Gravimetric Analysis, Solubility and Solubility Product of sparingly soluble salts

1. Gravimetric Methods
of Analysis
M.Sc previous
Course Instructor: Dr. Sajjad Ullah

2. Filtering a precipitate
dessicators
Laboratory oven (drying)
(1100–1700 °C)
muffle furnace
Folding a filter paper

3. Equipments and manipulations associated with Weighing
Weighing bottles
(drying and storing solids) arrangement for drying
of samples Transfer
(use gloves and tweezer)
Source: Skoog, West, Holler, Crouch,
Fundamentals of analytical Chemistry 9th Edition

4. Filtering crucibles
Source: Skoog, West, Holler, Crouch, Fundamentals of analytical Chemistry 9th Edition
Common crucibles
(igniton only)

5. Washing by decantation Transferring the precipitate
Filtering and Washing Precipitates
Moistening the
paper slightly

6. Transferring a filter paper and precipitate from a funnel to a crucible
and its subsequent ignition.
(1100–1700 °C)
muffle furnace

7. Gravimetric method
Contents
 Solubility and solubility product of salts
 Separation by precipitation
 Formation of Precipitate
 Types of Precipitate
 Impurities in precipitates
 Quantitative calculations
 Stoichiometric Reaction

8. Gravimetric method
 Selective precipitation of the analyte and non-selective
measurement of mass of the precipitate (classical method)
 In other words, insoluble derivate of analyte of known chemical
composition is prepared and weighed (absolute method)
 Accuracy and precision may be a few part per thousands
 Require large amount of analyte (mmoles or mg)

9. Ag+ + Cl-  AgCl(s)
F. Wt of AgCl=143.23 g/mol
At. Wt of Cl = 35.45 g/mol
GF= 35.45/143.23 = 0.247
mass of Cl- in sample = GF x mass of ppt.
Example:
Example:
Determination of:
water and
carbon dioxide
Removal of the analyte
involves separation by
heating or chemically
decomposing a volatile
sample at a suitable
temperature
AgNO3
Cl-
AgCl(s)
AgCl(s)

10. Solubility and Solubility Product
Solubility is the amount of solute that can be dissolved in a given
volume of solvent (g/L or mol/L) at a given temprature
Even “insoluble substances”
have slight solubility!!!
Types of electrolytes
AB type = AgCl
A2B type = Ag2CrO4
AB2 type = PBI2
It is the ionized form that determine
solubility and chemical stability
Ksp = [Ag+] [Cl-]
K = [Ag+] [Cl-] / [AgCl]
K [AgCl] = [Ag+] [Cl-]
[AgCl] const.
Ksp can be used to measure equilibrium solubility.
In calcualtions, use molL-1 for S

11. Ksp = [Ag+] [Cl-]
[Ag+] = [Cl-] = S
Ksp = (S)2
S = 𝐾 𝑠𝑝
S = molar solubility
As S = 𝐾 𝑠𝑝
So S = 1x 10−10
S = 1 x 10-5 M
AB type Salt: AgCl
Example: Find S for AgCl when Ksp = 1 x 10-10
Though AgCl is a Sparingly soluble salt; it
still is a Strong electrolyte
Ksp can be used to measure equilibrium solubility.

12. A2B type Salt: Ag2CrO4
Ag2CrO4  2Ag+ + CrO4
2-
S = [CrO4
2-] = 1/2 [Ag+]
Ksp = [CrO4
2-].[Ag+]2
Ksp = [CrO4
2-] . [2CrO4
2-]2
Ksp = 4. [CrO4
2-] . [CrO4
2-]2
Ksp = 4. [CrO4
2-]3
Ksp/4 = [CrO4
2-]3
[CrO4
2-] =
3 𝐾𝑠𝑝
4
𝑆 =
3 𝐾𝑠𝑝
4

