constant is known in this case as a solubility product.
3. Dissolution with reaction. This is characteristic of the dissolution of weak acids or
weak bases in aqueous media of varying pH.
In each case an equilibrium constant can be specified as a quotient of activities. This
equilibrium constant is dimensionless as activity is a dimensionless quantity. However,
use of activities is very inconvenient, so the equilibrium constant is usually divided by
the quotient of activity coefficients, to become a quotient of concentrations. Moreover,
the concentration of solvent is usually taken to be constant and so is also subsumed into
the equilibrium constant. For these reasons, the constant for a solubility equilibrium has

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dimensions related to the scale on which concentrations are measured. Solubility
constants defined in terms of concentrations are not only temperature dependent, but also
may depend on solvent composition when the solvent contains also species other than
those derived from the solute.
Phase effect
Equilibria are defined for specific crystal phases. Therefore, the solubility product is
expected to be different depending on the phase of the solid. For example, aragonite and
calcite will have different solubility products even though they have both the same
chemical identity (calcium carbonate). Nevertheless, under given conditions, most likely
only one phase is thermodynamically stable and therefore this phase enters a true
equilibrium.
Particle size effect
The thermodynamic solubility constant is defined for large monocrystals. Solubility will
increase with decreasing size of solute particle (or droplet) because of the additional
surface energy. This effect is generally small unless particles become very small,
typically smaller than 1 μm. The effect of the particle size on solubility constant can be
quantified as follows:
where *
KA is the solubility constant for the solute particles with the molar surface area A,
is the solubility constant for substance with molar surface area tending to zero
(i.e., when the particles are large), γ is the surface tension of the solute particle in the
solvent, Am is the molar surface area of the solute (in m2
/mol), R is the universal gas
constant, and T is the absolute temperature.
Salt effect
The salt effect refers to the fact that the presence of a salt which has no ion in common
with the solute, has an effect on the ionic strength of the solution and hence on activity
coefficients, so that the equilibrium constant, expressed as a concentration quotient,
changes.

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Temperature effect
Solubility is sensitive to changes in temperature. For example, sugar is more soluble in
hot water than cool water. It occurs because solubility constants, like other types of
equilibrium constant, are functions of temperature. In accordance with Le Chatelier's
Principle, when the dissolution process is endothermic (heat is absorbed), solubility
increases with rising temperature, but when the process is exothermic (heat is released)
solubility decreases with rising temperature. The temperature effect is the basis for the
process of recrystallization, which can be used to purify a chemical compound.
Sodium sulfate shows increasing solubility with temperature below about 32.4°C, but a
decreasing solubility at higher temperature. This is because the solid phase is the
decahydrate, Na2SO4.10H2O, below the transition temperature but a different hydrate
above that temperature.
Pressure effect
For condensed phases (solids and liquids), the pressure dependence of solubility is
typically weak and usually neglected in practice. Assuming an ideal solution, the
dependence can be quantified as:

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where the index i iterates the components, Ni is the mole fraction of the ith
component in
the solution, P is the pressure, the index T refers to constant temperature, Vi,aq is the
partial molar volume of the ith
component in the solution, Vi,cr is the partial molar volume
of the ith
component in the dissolving solid, and R is the universal gas constant.
The pressure dependence of solubility does occasionally have practical significance. For
example, precipitation fouling of oil fields and wells by calcium sulfate (which decreases
its solubility with decreasing pressure) can result in decreased productivity with time.
Simple dissolution
Dissolution of an organic solid can be described as an equilibrium between the substance
in its solid and dissolved forms. For example, when sucrose (table sugar) forms a
saturated solution
.
An equilibrium expression for this reaction can be written, as for any chemical reaction
(products over reactants):
where K is called the thermodynamic solubility constant. The braces indicate activity.
The activity of a pure solid is, by definition, unity. Therefore
The activity of a substance, A, in solution can be expressed as the product of the
concentration, [A], and an activity coefficient, γ. When K is divided by γ the solubility
constant, Ks,
is obtained. This is equivalent to defining the standard state as the saturated solution so
that the activity coefficient is equal to one. The solubility constant is a true constant only
if the activity coefficient is not affected by the presence of any other solutes that may be
present. The unit of the solubility constant is the same as the unit of the concentration of
the solute. For sucrose K = 1.971 mol dm−3
at 25 °C. This shows that the solubility of
sucrose at 25 °C is nearly 2 mol dm−3
(540 g/l). Sucrose is an unusual in that it does not

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easily form a supersaturated solution at higher concentrations, as do most other
carbohydrates.
Dissolution with dissociation
Ionic compounds normally dissociate into their constituent ions when they dissolve in
water. For example, for calcium sulfate:
As for the previous example, the equilibrium expression is:
where K is the thermodynamic equilibrium constant and braces indicate activity. The
activity of a pure solid is, by definition, equal to one.
When the solubility of the salt is very low the activity coefficients of the ions in solution
are nearly equal to one. By setting them to be actually equal to one this expression
reduces to the solubility product expression:
The solubility product for a general binary compound ApBq is given by
ApBq pAq+
+ qBp-
Ksp = [A]p
[B]q
(electrical charges omitted for simplicity of notation)
When the product dissociates the concentration of B is equal to q/p times the
concentration of A.
[B] = q/p [A]
Therefore
Ksp = [A]p
(q/p)q
[A]q
=(q/p)q
× [A]p+q
The solubility, S is 1/p [A]. One may incorporate 1/p and insert it under the root to obtain

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Examples
CaSO4: p=1, q=1,
Na2SO4: p=2, q=1,
Al2(SO4)3: p=2, q=3,
Solubility products are often expressed in logarithmic form. Thus, for calcium sulfate, Ksp
= 4.93×10−5
, log Ksp = -4.32. The smaller the value, or the more negative the log value, the lower the
solubility.
Some salts are not fully dissociated in solution. Examples include MgSO4, famously
discovered by Manfred Eigen to be present in seawater as both an inner sphere complex
and an outer sphere complex. The solubility of such salts is calculated by the method
outlined in dissolution with reaction.
Hydroxides
For hydroxides solubility products are often given in a modified form, K*sp, using
hydrogen ion concentration in place of hydroxide ion concentration. The two
concentrations are related by the self-ionization constant for water, Kw.
Kw=[H+
][OH-
]
For example,
Ca(OH)2 Ca2+
+ 2 OH-
Ksp = [Ca2+
][OH-
]2
= [Ca2+
]Kw
2
[H+
]-2
K*sp = Ksp/Kw
2
= [Ca2+
][H+
]-2
log Ksp for Ca(OH)2 is about -5 at ambient temperatures; log K*sp = -5 + 2 × 14 = 23,
approximately.
Common ion effect
The common-ion effect is the effect of decreasing the solubility of one salt, when another
salt, which has an ion in common with it, is also present. For example, the solubility of

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silver chloride, AgCl, is lowered when sodium chloride, a source of the common ion
chloride, is added to a suspension of AgCl in water.
AgCl(s) Ag+
(aq) + Cl-
(aq); Ksp = [Ag+
][Cl-
]
The solubility, S, in the absence of a common ion can be calculated as follows. The
concentrations [Ag+
] and [Cl-
] are equal because one mole of AgCl dissociates into one
mole of Ag+
and one mole of Cl-
. Let the concentration of [Ag+
](aq) be denoted by x.
Ksp = x2
; S = x =
Ksp for AgCl is equal to 1.77×10−10
mol2
dm−6
at 25°C, so the solubility is 1.33×10−5
mol dm−3
.
Now suppose that sodium chloride is also present, at a concentration of 0.01 mol dm−3
.
The solubility, ignoring any possible effect of the sodium ions, is now calculated by
Ksp = x(0.01 + x)
This is a quadratic equation in x, which is also equal to the solubility.
x2
+ 0.01 x - Ksp = 0
In the case of silver chloride x2
is very much smaller than 0.01 x, so this term can be
ignored. Therefore
S = x = Ksp / 0.01 = 1.77×10−8
mol dm-3
,
a considerable reduction. In gravimetric analysis for silver, the reduction in solubility due
to the common ion effect is used to ensure "complete" precipitation of AgCl.

