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3. The Kp of calcium sulfate, Caso. is 7.1 x 10* while that of calcium hydroxide,...

Question

3. The Kp of calcium sulfate, Caso. is 7.1 x 10* while that of calcium hydroxide,...

3. The Kp of calcium sulfate, Caso. is 7.1 x 10* while that of calcium hydroxide, Catoi is 4.68 x 10 (a) Calculate the solubi
3. The Kp of calcium sulfate, Caso. is 7.1 x 10* while that of calcium hydroxide, Catoi is 4.68 x 10 (a) Calculate the solubility of each salt. (b) Which salt is more soluble in water?

Answers

(S The general salubility evalilxium (S5 642 et) the ressim for Selubility prduet i SPf s isthe mel sauility of the compound then the euliLrum (mcentration o the ion im the Setu sated selu tiom uil be 20

(a)

1. The solubility equilibrium for CaSO4 is

CaSO_{4} \rightleftharpoons Ca^{2+}_{(aq)} + SO_{4}^{2-}_{(aq)}

The solubility product is,

K_{sp} = [Ca^{2+}] [SO_{4}^{2-}]

If S is the molar solubility then we have,

K_{sp} = x^{x}.y^{y}.S^{x+y} ....(1)

for CaSO4 x = y = 1

Therefor from eq(1) we have

K_{sp} = 1^{1}.1^{1}.S^{1+1}

K_{sp} = S^{2} ...(2)

Given:- for CaSO4  K_{sp} = 7.1 \times 10^{-5}

from eq(2) we have,

7.1 \times 10^{-5} = S^{2}

taking square root of both sides we get

S = \sqrt{7.1 \times 10^{-5}

S = 0.008426 mol/dm^{3}

solubility in g/dm3

S = molar solubility mol/dm^{3} \times molar mass g/mol

S = 0.00842 mol/dm^{3} \times 136.14 g/mol = 1.1462 g/dm^{3}

2.

The solubility equilibrium for Ca(OH)2 is

​​​​Ca(OH)_{3} \rightleftharpoons Ca^{2+}_{(aq)} + 2OH^{-}_{(aq)}

The solubility product is

K_{sp} = [Ca^{2+}] [OH^{-}]^{2}

if S is the molar solubility then we have,

K_{sp} = x^{x}.y^{y}.S^{x+y}...(1)

for Ca(OH)2 we have, x = 1 y = 2

Therefor from eq(1) we have,

K_{sp} = 1^{1}.2^{2}.S^{1+2} = 4S^{3}...(2)

Given :- for Ca(OH)2 K_{sp} = 4.68 \times 10^{-6}

From eq(2) we have,

4.68 \times 10^{-6} = 4S^{3}

1.17 \times 10^{-6} = S^{3}

taking cube root of both sides we get,

S = 0.01053 mol/dm^{3}

S = molar solubility mol/dm^{3} \times molar mass g/mol

S = 0.01053 mol/dm^{3} \times 74.1 g/mol = 0.7802 g/dm^{3}.

(b)

The solubility of CaSO4 is 1.1462 g/dm3 while the solubility of Ca(OH)2 is 0.7802 g/dm3.

Hence CaSO4 is more soluble salt in water than Ca(OH)2.


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