13. AB2 type Salt: PbI2
PbI2  Pb2+ + 2I-
S = [Pb2+] = 1
2 [I-]
Ksp =[Pb2+] . [I-]2
Ksp =1/2 [I-]3
Ksp =1/2[I-] . [I-]2
2Ksp = [I-]3
[I-] = 3
2Ksp
S =
[𝐼]
2
=
3 2𝐾𝑠𝑝
2
S =
[𝐼]
2
=
3 2𝐾𝑠𝑝
3 8
𝑆 =
[𝐼]
2
=
3 2𝐾𝑠𝑝
8
𝑎𝑠 2 =
3
8
𝑆 =
3 𝐾𝑠𝑝
4
𝑆 =
3 7.1 𝑥10^−9
4
= 1.2 x 10-3M
𝑖𝑓 𝐾𝑠𝑝 = 7.1 𝑥10−9, 𝑡ℎ𝑒 𝑆 𝑤𝑖𝑙𝑙 𝑏𝑒:

14. Common Ion Effect
For the reaction
𝐴𝑔𝐶𝑙 ↔ 𝐴𝑔
+
+ 𝐶𝑙
−
The solubility of AgCl will decreases if either Cl- (or Ag+) ions
are added from some external source (say NaCl).
Ksp = 1 x 10-10
S = [Ag+] = 1 x 10-5 M
Example:
Calculate the solubility of AgCl when 2.0 mmoles (10 mL of 0.2M) of AgNO3 are
mixed with 1.0 mmole (10 mL of 0.1M) NaCl .
Solution:
mmoles of Ag+ in excess = 2-1 = 1.0 mmoles
Solubility = [Cl-]
[Ag+] = 1 mmol/20 mL = 0.05M (this concentration is very high compared to Ag
concentration, 1 x 10-5 M, in absence of a common ion. So we can neglect 1 x 10-5 M
[0.05]. [Cl-] = 1 x 10-10
[Cl-] = 1 x 10-10 / 0.05 = 2 x 10-9 M
𝐴𝑔
+
+ 𝐶𝑙
−
↔ 𝐴𝑔𝐶𝑙
Decreased S in the presence of excess Ag

15. We take advantage of the common ion effect to decrease the
solubility of a precipitate in a gravimetric analysis. For instance,
SO4
2- ions are determined by precipitating BaSO4 with BaCl2.

16. Applications of Ksp
(1) Solubility Calculation : From Ksp value at a specific temperature,
equilibrium solubility can be calculated.
(see Table on next slide!)
(2) Prediction of precipitation
(3) Common Ion effect: The effect of a common ion on the precipitation
of a compound can be studied
(4) Selective precipitation (Qualitative Salt Analysis)

17. S is not necessarily directly proportional to the Ksp values since it depends on stoichiometry.
The Ksp of AgI is 5 x 1015 larger than Al(OH)3, but S of AgI is only two times larger than
Al(OH)3. A 1:1 salt (AB type) has a lower solubility than a nonsymmetric (AB2 or A2B type)
for a given value of Ksp
One Hg2+
and one S2-
in 1 L

18. Prediction of precipitation
For AgCl to precipitate, the product [Ag+].[Cl-] must exceed the Ksp (1 x 10-10)
value of AgCl.
Example:
What must be the concentration of added Ag+ to just start precipitation
of AgCl in a 1.0 x 10-3 M NaCl solution
[Ag+] . (1.0 x 10-3 ) = 1 x 10-10
[Ag+] = 1 x 10-7 M
[Ag+].[Cl-] = Ksp
The concentration of Ag+ must be greater than 1 x 10-7 M to start
precipitation