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Dissolution with reaction
When a concentrated solution of ammonia is added to a suspension of silver chloride
dissolution occurs because a complex of Ag+
is formed
A typical reaction with dissolution involves a weak base, B, dissolving in an acidic
aqueous solution.
B(s) + H+
(aq) BH+
(aq)
This reaction is very important for pharmaceutical products. Dissolution of weak acids in
alkaline media is similarly important.
HnA(s) + OH-
(aq) Hn-1A-
(aq) + H2O
The uncharged molecule usually has lower solubility than the ionic form, so solubility
depends on pH and the acid dissociation constant of the solute. The term "intrinsic
solubility" is used to describe the solubility of the un-ionized form in the absence of acid
or alkali.
Leaching of aluminium salts from rocks and soil by acid rain is another example of
dissolution with reaction: alumino-silicates are bases which react with the acid to form
soluble species, such as Al3+
(aq).
Formation of a chemical complex may also change solubility. A well-known example, is
the addition of a concentrated solution of ammonia to a suspension of silver chloride, in
which dissolution is favoured by the formation of an ammine complex.
AgCl(s) +2 NH3(aq) [Ag(NH3)2]+
(aq) + Cl-
(aq)
Another example involves the addition of water softeners to washing powders to inhibit
the precipitation of salts of magnesium and calcium ions, which are present in hard water,
by forming complexes with them.

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The calculation of solubility in these cases requires two or more simultaneous equilibria
to be considered. For example,
Intrinsic solubility
equilibrium
B(s) B(aq): Ks = [B(aq)]
Acid-base equilibrium
B(aq) + H+
(aq) BH+
(aq) Ka =
[B(aq)][H+
(aq)]/[BH+
(aq)]
A number of computer programs are available to do the calculations. They include:
• Geochem-EZ (freeware) a multi-purpose chemical speciation program, used in
plant nutrition and in soil and environmental chemistry research to perform
equilibrium speciation computations, allowing the user to estimate solution ion
activities and to consider simple complexes and solid phases.
• HySS (freeware) which was used to produce the diagram at the right.
• CHEMEQL A comprehensive computer program for the calculation of
thermodynamic equilibrium concentrations of species in homogeneous and
heterogeneous systems. Many geochemical applications.
• WinSGW A Windows version of the SOLGASWATER computer program.
• Visual MINTEQ A Windows version of MINTEQA2 (ver 4.0). MINTEQA2 is a
chemical equilibrium model for the calculation of metal speciation, solubility
equilibria etc. for natural waters.
• MINEQL+ A chemical equilibrium modeling system for aqueous systems.
Handles a wide range of pH, redox, solubility and sorption scenarios.
• JESS All types of chemical equilibria can be modelled including protonation,
complex formation, redox, solubility and adsorption interactions. Includes an
extensive database.
Experimental determination
The determination of solubility is fraught with difficulties. First and foremost is the
difficulty in establishing that the system is in equilibrium at the chosen temperature. This
is because both precipitation and dissolution reactions may be extremely slow. If the
process is very slow solvent evaporation may be an issue. Supersaturation may occur.
With very insoluble substances, the concentrations in solution are very low and difficult
to determine. The methods used fall broadly into two categories, static and dynamic.
Static methods
In static methods a mixture is brought to equilibrium and the concentration of a species in
the solution phase is determined by chemical analysis. This usually requires separation of
the solid and solution phases. In order to do this the equilibration and separation should
be performed in a thermostatted room. Very low concentrations can be measured if a
radioactive tracer is incorporated in the solid phase.

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A variation of the static method is to add a solution of the substance in a non-aqueous
solvent, such as dimethyl sulfoxide, to an aqueous buffer mixture. Immediate
precipitation may occur giving a cloudy mixture. The solubility measured for such a
mixture is known as "kinetic solubility". The cloudiness is due to the fact that the
precipitate particles are very small resulting in Tyndall scattering. In fact the particles are
so small that the particle size effect comes into play and kinetic solubility is often greater
than equilibrium solubility. Over time the cloudiness will disappear as the size of the
crystallites increases, and eventually equilibrium will be reached in a process known as
precipitate ageing.
Dynamic methods
Solubility values of organic acids, bases, and ampholytes of pharmaceutical interest may
be obtained by a proceess called "Chasing equilibrium solubility". In this procedure, a
quantity of substance is first dissolved at a pH where it exists predominantly in its ionized
form and then a precipitate of the neutral (un-ionized) species is formed by changing the
pH. Subsequently, the rate of change of pH due to precipitation or dissolution is
monitored and strong acid and base titrant are added to adjust the pH to discover the
equilibrium conditions when the two rates are equal. The advantage of this method is that
it is relatively fast as the quantity of precipitate formed is quite small. However, the
performance of the method may be affected by the formation supersaturated solutions.

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Chapter 4
Solvation and Solvation Shell
Solvation
A sodium ion solvated by water molecules. It has to be assumed that delta on hydrogen is
1/2 of delta on oxygen for this diagram to be correct

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Solvation, also sometimes called dissolution, is the process of attraction and association
of molecules of a solvent with molecules or ions of a solute. As ions dissolve in a solvent
they spread out and become surrounded by solvent molecules.
Distinction between solvation, dissolution and solubility
By an IUPAC definition, solvation is an interaction of a solute with the solvent, which
leads to stabilization of the solute species in the solution. One may also refer to the
solvated state, whereby an ion in a solution is complexed by solvent molecules. The
concept of the solvation interaction can also be applied to an insoluble material, for
example, solvation of functional groups on a surface of ion-exchange resin.
Solvation is, in concept, distinct from dissolution and solubility. Dissolution is a kinetic
process, and is quantified by its rate. Solubility quantifies the dynamic equilibrium state
achieved when the rate of dissolution equals the rate of precipitation.
The consideration of the units makes the distinction clearer. Complexation can be
described by coordination number and the complex stability constants. The typical unit
for dissolution rate is mol/s. The unit for solubility can be mol/kg.
Liquefaction accompanied by an irreversible chemical change is also distinct from
solvation. For example, zinc cannot be solvated by hydrochloric acid, but it can be
converted into the soluble salt zinc chloride by a chemical reaction.
Solvents and intermolecular interactions
Polar solvents are those with a molecular structure that contains dipoles. Such
compounds are often found to have a high dielectric constant. The polar molecules of
these solvents can solvate ions because they can orient the appropriate partially-charged
portion of the molecule towards the ion in response to electrostatic attraction. This
stabilizes the system and creates a solvation shell (or hydration shell in the case of water).
Water is the most common and well-studied polar solvent, but others exist, such as
acetonitrile, dimethyl sulfoxide, methanol, propylene carbonate, ammonia, ethanol, and
acetone. These solvents can be used to dissolve inorganic compounds such as salts.
Solvation involves different types of intermolecular interactions: hydrogen bonding, ion-
dipole, and dipole-dipole attractions or van der Waals forces. The hydrogen bonding, ion-
dipole, and dipole-dipole interactions occur only in polar solvents. Ion-ion interactions
occur only in ionic solvents. The solvation process will be thermodynamically favored
only if the overall Gibbs energy of the solution is decreased, compared to the Gibbs
energy of the separated solvent and solid (or gas or liquid). This means that the change in
enthalpy minus the change in entropy (multiplied by the absolute temperature) is a
negative value, or that the Gibbs free energy of the system decreases.
The conductivity of a solution depends on the solvation of its ions.

