Determine the solubilities of silver chromate, barium chromate, ferric hydroxide, lead chloride and mercurous iodide at 298K from their solubility product constants given in Table 7.9. Determine also the molarities of individual ions.
To determine the solubility, we apply the formula
Ksp = [A+][B-]
Where Ksp is the solubility product which is equal to the product of ionic concentrations in a saturated solution.
a) Silver chromate
ionization of silver chromate:
Ag2CrO4 ↔ 2Ag+ + CrO42-
As we know that,
Ksp = [A+] [B-]
Where A and B are the ions dissolved
In the above reaction,
⇒[A+] = [Ag+]
⇒[B-] = [CrO42-]
∴ Ksp = [Ag+]2 + [CrO42-]
As Ksp of Ag2CrO4 =1.1 × 10-12 (given)
Let ‘s’ be the solubility of Ag2CrO4
[Ag+] = 2s
[CrO42-] =s
∴ 1.1 × 10–12 = (2s)2 s
⇒1.1 × 10-12 = 4(s)3
⇒0.275 × 10–12 = s3
⇒s =
⇒s = 0.65 × 10-4
Thus, Molarity of Ag+ = 2s= 2× 0.65× 10-4 = 1.30× 10-4 M
Molarity of CrO42- = s = 0.65 × 10-4 M
b) Barium chromate
ionization of barium chromate:
BaCrO4 ↔ Ba2+ + CrO42-
As we know that,
Ksp = [A+] [B-]
Where A and B are the ions dissolved
In the above reaction,
⇒[A+] = [Ba2+]
[B-] = [CrO42-]
∴ Ksp = [Ba2+] + [CrO42-]
As Ksp of BaCrO4 =1.2 × 10-10 (given)
Let ‘s’ be the solubility of BaCrO4
[Ba2+] =s
[CrO42-] =s
∴ 1.2 × 10–10 = (s× s)
⇒1.2 × 10-10 = (s)2
⇒s =
⇒s = 1.09 × 10-5
Thus, Molarity of Ba2+ and CrO42- = s= 1.09× 10-5M
c) Ferric hydroxide
ionization of ferric hydroxide
Fe(OH)3 ↔ Fe3+ + 3OH-
As we know that,
Ksp = [A+] [B-]
Where A and B are the ions dissolved
In the above reaction,
⇒[A+] = [Fe3+]
⇒[B-] = [OH-]
∴ Ksp = [Fe3+] + [OH-]
As Ksp of Fe(OH)3 =1.0 × 10-38 (given)
Let ‘s’ be the solubility of Fe(OH)3
[Fe3+] =s
[3OH-] = 3s
∴ 1.0× 10–38 = (s)(3s)3
⇒1.0 × 10-38 = (27s)4
⇒0.37 × 10–38 = s3
⇒s =
⇒s = 1.39 × 10-10
Thus, Molarity of Fe3+ = s= 1.39× 10-10 M
Molarity of OH- = 3s = 4.17 × 10-10M
d) Lead chloride
ionization of lead chloride:
PbCl2 ↔ Pb2+ + 2Cl-
As we know that,
Ksp = [A+] [B-]
Where A and B are the ions dissolved
In the above reaction,
⇒[A+] = [Pb2+]
⇒[B-] = [Cl-]
∴ Ksp = [Pb2+] + [Cl-]2
As Ksp of PbCl2 =1.6 × 10-5 (given)
Let ‘s’ be the solubility of PbCl2
[Pb2+] =s
[Cl-] =2 s
∴ 1.6 × 10–5 = (s)(2s)2
⇒1.6 × 10-5 = (4s)3
⇒0.4 × 10–5 = s3
⇒s =
⇒s = 1.58 × 10-2
Thus, Molarity of Pb2+ = s= 1.58× 10-2 M
Molarity of Cl- = 2s = 3.16 × 10-2 M
e) Mercurous Iodide
ionization of mercurous iodide:
Hg2I2 ↔ Hg22+ + 2I-
As we know that,
Ksp = [A+] [B-]
Where A and B are the ions dissolved
In the above reaction,
⇒[A+] = [Hg22+]
⇒[B-] = [I-]2
∴ Ksp = [Hg22+] + [I-]2
As Ksp of Hg2I2 = 4.5 × 10–29
Let ‘s’ be the solubility of Hg2I2
[Hg22+] =s
[I-] 2s
∴ 4.5 × 10–29 = (s)(2s)2
⇒4.5 × 10–29 = (4s)3
⇒4.5 × 10–29 = s3
⇒s =
⇒s = 2.24× 10-10
Thus, Molarity of Hg22+ = s= 2.24× 10-10 M
Molarity of I- = 2s = 4.48 × 10-10 M
Note: Ksp increases with increase in temperature.
⇒In a saturated solution, Ksp = [A+][B-]
⇒In an unsaturated solution of AB, Ksp> [A+][B-] means more solute can be dissolved.
⇒In a super saturated solution of AB, Ksp< [A+][B-] means precipitation will start to occur