19. Group I Cations Group reagent Product (ppt.) formed
1 Ag+
, Hg2
2+
, Pb2+
. Dil. HCl Metal Chlorides
2 Cd2+
, Bi3+
, Cu2+
, As3+
Dil. HCl + H2S Acid-insoluble sulphides
3 Fe2+
, Fe3+
, Al3+
, Cr3+
. NH4Cl + NH4OH (pH of 8–9) Insoluble hydroxide
4 Zn2+
, Ni2+
, Co2+
, Mn2+
NH4OH + H2S Metal sulphides
5 Ba2+
, Ca2+
, and Sr2+ (NH4)2CO3 + NH4Cl +
NH4OH
Insoluble carbonates
The Ksp value of group (II) sulphides is lower than Group (IV) sulphides, so Group (II)
precipitates earlier (at lower S2
- concentartion) than Group (IV)
Qualitative Salt Analysis (basic radicals)
 Salt cations analysis is based on Ksp values of the salt formed.
2nd group – H2S in the presence of dilute HCl. Its purpose is to keep the sulfide ion concentration at a required
minimum, so as to allow the precipitation of 2nd group cations alone. Otherwise Group IV will also precipitate
3rd Group : NH4
+ ions from NH4Cl keeps ionization of
NH4OH minimum, so that only GPIII hydroxide precipitate
out.

20. Factors affect Solubility
 Common Ion Effect (slides 13-14)
 Diverse Ion Effect (Salt or Electrolyte Effect)
 pH
 Temperature
 Complex Ion Formation
 Solvent Effect

21. Diverse Ion Effect (Salt Effect)
Since Ksp = [Ag+] [Cl-]
In the presence of an inert electrolyte (diverse salt), it is more appropriate to use
Activity (A= f.C) of ions rather concentration (C) in the equilibrium expressions
because the activity coefficient (f), and hence activity, depends on total ionic
strength.
For instance, for the case of AgCl, the K0
sp can be written as:
K0
sp = aAg+. aCl- = [Ag+]fAg+ . [Cl-] fCl-
Ksp = [Ag+] [Cl-]
Ksp =
K0
sp
fAg+ . fCl−
[Ag+] [Cl-] =
K0
sp
fAg+ . fCl−
OR
This equation shows that as activities of ions decrease (f increases), the Ksp will
increase (and so the molar solubility also increases)

22. Diverse Ion Effect: Example
Calculate the Solubility of AgCl in the absence and presence of 0.1M NaNO3.
In the absence of NaNO3, (zero Ionic strength):
K0
sp = 1 x 10-10
In the presence of 0.1M NaNO3
Ksp =
K0
sp
fAg+ . fCl−
µ = ½ ∑CiZi2
µ = 0.1
fCl− = 0.76
fAg+ = 0.75
Ksp=
1x 10−10
0.75 (0.76)
= 1.8 x 10-10
New solubility= S = 𝐾 𝑠𝑝
S = 1.3 x 10-5 M (30% more than in the absence of NaNO3)
= 1.8 x 10−10
S = [Ag+] = 𝐾 𝑠𝑝 = 1 x 10-5 M

23. • The presence of a diverse salt will
generally increase the solubility of
precipitates due de to shielding of
the dissociated ion species.
• The increases in solubility due to
salt effect is greater with
precipitates containing multiply
charged ions.
• At very high ionic strength (where f
may become greater than 1), the
solubility is decreased. In
Gravimetric analysis, a sufficiently
large excess of precipitating
agents is added so that the
solubility is reduced to such a
small value that we do not need to
worry about this effect.

24. G. D Christian, 6th Ed. page 213

25. Effect of pH on solubility
Acids frequently affect the solubility of a precipitate as the H+ ions (of the acid)
may compete with metal ions (Mn+) of interest for the precipitating reagent (R-,
which may be the anion of a weak acid).
With less free reagent (R-) available, and a constant Ksp, the solubility
of the salt must increase
CaF2(s) ⇋ Ca2+ + 2F-
F- + H+ ⇋ HF
Example: Solubility of CaF2 increases in the presence of an acid as the H+
competes with Ca2+ ions for F- ions.