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Thermodynamic considerations
For solvation to occur, energy is required to release individual ions from the crystal
lattices in which they are present. This is necessary to break the attractions the ions have
with each other and is equal to the solid's lattice free energy (the energy released at the
formation of the lattice as the ions bonded with each other). The energy for this comes
from the energy released when ions of the lattice associate with molecules of the solvent.
Energy released in this form is called the free energy of solvation.
The enthalpy of solution is the solution enthalpy minus the enthalpy of the separate
systems, whereas the entropy is the corresponding difference in entropy. Most gases have
a negative enthalpy of solution. A negative enthalpy of solution means that the solute is
less soluble at high temperatures.
Although early thinking was that a higher ratio of a cation's ion charge to the size, or the
charge density, resulted in more solvation, this does not stand up to scrutiny for ions like
iron(III) or lanthanides and actinides, which are readily hydrolyzed to form insoluble
(hydrous) oxides. As solids, these are, it is apparent, not solvated.
Enthalpy of solvation can help explain why solvation occurs with some ionic lattices but
not with others. The difference in energy between that which is necessary to release an
ion from its lattice and the energy given off when it combines with a solvent molecule is
called the enthalpy change of solution. A negative value for the enthalpy change of
solution corresponds to an ion that is likely to dissolve, whereas a high positive value
means that solvation will not occur. It is possible that an ion will dissolve even if it has a
positive enthalpy value. The extra energy required comes from the increase in entropy
that results when the ion dissolves. The introduction of entropy makes it harder to
determine by calculation alone whether a substance will dissolve or not. A quantitative
measure for solvation power of solvents is given by donor numbers.
In general, thermodynamic analysis of solutions is done by modeling them as reactions.
For example; if you add sodium chloride(s) to water, the salt will dissociate into the ions
sodium(+aq) and chloride(-aq). The equilibrium constant for this dissociation can be
predicted by the change in gibb's free energy of this reaction.

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Solvation shell
The first solvation shell of a sodium ion dissolved in water
A Solvation shell is a shell of any chemical species acting as a solvent, surrounding a
solute species. When the solvent is water it is often referred to as a hydration shell.
A classic example is water molecules solvating a metal ion. The electronegative oxygen
atom contained in the water molecule attracts electrostatically to the positive charge on
the metal ion. The result is a 'solvation shell' of water molecules surrounding the ion. This
shell can be several molecules thick, dependent on the charge of the ion.
Hydration Shells of Proteins
The hydration shell (also sometimes called hydration layer) that forms around proteins is
of particular importance in biochemistry. This interaction of the protein surface with the

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surrounding water is often referred to as protein hydration and is fundamental to the
activity of the protein. The hydration layer around a protein has been found to have
dynamics distinct from the bulk water to a distance of 1 nm with effects on the
surrounding water network extending beyond 2 nm. The duration of contact of a specific
water molecule with the protein surface may be in the subnanosecond range while
molecular dynamics simulations suggest the time water spends in the hydration shell
before mixing with the outside bulk water could be in the femtosecond to picosecond
range.
With other solvents and solutes, varying steric and kinetic factors can also affect the
solvation shell. It is a very useful concept in Biochemistry.

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Chapter 5
Ideal Solution
In chemistry, an ideal solution or ideal mixture is a solution in which the enthalpy of
solution (or "enthalpy of mixing") is zero; the closer to zero the enthalpy of solution is,
the more "ideal" the behavior of the solution becomes. Equivalently, an ideal mixture is
one in which the activity coefficients (which measure deviation from ideality) are equal
to one.
The concept of an ideal solution is fundamental to chemical thermodynamics and its
applications, such as the use of colligative properties.
Physical origin
Ideality of solutions is analogous to ideality for gases, with the important difference that
intermolecular interactions in liquids are strong and can not simply be neglected as they
can for ideal gases. Instead we assume that the mean strength of the interactions are the
same between all the molecules of the solution.
More formally, for a mix of molecules of A and B, the interactions between unlike
neighbors (UAB) and like neighbors UAA and UBB must be of the same average strength
i.e. 2UAB=UAA+ UBB and the longer-range interactions must be nil (or at least
indistinguishable). If the molecular forces are the same between AA, AB and BB, i.e.
UAB=UAA=UBB, then the solution is automatically ideal.
If the molecules are almost identical chemically, e.g. 1-butanol and 2-butanol, then the
solution will be ideal. Since the interaction energies between A and B are the same, it
follows that there is no overall energy (enthalpy) change when the substances are mixed.
The more dissimilar the nature of A and B, the more strongly the solution is expected to
deviate from ideality.
Formal definition
An ideal mixture is defined as a mixture that satisfies:

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where fi is the fugacity of component i and is the fugacity of i as a pure substance.
Since the definition of fugacity in a pure substance is:
Where ggas
(T,pu
) is the molar free energy of an ideal gas at a temperature T and a
reference pressure pu
which might be taken as P0
or the pressure of the mix to ease
operations.
If we differentiate this last equation with respect to P at T constant we get:
but we know from the Gibbs potential equation that:
These last two equations put together give:
Since all this, done as a pure substance is valid in a mix just adding the subscript i to all
the intensive variables and changing v to , standing for Partial molar volume.
Applying the first equation of this section to this last equation we get
which means that in an ideal mix the volume is the addition of the volumes of its
components.
Proceeding in a similar way but derivative with respect of T we get to a similar result
with enthalpies

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derivative with respect to T and remembering that we get:
which in turn is .
Meaning that the enthalpy of the mix is equal to the sum of its components.
Since and :
It is also easily verifiable that
Finally since
Which means that
Δgi,mix = RTlnxi
and since
G = ∑xigi
i
then
ΔGmix = RT ∑xilnxi
i

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At last we can calculate the entropy of mixing since and
Δsi,mix = − R ∑lnxi
i
ΔSmix = − R ∑xilnxi
i
Consequences
Solvent-Solute interactions are similar to solute-solute and solvent-solvent interactions
Since the enthalpy of mixing (solution) is zero, the change in Gibbs free energy on
mixing is determined solely by the entropy of mixing. Hence the molar Gibbs free energy
of mixing is
ΔGm,mix = RT ∑xilnxi
i
or for a two component solution
ΔGm,mix = RT(xAlnxA + xBlnxB)
where m denotes molar i.e. change in Gibbs free energy per mole of solution, and xi is the
mole fraction of component i.
Note that this free energy of mixing is always negative (since each xi is positive and each
lnxi must be negative) i.e. ideal solutions are always completely miscible.
The equation above can be expressed in terms of chemical potentials of the individual
components
ΔGm,mix = ∑xiΔμi,mix
i
where Δμi,mix = RTlnxi is the change in chemical potential of i on mixing.
If the chemical potential of pure liquid i is denoted , then the chemical potential of i in
an ideal solution is

