Ionic equilibria: ph, determination of ph of different acids and bases, salt solutions and buffers. Titration curves of acids and bases and indicators.

2. The pH concept is very convenient for expressing hydrogen ion concentration.
It was introduced by Sorensen in 1909. It is defined as the negative of the
base-10 logarithm (log) of the H+ concentration. Mathematically it may be
expressed as
pH = – log [H+] or, [H+] = 10– pH
Where [H+] is the concentration of hydrogen ions in moles per litre.
(a) Concentration of OH– ions in aqueous solution of a base is expressed as
pOH = – log [OH–]
(b) Equilibrium constant for water is written as
pKw = –log [Kw]
For any quantity X, we can write
pX = –log [X]
The “p” in these expression means “ –log of the quantity”
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3. In order to express the hydrogen ion concentration or acidity of a solution, a pH scale was evolved.
The scale on which pH values are computed is called the pH scale. pH values are calculated in
this scale taking water as their reference standard.
The highest value is [H+] = 100 mole/L-------------------------------------(1).
From the dissociation of water we got the lowest value [H+] = 10– 14mole/L----(2)
Taking negative logarithm on the both side of the equation 1 and 2 we get,
-log[H+] = -log100=0
and -log[H+] = -log10-14=14
On this scale the values range from 0 to 14. Since pH is defined as – log [H+] and
the hydrogen ion concentration of water is 10–7, the pH of water is 7.
All solutions having pH less than 7 are acidic and
those with pH greater than 7 are basic, and equal 7 is neutral solution.
As shown by the pH scale, pH decreases with the increase of [H+].
The lower the pH, higher is the [H+] or acidity.
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4. Water dissociates to H+ and OH– ions to a very small degree so that we have the
equilibrium.
H2O⇌ H+ + OH– ...............................................................(1)
We can write the equilibrium expression as
---------------------------------------------------------------------------(2)
Since water is so little dissociated, the concentration of un-dissociated molecules,
[H2O], is presumed to be constant. Therefore from expression (2) we can write
[H+] [OH–] = K [H2O] = Kw = a constant………………………………..(3)
where Kw is called the water dissociation constant or the water ionisation
constant.
When the concentrations of H+ and OH– ions in water are expressed in mole per
litre, the value of Kw found experimentally is 1.0 × 10–14.
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5. [H+] [OH–] = K [H2O] = Kw--------(3)
The concentration of H+ and OH– ions in pure water is equal. Using the expression (3), we
have
Or, [H+] = [OH–] = 1.0 × 10– 7 mol/l
Thus the H+ ion and OH– ion concentrations in pure water are both 10–7 mol l–1 at 25°C and it
is said to be neutral. Now taking negative logarithm on the both sides of the equation 3 we
get,
–log ([H+] [OH–]) = -log Kw
Or, (–log [H+]) +(–log [OH–]) = –log Kw
pH+pOH=pKw---------------(4)
Thus, pKw = pH + pOH
Since Kw = 1.0 × 10–14
So, pKw = –log Kw= –log (1.0 × 10–14) = 14.00
Hence, for any aqueous solution at 25°C, pH and pOH add up to 14.00.
That is,pH + pOH = 14.00
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6. PROBLEM. The hydrogen ion concentration of a fruit juice is
3.3 × 10–2 M. What is the pH of the juice ? Is it acidic or basic ?
PROBLEM. If a solution has a pH of 7.41, determine its H+
concentration.
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8. Titrant/Titrator:Analyte/Titrand:Indicator:
Equivalence point
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9. Titration(aka titrimetry) is a common laboratory technique used for quantitative chemical
analysis.
Titration is a process of neutralization whereby a titrant (a solution of known
concentration) is added into an analyte (a solution of unknown concentration) until
the unknown solution is completely neutralized. Because volume measurement plays a
key role in titration, it is also known as volumetric analysis.
An indicator can signal the completion of the reaction (by colour change) and the
concentration of the unknown solution can be determined.
Any chemicals that react in solution can be titrated with each other. Since acids and bases are
usually found in solution, they are commonly involved in titrations. Titrations of a strong acid
or a strong base involve the neutralization reaction between hydrogen ions and hydroxyl ions.
These ions combine to form the neutral water molecule:H2O⇌ H+ + OH–
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10. Titrant/Titrator: The standard solution of known concentration that is being added to the
solution of unknown concentration is called titrant. This is more often the acid than the
base.
Analyte/Titrand: The solution of unknown concentration. Usually the base.
Equivalence point (neutralization or endpoint): The point when the titration is
theoretically stopped, where the number of moles of titrant is equal to the number of moles
of analyte, or some multiple thereof (as in di- or tri- protic acids).
Indicator: An acid-base indicator is an organic dye that signals the end-point by a
visual change in colour. It changes colour over a certain pH range, and indicates the end
of the titration. e.g. Phenolphthalein and methyl orange .
Phenolphthalein is pink in base solution and colourless in acid solution. Thus
phenolphthalein signals the end-point by a colour change from colourless to pink. Similarly
methyl orange indicates the end-point by a colour change from red (in acid) to yellow (in
base). pH range of indicators
Most indicators do not change colour at a particular pH. They do so over a range of pH
from two to three units. This is called the pH range which is different for various
indicators.
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14. During an acid-base titration the pH of the solution in the receiver flask changes
with the addition of the titrant from the burette. A plot of pH against the volume of
the titrant being added is known as pH curve or titration curve.
For illustration, the pH curve produced by titration of HCl solution with NaOH
solution is shown in figure following figure. As NaOH is added, the pH of the
solution increases slowly at first, then rapidly in the vicinity of the equivalence point and again
slowly. The equivalence point lies in the middle of the vertical portion of
the curve (pH=7). It must be clearly understood that equivalence point is the
theoretical end-point of a titration. The end-point of a titration determined by a
colour change of the indicator in titration solution is the experimental estimate of
the equivalence point.
The titration curve in Fig. 1. Shows that it remains vertical around the equivalence point.
Thus, a suitable indicator for a given titration may be defined as one which has as
narrow a pH range as possible that lies entirely on the upright part of the titration
curve. For example, as shown in figure 2, phenolphthalein, litmus and methyl orange may be
used as indicators for acid-base titrations.
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16. Titration error
100% accurate measurement is not possible. Practical value and theoretical value is never same.
So, the difference between the theoretical value and practical value of a titration is known as
titration error.
Titration error = theoretical value – practical value
For example, if the theoretical value of a titration is 5 but the examination value is 4.91 then
titration error = 5 - 4.91= 0.09.
CHOICE OF A SUITABLE INDICATOR
The choice of a suitable indicator for a particular acid-base titration depends on the nature of the
acid and the base involved in the titration.
Titrating a Strong acid with a Strong base: Both methyl orange and phenolphthalein are suitable
indicators for strong acid/strong base titrations.
Titrating a Weak acid with a Strong base: Phenolphthalein is a suitable indicator, while methyl
orange is not.
Titrating a Strong acid with a Weak base: Evidently, methyl orange and methyl red are suitable
indicators for strong acid/weak base titrations.
Titrating a acid with a Weak base: Under these conditions, all indicators change colour only
gradually and no indicator is suitable.
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