26. In General, the solubility of a precipitate (MA) whose anion (A-) is derived from a weak
acid (HA) will increase in the presence of added acid (H+) because the acid will tend to
combine with the anion (A-) and thus remove the A- from solution (equilibrium shift to
RHS, leading to solubility of MA).
[A-] + [HA] = [M]
For Instance, the solubility of CaC2O4 in
the presence of acid increases as the H+
ion may take up oxalate (C2O4
2-) ions in
two steps:
Thus we must take into account the effect of pH if we need to determine
the solubility of CaC2O4 from Ksp expression Ksp= [Ca2+].[C2O4
2-].
Solubility of CaC2O4 = Ca2+ = CH2C2O4
CH2C2O4 = [H2C2O4] + [HC2O4
-] + [C2O4
2-]
To calculate the fraction (α2) of CH2C2O4 that exist as C2O4
2-, we need
Need an expression that accounts for pH or H+ ion concentration.
(SEE NEXT SLIDE)

27. Ksp= [Ca2+].[C2O4
2-].
α2=
[𝐶2
𝑂4
2
−
]
[𝐶𝐻2𝐶2𝑂4
]
=
CH2C2O4 = [H2C2O4] + [HC2O4
-] + [C2O4
2-]
Or
is called conditional solubility product and its value holds for only a specified pH

28. pH Effect Example: Calculate the solubility of CaC2O4 in the absence
and presence of 0.001M HCl
As S = 𝐾 𝑠𝑝
So S = 2.6x 10−9
S = 5.1 x 10-5 M
In the absence of HCl:In the presence of HCl:
S = √(
𝐾 𝑠𝑝
𝛼2
S = √(
2.6 x10−9
5.7 𝑥 10−2
= 2.1 x 10-4 M (400% increase in S)

29. Effect of Complexation
For example, NH3 (complexing agent) reacts with metal ion (Ag+) of the
precipitate (AgCl) to increase its solubility. For example
AgCl + 2NH3 ⇋ Ag(NH3)2
+ + Cl-
(soluble)
For a precipitate MA that dissociates to give M+ and A- and whose M+
complexes with L to form ML+, the equilibria are:
CM = [M+] + [ML+] = [A-]
Where
CM= analytical
concentration
NH3 competes with
Cl- for Ag+ ions

30. Ksp= [Ag+] [Br-] = 4 x 10-13
Consider the effect of NH3 on solubility of AgBr.
S =[Br-] = CAg
CAg= [Ag+] + [Ag(NH3)+] +[Ag(NH3)2
+]
We can substitute CAg.β0 for [Ag+]
in the Ksp relation:
β0 is the fraction of
silver species that
exists as Ag+
β0 = [Ag+]
CAg
s2= ks 𝑃
β0
s= ks 𝑃
β0
OR

31. Example: Calculate the molar solubility of AgBr in the
absence and presence of 0.1M NH3 solution
In the Absence of NH3 In the Presence of NH3
S = 𝐾 𝑠𝑝
So, S = 4x 10−13
S = 6.3 x 10-7 M
Ksp= [Ag+] [Br-] = 4 x 10-13
β0 for 0.1M NH3= 4 X 10-6
s= ks 𝑃
β0
s= 4 𝑥10
−
13
4 x 10−6
s= 3.2 x 10-4 M
(530 times more soluble in
the presence of NH3)

32. Other examples
AgNO3 (aq) + KCN (aq ⇋ AgCN(s) + KNO3 (aq
However, if excess of KCN is added, the AgCN precipitate dissolves due to the
formation of soluble [Ag(CN)2]- complex ion.
AgCN precipitates as the Ksp value of AgCN is exceeded by addition of KCN to
AgNO3 solution:
AgCN(s) + KCN (aq ⇋ [Ag(CN)2]-
(aq) + KNO3 (aq
(soluble)
Al3+
(aq) + OH-
(aq ⇋ Al(OH)3(s)
In the presence of F- ions (that compete with OH- ion), the solubility of Al(OH)3
increases due to the formation of [AlF6]3- ions.
Al(OH)3(s) + 6F-
(aq ⇋ Al(F)6 ]3-
(aq)

33. Effect of Temperature on solubility and Ksp

34. An increase in T generally increase the S of a sparingly soluble salt the
solid phase of which is in equilibrium with the components in solution.
The Effect of T on S is different for different substances.
For AgCl:
S (mg/L)= 1.77 (10 °C) and 21.1 (100 °C)
While for For BaSO4:
S (mg/L)= 2.2 (10 °C) and 3.9 (100 °C)
In the presence of excess of precipitating agent, the effect of T on S
becomes very small.