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Any component i of an ideal solution obeys Raoult's Law over the entire composition
range:
where
is the equilibrium vapor pressure of the pure component
is the mole fraction of the component in solution
It can also be shown that volumes are strictly additive for ideal solutions.
Non-ideality
Deviations from ideality can be described by the use of Margules functions or activity
coefficients. A single Margules parameter may be sufficient to describe the properties of
the solution if the deviations from ideality are modest; such solutions are termed regular.
In contrast to ideal solutions, where volumes are strictly additive and mixing is always
complete, the volume of a non-ideal solution is not, in general, the simple sum of the
volumes of the component pure liquids and solubility is not guaranteed over the whole
composition range.

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Chapter 6
Aqueous Solution, Solid Solution and
Buffer Solution
Aqueous solution
The first solvation shell of a sodium ion dissolved in water
An aqueous solution is a solution in which the solvent is water. It is usually shown in
chemical equations by appending (aq) to the relevant formula. The word aqueous means
pertaining to, related to, similar to, or dissolved in water. As water is an excellent solvent
and is also naturally abundant, it is an ubiquitous solvent in chemistry.

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Substances which are hydrophobic ('water fearing') often do not dissolve well in water
whereas those that hydrophilic ('water-loving') do. An example of a hydrophilic
substance would be sodium chloride (ordinary table salt). Acids and bases are aqueous
solutions, as part of their Arrhenius definitions.
The ability of a substance to dissolve in water is determined by whether the substance can
match or exceed the strong attractive forces that water molecules generate between
themselves. If the substance lacks the ability to dissolve in water the molecules form a
precipitate.
Aqueous solutions that conduct electric current efficiently contain strong electrolytes,
while ones that conduct poorly are considered to have weak electrolytes. Those strong
electrolytes are substances that are completely ionized in water, whereas the weak
electrolytes exhibit only a small degree of ionization in water.
Nonelectrolytes are substances that dissolve in water, but which maintain their molecular
integrity (do not dissociate into ions). Examples include sugar, urea, glycerol, and
methylsulfonylmethane (MSM).
When performing calculations regarding the reacting of one or more aqueous solutions,
one generally must know the concentration, or molarity, of the aqueous solutions.
Solution concentration is given in terms of the form of the solute prior to it dissolving.

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Solid solution
Fig. 1 A binary phase diagram displaying solid solutions over the full range of relative
concentrations.
A solid solution is a solid-state solution of one or more solutes in a solvent. Such a
mixture is considered a solution rather than a compound when the crystal structure of the
solvent remains unchanged by addition of the solutes, and when the mixture remains in a
single homogeneous phase.This often happens when the two elements (generally metals)
involved are close together on the periodic table; conversely, a chemical compound is
generally a result of the non proximity of the two metals involved on the periodic table.
Details
The solute may incorporate into the solvent crystal lattice substitutionally, by replacing a
solvent particle in the lattice, or interstitially, by fitting into the space between solvent
particles. Both of these types of solid solution affect the properties of the material by
distorting the crystal lattice and disrupting the physical and electrical homogeneity of the
solvent material.

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Some mixtures will readily form solid solutions over a range of concentrations, while
other mixtures will not form solid solutions at all. The propensity for any two substances
to form a solid solution is a complicated matter involving the chemical, crystallographic,
and quantum properties of the substances in question. Solid solutions, in accordance with
the Hume-Rothery rules, may form if the solute and solvent have:
• Similar atomic radii (15% or less difference)
• Same crystal structure
• Similar electronegativities
• Similar valency
The phase diagram in Fig. 1 displays an alloy of two metals which forms a solid solution
at all relative concentrations of the two species. In this case, the pure phase of each
element is of the same crystal structure, and the similar properties of the two elements
allow for unbiased substitution through the full range of relative concentrations.
Solid solutions have important commercial and industrial applications, as such mixtures
often have superior properties to pure materials. Many metal alloys are solid solutions.
Even small amounts of solute can affect the electrical and physical properties of the
solvent.
Fig. 2 This binary phase diagram shows two solid solutions: α and β
The binary phase diagram in Fig. 2 at right shows the phases of a mixture of two
substances in varying concentrations, α and β. The region labeled "α" is a solid solution,
with β acting as the solute in a matrix of α. On the other end of the concentration scale,
the region labeled "β" is also a solid solution, with α acting as the solute in a matrix of β.
The large solid region in between the α and β solid solutions, labeled "α and β", is not a
solid solution. Instead, an examination of the microstructure of a mixture in this range
would reveal two phases — solid solution α-in-β and solid solution β-in-α would form
separate phases, perhaps lamella or grains.

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Application
In the phase diagram, the unalloyed extreme left and right concentrations, and the dip in
the center, the material will be solid and become liquid as heat is added, where at other
proportions the material will enter a mushy or pasty phase. The mixture at dip point of
the diagram is called a eutectic alloy. Lead-tin mixtures formulated at that point (37/63
mixture) are useful when soldering electronic components, particularly if done manually,
since the solid phase is quickly entered as the solder cools. In contrast, when lead-tin
mixtures were used to solder seams in automobile bodies a pasty state enabled a shape to
be formed with a wooden paddle or tool, so a 70-30 lead to tin ratio was used. (Lead is
being removed from such applications owing to its toxicity and consequent difficulty in
recycling devices and components that include lead.)
Exsolution
When a solid solution becomes unstable — due to a lower temperature, for example —
exsolution occurs and the two phases separate into distinct microscopic to megascopic
lamellae. This is mainly caused by cation size, cations who have a large difference in
radii are not likely to readily substitute.
Take the alkali feldspar minerals for example, whose end members are albite, NaAlSi3O8
and microcline, KAlSi3O8. At high temperatures Na+
and K+
readily substitute for each
other and so the minerals will form a solid solution, yet at low temperatures albite can
only substitute a small amount of K+
and the same applies for Na+
in the microcline, this
leads to exsolution where they will separate into two separate phases. In the case of the
alkali feldspar minerals, thin white albite layers will alternate between typically pink
microcline.
Buffer solution
A buffer solution is an aqueous solution consisting of a mixture of a weak acid and its
conjugate base or a weak base and its conjugate acid. It has the property that the pH of
the solution changes very little when a small amount of strong acid or base is added to it.
Buffer solutions are used as a means of keeping pH at a nearly constant value in a wide
variety of chemical applications. Many life forms thrive only in a relatively small pH
range; an example of a buffer solution is blood.
Principles of Buffering
Buffer solutions achieve their resistance to pH due to the presence of a 'reservoir' of both
acid HA and conjugate base A-
. In contrast to a buffer, strong acids in solution will be
almost entirely in the form of the conjugate base A-
, while weak acids will be

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predominantly HA. Because the buffering effect depends on the presence of both species,
buffer solutions are most effective at pH values near to the pKa of the acid, where the
concentrations are equal.
Adding H+
to the solution will result in the reaction H+
+ A-
→ HA. Because HA is a
weak acid, it will remain mostly in its protonated state, so the increase in free H+
concentration will be lower than the amount of H+
added to the solution.
Adding OH-
to the solution will decrease the H+
concentration by combining with H+
to
form H2O. However, this will perturb the dissociation equilibrium of HA: HA H+
+ A-
,
so that more H+
dissociates from HA to counteract the change.
Calculating Buffer pH
The acid dissociation constant for a weak acid, HA, is defined as
Simple manipulation with logarithms gives the Henderson-Hasselbalch equation, which
describes pH in terms of pKa
In this equation [A−
] is the concentration of the conjugate base and [HA] is the
concentration of the acid. By manipulating this equation, it is possible either to calculate
the pH of a buffer solution of known composition, or to calculate the relative
concentrations of acid and conjugate base required to achieve a specific pH value. An
ICE table can also be used for this purpose. When the concentrations of acid and
conjugate base are equal, often described as half-neutralization, pH = pKa.
The calculated pH may be different from measured pH. Glass electrodes found in
common pH meters respond not to the concentration of hydrogen ions ([H+
]), but to their
activity, which depends on several factors, primarily on the ionic strength of the media.
For example, calculation of pH of phosphate-buffered saline would give the value of
7.96, whereas the actual pH is 7.4.
The same considerations apply to a mixture of a weak base, B and its conjugate acid BH+
.
B + H2O BH+
+ OH-
.
The pKa value to be used is that of the acid conjugate to the base.

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In general a buffer solution may be made up of more than one weak acid and its
conjugate base; if the individual buffer regions overlap a wider buffer region is created by
mixing the two buffering agents.
Applications
Buffer solutions are necessary to keep the correct pH for enzymes in many organisms to
work. Many enzymes work only under very precise conditions; if the pH strays too far
out of the margin, the enzymes slow or stop working and can denature, thus permanently
disabling their catalytic activity. A buffer of carbonic acid (H2CO3) and bicarbonate
(HCO3
−
) is present in blood plasma, to maintain a pH between 7.35 and 7.45.
Industrially, buffer solutions are used in fermentation processes and in setting the correct
conditions for dyes used in colouring fabrics. They are also used in chemical analysis and
calibration of pH meters.
The majority of biological samples that are used in research are made in buffers,
especially phosphate buffered saline (PBS) at pH 7.4.
Useful buffer mixtures
Components pH range
HCl, Sodium citrate 1 - 5
Citric acid, Sodium citrate 2.5 - 5.6
Acetic acid, Sodium acetate 3.7 - 5.6
K2HPO4, KH2PO4 5.8 - 8
Na2HPO4, NaH2PO4 6 - 7.5
Borax, Sodium hydroxide 9.2 - 11
"Universal" buffer mixtures
By combining substances with pKa values differing by only two or less and adjusting the
pH a wide-range of buffers can be obtained. Citric acid is a useful component of a buffer
mixture because it has three pKa values, separated by less than two. The buffer range can
be extended by adding other buffering agents. The following two-component mixtures
(McIlvaine's buffer solutions) have a buffer range of pH 3 to 8.
0.2M Na2HPO4 /mL 0.1M Citric Acid /mL pH...
20.55 79.45 3.0
38.55 61.45 4.0
51.50 48.50 5.0
63.15 36.85 6.0
82.35 17.65 7.0
97.25 2.75 8.0

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A mixture containing citric acid, potassium dihydrogen phosphate, boric acid, and diethyl
barbituric acid can be made to cover the pH range 2.6 to 12.
Other universal buffers are Carmody buffer and Britton-Robinson buffer, developed in
1931.
Common buffer compounds used in biology
Common
Name
pKa
at
25°C
Buffer
Range
Temp
Effect
dpH/dT
in
(1/K)
**
Mol.
Weight
Full Compound Name
TAPS 8.43
7.7–
9.1
−0.018 243.3
3-
{[tris(hydroxymethyl)methyl]amino}propanesulfonic
acid
Bicine 8.35
7.6–
9.0
−0.018 163.2 N,N-bis(2-hydroxyethyl)glycine
Tris 8.06
7.5–
9.0
−0.028 121.14 tris(hydroxymethyl)methylamine
Tricine 8.05
7.4–
8.8
−0.021 179.2 N-tris(hydroxymethyl)methylglycine
HEPES 7.55
6.8–
8.2
−0.014 238.3 4-2-hydroxyethyl-1-piperazineethanesulfonic acid
TES 7.40
6.8–
8.2
−0.020 229.20
2-
{[tris(hydroxymethyl)methyl]amino}ethanesulfonic
acid
MOPS 7.20
6.5–
7.9
−0.015 209.3 3-(N-morpholino)propanesulfonic acid
PIPES 6.76
6.1–
7.5
−0.008 302.4 piperazine-N,N′-bis(2-ethanesulfonic acid)
Cacodylate 6.27
5.0–
7.4
138.0 dimethylarsinic acid
SSC 7.0
6.5-
7.5
189.1 saline sodium citrate
MES 6.15
5.5–
6.7
−0.011 195.2 2-(N-morpholino)ethanesulfonic acid
** Values are approximate.

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Chapter 7
Mixture and Suspension
Mixture
A suspension of flour in water, a heterogeneous mixture
In chemistry, a mixture is a material system made up by two or more different
substances which are mixed together but are not combined chemically. Mixture refers to

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the physical combination of two or more substances the identities of which are retained
and are mixed in the form of alloys, solutions, suspensions, and colloids.
Mixtures are the product of a mechanical blending or mixing of chemical substances like
elements and compounds, without chemical bonding or other chemical change, so that
each ingredient substance retains its own chemical properties and makeup. Nonetheless,
despite there are no chemical changes to its constituents, the physical properties of a
mixture, such as its melting point, may differ from those of the components. Some
mixtures can be separated into their components by physical (mechanical or thermal)
means. Azeotropes can be considered as a kind of mixture which usually pose
considerable difficulties regarding the separation processes required to obtain their
constituents (physical or chemical processes or, even a blend of them).
Mixtures can be either homogeneous or heterogeneous. A homogeneous mixture is a type
of mixture in which the composition is uniform. A heterogeneous mixture is a type of
mixture in which the components can easily be identified, as there are two or more phases
present. Air is a homogeneous mixture of the gaseous substances nitrogen, oxygen, and
smaller amounts of other substances. Salt, sugar, and many other substances dissolve in
water to form homogeneous mixtures. A homogeneous mixture in which there is both a
solute and solvent present is also a solution.
The following table shows the main properties of the three families of mixtures.
Solution Colloid Dispersion
Mixture
homogeneity
Homogeneous
Visually homogeneous but
microscopically heterogeneous
Heterogeneous
Particle size
< 1
nanometer
between 1 nanometer and 1
micrometer
> 1 micrometer
Physical stability Yes Yes
No: needs
stabilizing agents
Tyndall effect No Yes Yes
Separates by
centrifugation
No Yes Yes
Separates by
decantation
No No Yes