35. Contents
 Solubility and solubility product of salts
 Sepration by precipitation
 Formation of Precipitate
 Types of Precipitate
 Impurities in precipitates
 Quantitative calculations
 Stoichiometric Reaction

36. Formation of Precipitate

38. Steps involved in Gravimetric Analysis
 Solution Preparation (volume, pH, concentration)
 Precipitation (Formation mechanism, Crystal Size)
 Digestion of Precipitate
 Filtration
 Washing
 Drying/Ignition

Calculations

39. 1. Solution Preparation (volume, pH, concentration)
Steps involved in Gravimetric Analysis…
 Preliminary separation to eliminate interferences
 Adjust conditions (T, V, pH, Conc.) to achieve (i) low S of precipitate and suitable
forms of filtrations
 pH is important as it may affect (i) solubility (ii) possibility of interferences from
other constituents
e.g., calcium oxalate, CaC2O4, is insoluble in basic media but soluble in acidic media
(as oxalic acid)
Basic media Acidic media

40. 8-hydorxyquinoline (oxine) can be made selective by pH
adjustment
9-hydroxyquinoline + Mg+2/Al+3 Alq3 + Mg2+ (free)
pH 4
9-hydroxyquinoline + Mg+2/Al+3 Alq3 + Mg(OH)2 (ppt)
pH>12
9-hydroxyquinoline + Mg+2/Al+3 Alq3 + Mgq2
pH>4
Mgq2
oxine
Alq3
Concentration of anion form of oxine is too low at pH 4 to precipitate
magnesium ion. Higher pH (> 4) is required to shift the ionization step and
precipitate the magnesium.
If the pH is too high magnesium hydroxide will precipitate causing
interference
Aluminium ions can be easily precipitated at pH 4.

41. Steps involved in Gravimetric Analysis…
2. Precipitation (Formation mechanism, Crystal Size)
 Precipitate should
be sufficiently insoluble to avoid “solubility loss”
have large crystal size (easy filtration and low contamination)
(i) Supersaturation:
The solutions contains more soluble substances than what exists
under equilibrium conditions.
Supersaturation is a metastable state which reverts to equilibrium
state (saturation) by the start of nucleation.
 Precipitate Process
(ii) Nucleation:
Few particle/molecules come together to form nuclei (microscopic
clusters of atoms or ion) of solid phase.
Nucleation may be induced by introducing a seed crystal or on
dust particles, scratches on vessels.
(iii) Growth:
The nuclei then grow by addition of other
precipitate particles and form a certain shape particles.
It requires addition of a precipitating agent solution to
the sample solution

42. Formation of a crystal according to classical nucleation theory
DOI: 10.13140/RG.2.1.4660.6960
Time
Radius

43. Steps involved in Gravimetric Analysis…
Desired Properties of Precipitate
- Insoluble, No appreciable loss on filtration
- Physical Form such that readily separated, washed free of impurity
- Can be converted to Pure substance of definite chemical composition

44. The Physical nature of Precipitate will be determined by relative rates of
nucleation and particle growth
Nucleation vs Particle Growth
When Nucleation rate > Particle Growth rate, then
• More number of nuclei formed
• Smaller particle produced
• Colloidal precipitate formed
• Higher surface area of precipitate ( more adsorbed/trapped impurities)
• Increased chance of imperfection in the crystal
• Not easily filterable, do not settle
Higher Nucleation Rate
Double layer
stabilized colloid
AgCl surrounded
by Ag or Cl ions
1. Neutralize electrical double
2. Remove adsorbed ions by
heating/stirring
AgCl surrounded
by Ag+ ions