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The following table shows examples of the three types of mixtures.
Dissolved
or
dispersed
phase
Continuous
medium
Solution Colloid Dispersion
Gas Gas
Gas mixture: air
(oxygen and
other gases in
nitrogen)
None None
Liquid Gas None
Aerosol: fog, mist,
vapor, hair sprays
Aerosol
Solid Gas None
Solid aerosol:
smoke, cloud, air
particulates
Solid aerosol: dust
Gas Liquid
Solution: oxygen
in water
Foam: whipped
cream, shaving
cream
Foam
Liquid Liquid
Solution:
alcoholic
beverages
Emulsion:
miniemulsion,
microemulsion
Emulsion: milk,
mayonnaise, hand
cream
Solid Liquid
Solution: sugar in
water
Sol: pigmented
ink, blood
Suspension: mud (soil,
clay or silt particles are
suspended in water),
chalk powder
suspended in water
Gas Solid
Solution:
hydrogen in
metals
Solid foam:
aerogel,
styrofoam, pumice
Foam: dry sponge
Liquid Solid
Solution:
amalgam
(mercury in
gold), hexane in
paraffin wax
Gel: agar, gelatin,
silicagel, opal
Wet sponge
Solid Solid
Solution: alloys,
plasticizers in
plastics
Solid sol:
cranberry glass
Gravel, granite
Physics and Chemistry
A heterogeneous mixture is a mixture of two or more compounds. Examples are:
mixtures of sand and water or sand and iron filings, a conglomerate rock, water and oil, a
salad, trail mix, and concrete (not cement).

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Making a distinction between homogeneous and heterogeneous mixtures is a matter of
the scale of sampling. On a coarse enough scale, any mixture can be said to be
homogeneous, if you'll allow the entire article to count as a "sample" of it. On a fine
enough scale, any mixture can be said to be heterogeneous, because a sample could be as
small as a single molecule. In practical terms, if the property of interest of the mixture is
the same regardless of which sample of it is taken for the examination used, the mixture
is homogeneous.
Gy's sampling theory quantitatively defines the heterogeneity of a particle as:
where hi, ci, cbatch, mi, and maver are respectively: the heterogeneity of the ith particle of
the population, the mass concentration of the property of interest in the ith particle of the
population, the mass concentration of the property of interest in the population, the mass
of the ith particle in the population, and the average mass of a particle in the population.
During the sampling of heterogeneous mixtures of particles, the variance of the sampling
error is generally non-zero.
Pierre Gy derived, from the Poisson sampling model, the following formula for the
variance of the sampling error in the mass concentration in a sample:
in which V is the variance of the sampling error, N is the number of particles in the
population (before the sample was taken), q i is the probability of including the ith
particle of the population in the sample (i.e. the first-order inclusion probability of the ith
particle), m i is the mass of the ith particle of the population and a i is the mass
concentration of the property of interest in the ith particle of the population.
It must be noted that the above equation for the variance of the sampling error is an
approximation based on a linearization of the mass concentration in a sample.
In the theory of Gy, correct sampling is defined as a sampling scenario in which all
particles have the same probability of being included in the sample. This implies that q i
no longer depends on i, and can therefore be replaced by the symbol q. Gy's equation for
the variance of the sampling error becomes:

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where abatch is the concentration of the property of interest in the population from which
the sample is to be drawn and Mbatch is the mass of the population from which the sample
is to be drawn.
Suspension
Flour suspended in water (appears light blue because blue light is scattered off the flour
particles to a greater extent than red light)
In chemistry, a suspension is a heterogeneous fluid containing solid particles that are
sufficiently large for sedimentation. Usually they must be larger than 1 micrometer. The
internal phase (solid) is dispersed throughout the external phase (fluid) through

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mechanical agitation, with the use of certain excipients or suspending agents. Unlike
colloids, suspensions will eventually settle. An example of a suspension would be sand in
water. The suspended particles are visible under a microscope and will settle over time if
left undisturbed. This distinguishes a suspension from a colloid, in which the suspended
particles are smaller and do not settle. Colloids and suspensions are different from
solutions, in which the dissolved substance (solute) does not exist as a solid, and solvent
and solute are homogeneously mixed.
A suspension of liquid droplets or fine solid particles in a gas is called an aerosol or
particulate. In the atmosphere these consist of fine dust and soot particles, sea salt,
biogenic and volcanogenic sulfates, nitrates, and cloud droplets.
Suspensions are classified on the basis of the dispersed phase and the dispersion medium,
where the former is essentially solid while the latter may either be a solid, a liquid, or a
gas.
In modern chemical process industries, high shear mixing technology has been used to
create many novel suspensions.
Suspensions are unstable from the thermodynamic poin of view; however, they can be
kinetically stable over a large period of time, which determines their shelf life. This time
span needs to be measured to ensure the best product quality to the final consumer.
“Dispersion stability refers to the ability of a dispersion to resist change in its properties
over time.” D.J. McClements.
Destabilisation phenomena of a dispersion
Major destabilisation mechanisms for liquid dispersions
These destabilisations can be classified into two major processes:
1-Migration phenomena: whereby the difference in density between the
continuous and dispersed phase, leads to gravitational phase separation. In the

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case of suspensions sedimentation occurs as the dispersed phase is denser than the
continuous phase.
2-Particle size increase phenomena: whereby the suspended particles join together
and increase in size. Below are the two types of this phenomena.
• reversibly (flocculation)
• irreversibly (aggregation)
Technique monitoring physical stability
Multiple light scattering coupled with vertical scanning is the most widely used technique
to monitor the dispersion state of a product, hence identifying and quantifying
destabilisation phenomena. It works on concentrated dispersions without dilution. When
light is sent through the sample, it is backscattered by the particles. The backscattering
intensity is directly proportional to the size and volume fraction of the dispersed phase.
Therefore, local changes in concentration (sedimentation) and global changes in size
(flocculation, aggregation) are detected and monitored.
Accelerating methods for shelf life prediction
The kinetic process of destabilisation can be rather long (up to several months or even
years for some products) and it is often required for the formulator to use further
accelerating methods in order to reach reasonable development time for new product
design. Thermal methods are the most commonly used and consists in increasing
temperature to accelerate destabilisation (below critical temperatures of phase inversion
or chemical degradation). Temperature affects not only the viscosity, but also interfacial

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tension in the case of non-ionic surfactants or more generally interactions forces inside
the system. Storing a dispersion at high temperatures enables to simulate real life
conditions for a product (e.g. tube of sunscreen cream in a car in the summer), but also to
accelerate destabilisation processes up to 200 times.
Mechanical acceleration including vibration, centrifugation and agitation are sometimes
used. They subject the product to different forces that pushes the particles / droplets
against one another, hence helping in the film drainage. However, some emulsions would
never coalesce in normal gravity, while they do under artificial gravity. Moreover,
segregation of different populations of particles have been highlighted when using
centrifugation and vibration.
Common examples
• Mud or muddy water, is where soil, clay, or silt particles are suspended in water
• Flour suspended in water, as pictured to the right (at the top of the page)
• Paint
• Chalk powder suspended in water
• Dust particles suspended in air
• Algae in water

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Chapter 8
Colloid
Milk is an emulsified colloid of liquid butterfat globules dispersed within a water-based
liquid.
A colloid is a substance microscopically dispersed evenly throughout another substance.
A colloidal system consists of two separate phases: a dispersed phase (or internal phase)
and a continuous phase (or dispersion medium). A colloidal system may be solid, liquid,
or gaseous.