45. Rate of Nucleation vs. Particle Growth
Relative Supersaturation =
𝑄−𝑆
𝑆
Von Weimarn discovered that Particle size of precipitate is inversely
proportional to the relative super-saturation of the solution during the
precipitation process
Q = actual concentration of mixed
reagents before precipitation occurs
S = solubility of precipitate at
equilibrium
Keep the relative super-saturation ratio as small as possible in order to
get large particles (get crystal growth instead of further nucleation)
Particle size =
1
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑆𝑢𝑝𝑒𝑟𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑖𝑜𝑛
How?
doi:10.1016/j.jcrysgro.2003.12.047
https://pubs.acs.org/doi/abs/10.1021/cr60006a002

46.  Precipitation using dilute solutions (low Q)
 Slow addition of precipitating agent (keep Q low)
 Stirring the solution during addition of precipitating agent to avoid concentration
sites (keeps Q low)
 Increase solubility by precipitation from hot solution (high S). The bulk of the
precipitation may be performed in the hot solution, and then this solution may be
cooled to make the precipitation quantitative
 Adjust the pH to increase S (Note: Too much increase may result in loss of ppt
by dissolution
 Usually add a little excess of the precipitating agent for quantitative precipitation
and check for completeness of the precipitation
Relative Supersaturation =
𝑄−𝑆
𝑆
Optimum conditions for precipitation
(keeping supersaturation low)

47.  Increase nucleation
 Many small crystals (Colloidal form)
 High surface area
 More adsorption of impurities
 Difficult to wash and filter
Low relative supersaturation
 Less nucleation
 Fewer larger crystals (Crystalline Form)
 Low surface area
 Less adsorption of impurities
Supersaturation and Nucleation
High relative supersaturation
Maintain crystalline precipitate
and avoid colloidal precipitate
Try to get crystalline
precipitate with small number
of larger particles

48. Digestion of the precipitate:
 Digestion is a process keeping the precipitate within the mother liquor for a
certain period of time to encourage densification
 The precipitate is left hot (below boiling) for 30 min to one hour for the particles to
be digested.
 Digestion involves dissolution of small particles and re-precipitation on larger
ones resulting in particle growth and better precipitate characteristics (Ostwald
ripening).
 Ostwald ripening improves the purity and crystallinity of the precipitate
 Digestion forces the small colloidal particles to agglomerate which decreases
their surface area and thus adsorption.

49. -Wash the precipitate thoroughly to remove all adsorbed species that
would add to the weight of the precipitate.
- Co-precipitate impurities, especially these on the substance can be
removed by washing the precipitate after filtering
- Avoid excessive washing since part of the precipitate may be lost
and peptization may occur.
- Many precipitate cannot be washed with pure water because
peptization occurs (reverse of coagulation) in such cases, use
dilute nitric acid, ammonium nitrate, or dilute acetic acid for
washing to avoid peptization.
- Usually, it is a good practice to check for the presence of
precipitating agent in the filtrate of the final washing solution. The
presence of precipitating agent means that extra washing is
required.
- Filtration should be done in appropriate sized Gooch or ignition
filter paper.
Washing and Filtering the Precipitate

50. Drying and Ignition: The purpose of drying (heating at about 120-150 °C in an
oven) or ignition in a muffle furnace at temperatures ranging from 600-1200 °C is
to get a material with exactly known chemical structure so that the amount of
analyte can be accurately determined.
• Precipitate must be in suitable form for weighing.
• Precipitate must be pure, stable, of certain known composition.
• Remove water efficiently; electrolytes in washing solvent.
• Appropriate chemical changes during heating.
 AgCl–drying in over 100 -130 °C to remove physically-bound
water.
 Higher temperature is necessary if water is trapped in crystals (chemically-bound
water) or ensure appropriate chemical changes
MgNH4PO --> Mg2P2O7 (T= 900 °C)
CaC2O4 --> CaO (T= 1100 °C)
EXAMPLE

53. Analytical chemistry- Gary D. Christian
5th edition. Page no. 145-168.
en.wikipedia.org/wiki/Gravimetry
http://www.ecs.umass.edu/cee/reckho
w/courses/572/572bk15/572BK15.html
doi:10.1016/j.jcrysgro.2003.12.047
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