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Many familiar substances are colloids, as shown in the chart below. As well as these
naturally occurring colloids, modern chemical process industries utilize high shear
mixing technology to create novel colloids.
The dispersed-phase particles have a diameter of between approximately 5 and 200
nanometers. Such particles are normally invisible in an optical microscope, though their
presence can be confirmed with the use of an ultramicroscope or an electron microscope.
Homogeneous mixtures with a dispersed phase in this size range may be called colloidal
aerosols, colloidal emulsions, colloidal foams, colloidal dispersions, or hydrosols. The
dispersed-phase particles or droplets are affected largely by the surface chemistry present
in the colloid.
Some colloids are translucent because of the Tyndall effect, which is the scattering of
light by particles in the colloid. Other colloids may be opaque or have a slight color.
Colloidal systems (also called colloidal solutions or colloidal suspensions) are the subject
of interface and colloid science. This field of study was introduced in 1861 by Scottish
scientist Thomas Graham.
Classification of colloids
Because the size of the dispersed phase may be difficult to measure, and because colloids
have the appearance of solutions, colloids are sometimes identified and characterized by
their physico-chemical and transport properties. For example, if a colloid consists of a
solid phase dispersed in a liquid, the solid particles will not diffuse through a membrane,
whereas with a true solution the dissolved ions or molecules will diffuse through a
membrane. Because of the size exclusion, the colloidal particles are unable to pass
through the pores of an ultrafiltration membrane with a size smaller than their own
dimension. The smaller the size of the pore of the ultrafiltration membrane, the lower the
concentration of the dispersed colloidal particules remaining in the ultrafiltred liquid. The
exact value of the concentration of a truly dissolved species will thus depend on the
experimental conditions applied to separate it from the colloidal particles also dispersed
in the liquid. This is, a.o., particularly important for solubility studies of readily
hydrolysed species such as Al, Eu, Am, Cm, ... or organic matter complexing these
species.

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Colloids can be classified as follows:
Medium / Phases
Dispersed phase
Gas Liquid Solid
Continuous
medium
Gas
NONE
(All gases are
mutually miscible)
Liquid aerosol
Examples: fog, mist,
hair sprays
Solid aerosol
Examples: smoke,
cloud, air
particulates
Liquid
Foam
Example: whipped
cream, Shaving
cream
Emulsion
Examples: milk,
mayonnaise, hand
cream
Sol
Examples:
pigmented ink, blood
Solid
Solid foam
Examples: aerogel,
styrofoam, pumice
Gel
Examples: agar,
gelatin, jelly, opal
Solid sol
Example: cranberry
glass
In some cases, a colloid can be considered as a homogeneous mixture. This is because the
distinction between "dissolved" and "particulate" matter can be sometimes a matter of
approach, which affects whether or not it is homogeneous or heterogeneous.
Hydrocolloids
A hydrocolloid is defined as a colloid system wherein the colloid particles are dispersed
in water. A hydrocolloid has colloid particles spread throughout water, and depending on
the quantity of water available that can take place in different states, e.g., gel or sol
(liquid). Hydrocolloids can be either irreversible (single-state) or reversible. For example,
agar, a reversible hydrocolloid of seaweed extract, can exist in a gel and sol state, and
alternate between states with the addition or elimination of heat.
Many hydrocolloids are derived from natural sources. For example, agar-agar and
carrageenan are extracted from seaweed, gelatin is produced by hydrolysis of proteins of
bovine and fish origins, and pectin is extracted from citrus peel and apple pomace.
Gelatin desserts like jelly or Jell-O are made from gelatin powder, another effective
hydrocolloid. Hydrocolloids are employed in food mainly to influence texture or
viscosity (e.g., a sauce). Hydrocolloid-based medical dressings are used for skin and
wound treatment.
Other main hydrocolloids are xanthan gum, gum arabic, guar gum, locust bean gum,
cellulose derivatives as carboxymethyl cellulose, alginate and starch

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Interaction between colloid particles
The following forces play an important role in the interaction of colloid particles:
• Excluded volume repulsion: This refers to the impossibility of any overlap
between hard particles.
• Electrostatic interaction: Colloidal particles often carry an electrical charge and
therefore attract or repel each other. The charge of both the continuous and the
dispersed phase, as well as the mobility of the phases are factors affecting this
interaction.
• van der Waals forces: This is due to interaction between two dipoles that are
either permanent or induced. Even if the particles do not have a permanent dipole,
fluctuations of the electron density gives rise to a temporary dipole in a particle.
This temporary dipole induces a dipole in particles nearby. The temporary dipole
and the induced dipoles are then attracted to each other. This is known as van der
Waals force, and is always present (unless the refractive indexes of the dispersed
and continuous phases are matched), is short-range, and is attractive.
• Entropic forces: According to the second law of thermodynamics, a system
progresses to a state in which entropy is maximized. This can result in effective
forces even between hard spheres.
• Steric forces between polymer-covered surfaces or in solutions containing non-
adsorbing polymer can modulate interparticle forces, producing an additional
steric repulsive force (which is predominantly entropic in origin) or an attractive
depletion force between them. Such an effect is specifically searched for with
tailor-made superplasticizers developed to increase the workability of concrete
and to reduce its water content.
Stabilization of a colloidal dispersion (peptization)
Stabilization serves to prevent colloids from aggregating. Steric stabilization and
electrostatic stabilization are the two main mechanisms for colloid stabilization.
Electrostatic stabilization is based on the mutual repulsion of like electrical charges. In
general, different phases have different charge affinities, so that a electrical double layer
forms at any interface. Small particle sizes lead to enormous surface areas, and this effect
is greatly amplified in colloids. In a stable colloid, mass of a dispersed phase is so low
that its buoyancy or kinetic energy is too weak to overcome the electrostatic repulsion
between charged layers of the dispersing phase. The charge on the dispersed particles can
be observed by applying an electric field: All particles migrate to the same electrode and
therefore must all have the same sign charge.
Destabilizing a colloidal dispersion (flocculation)
Unstable colloidal dispersions form flocs as the particles aggregate due to interparticle
attractions. In this way photonic glasses can be grown. This can be accomplished by a
number of different methods:

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• Removal of the electrostatic barrier that prevents aggregation of the particles. This
can be accomplished by the addition of salt to a suspension or changing the pH of
a suspension to effectively neutralize or "screen" the surface charge of the
particles in suspension. This removes the repulsive forces that keep colloidal
particles separate and allows for coagulation due to van der Waals forces.
• Addition of a charged polymer flocculant. Polymer flocculants can bridge
individual colloidal particles by attractive electrostatic interactions. For example,
negatively-charged colloidal silica or clay particles can be flocculated by the
addition of a positively-charged polymer.
• Addition of non-adsorbed polymers called depletants that cause aggregation due
to entropic effects.
• Physical deformation of the particle (e.g., stretching) may increase the van der
Waals forces more than stabilization forces (such as electrostatic), resulting
coagulation of colloids at certain orientations.
Unstable colloidal suspensions of low-volume fraction form clustered liquid suspensions,
wherein individual clusters of particles fall to the bottom of the suspension (or float to the
top if the particles are less dense than the suspending medium) once the clusters are of
sufficient size for the Brownian forces that work to keep the particles in suspension to be
overcome by gravitational forces. However, colloidal suspensions of higher-volume
fraction form colloidal gels with viscoelastic properties. Viscoelastic colloidal gels, such
as bentonite and toothpaste, flow like liquids under shear, but maintain their shape when
shear is removed. It is for this reason that toothpaste can be squeezed from a toothpaste
tube, but stays on the toothbrush after it is applied.
Technique monitoring colloidal stability
Measurement principle of multiple light scattering coupled with vertical scanning

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Multiple light scattering coupled with vertical scanning is the most widely used technique
to monitor the dispersion state of a product, hence identifying and quantifying
destabilisation phenomena. It works on concentrated dispersions without dilution. When
light is sent through the sample, it is backscattered by the particles / droplets. The
backscattering intensity is directly proportional to the size and volume fraction of the
dispersed phase. Therefore, local changes in concentration (e.g.Creaming and
Sedimentation) and global changes in size (e.g.flocculation, coalescence) are detected
and monitored.
Accelerating methods for shelf life prediction
The kinetic process of destabilisation can be rather long (up to several months or even
years for some products) and it is often required for the formulator to use further
accelerating methods in order to reach reasonable development time for new product
design. Thermal methods are the most commonly used and consists in increasing
temperature to accelerate destabilisation (below critical temperatures of phase inversion
or chemical degradation). Temperature affects not only the viscosity, but also interfacial
tension in the case of non-ionic surfactants or more generally interactions forces inside
the system. Storing a dispersion at high temperatures enables to simulate real life
conditions for a product (e.g. tube of sunscreen cream in a car in the summer), but also to
accelerate destabilisation processes up to 200 times. Mechanical acceleration including
vibration, centrifugation and agitation are sometimes used. They subject the product to
different forces that pushes the particles / droplets against one another, hence helping in
the film drainage. However, some emulsions would never coalesce in normal gravity,
while they do under artificial gravity. Moreover segregation of different populations of
particles have been highlighted when using centrifugation and vibration.
Colloids as a model system for atoms
In physics, colloids are an interesting model system for atoms. Micrometre-scale
colloidal particles are large enough to be observed by optical techniques such as confocal
microscopy. Many of the forces that govern the structure and behavior of matter, such as
excluded volume interactions or electrostatic forces, govern the structure and behavior of
colloidal suspensions. For example, the same techniques used to model ideal gases can be
applied to model the behavior of a hard sphere colloidal suspension. In addition, phase
transitions in colloidal suspensions can be studied in real time using optical techniques,
and are analogous to phase transitions in liquids.
Colloidal crystals
A colloidal crystal is a highly ordered array of particles that can be formed over a very
long range (typically on the order of a few millimeters to one centimeter) and that appear
analogous to their atomic or molecular counterparts. One of the finest natural examples of
this ordering phenomenon can be found in precious opal, in which brilliant regions of
pure spectral color result from close-packed domains of amorphous colloidal spheres of
silicon dioxide (or silica, SiO2). These spherical particles precipitate in highly siliceous

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pools in Australia and elsewhere, and form these highly ordered arrays after years of
sedimentation and compression under hydrostatic and gravitational forces. The periodic
arrays of submicrometre spherical particles provide similar arrays of interstitial voids,
which act as a natural diffraction grating for visible light waves, particularly when the
interstitial spacing is of the same order of magnitude as the incident lightwave.
Thus, it has been known for many years that, due to repulsive Coulombic interactions,
electrically charged macromolecules in an aqueous environment can exhibit long-range
crystal-like correlations with interparticle separation distances, often being considerably
greater than the individual particle diameter. In all of these cases in nature, the same
brilliant iridescence (or play of colors) can be attributed to the diffraction and
constructive interference of visible lightwaves that satisfy Bragg’s law, in a matter
analogous to the scattering of X-rays in crystalline solids.
The large number of experiments exploring the physics and chemistry of these so-called
"colloidal crystals" has emerged as a result of the relatively simple methods that have
evolved in the last 20 years for preparing synthetic monodisperse colloids (both polymer
and mineral) and, through various mechanisms, implementing and preserving their long-
range order formation.
Colloids in biology
In the early 20th century, before enzymology was well understood, colloids were thought
to be the key to the operation of enzymes; i.e., the addition of small quantities of an
enzyme to a quantity of water would, in some fashion yet to be specified, subtly alter the
properties of the water so that it would break down the enzyme's specific substrate, such
as a solution of ATPase breaking down ATP. Furthermore, life itself was explainable in
terms of the aggregate properties of all the colloidal substances that make up an
organism. As more detailed knowledge of biology and biochemistry developed, the
colloidal theory was replaced by the macromolecular theory, which explains an enzyme
as a collection of identical huge molecules that act as very tiny machines, freely moving
about between the water molecules of the solution and individually operating on the
substrate, no more mysterious than a factory full of machinery. The properties of the
water in the solution are not altered, other than the simple osmotic changes that would be
caused by the presence of any solute. In humans, both the thyroid gland and the
intermediate lobe (pars intermedia) of the pituitary gland contain colloid follicles.
Colloids in the environment
Colloidal particles can also serve as transport vector of diverse contaminants in the
surface water (sea water, lakes, rivers, fresh water bodies) and in underground water
circulating in fissured rocks (limestone, sandstone, granite, ...). Radionuclides and heavy
metals easily sorb onto colloids suspended in water. Various types of colloids are
recognised: inorganic colloids (clay particles, silicates, iron oxy-hydroxides, ...), organic
colloids (humic and fulvic substances). When heavy metals or radionuclides form their
own pure colloids, the term "Eigencolloid" is used to designate pure phases, e.g.,

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Tc(OH)4, U(OH)4, Am(OH)3. Colloids have been suspected for the long-range transport
of plutonium on the Nevada Nuclear Test Site. They have been the subject of detailed
studies for many years. However, the mobility of inorganic colloids is very low in
compacted bentonites and in deep clay formations because of the process of ultrafiltration
occurring in dense clay membrane. The question is less clear for small organic colloids
often mixed in porewater with truly dissolved organic molecules.
Use in intravenous therapy
Colloid solutions used in intravenous therapy belong to a major group of volume
expanders, and can be used for intravenous fluid replacement. Colloids preserve a high
colloid osmotic pressure in the blood, and therefore, they should theoretically
preferentially increase the intravascular volume, whereas other types of volume
expanders called crystalloids also increases the interstitial volume and intracellular
volume. However, there is still controversy to the actual difference in efficacy by this
difference. Another difference is that crystalloids generally are much cheaper than
colloids.

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Chapter 9
Total Dissolved Solids
Bottled mineral water usually contains higher TDS levels than tap water
Total Dissolved Solids (often abbreviated TDS) is a measure of the combined content of
all inorganic and organic substances contained in a liquid in: molecular, ionized or micro-
granular (colloidal sol) suspended form. Generally the operational definition is that the
solids must be small enough to survive filtration through a sieve the size of two
micrometer. Total dissolved solids are normally discussed only for freshwater systems, as
salinity comprises some of the ions constituting the definition of TDS. The principal
application of TDS is in the study of water quality for streams, rivers and lakes, although
TDS is not generally considered a primary pollutant (e.g. it is not deemed to be
associated with health effects) it is used as an indication of aesthetic characteristics of
drinking water and as an aggregate indicator of the presence of a broad array of chemical
contaminants.

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