First slide

Solubility product(KSP)

Question

The solubility of PbSO₄ in 0.01M Na₂SO₄ solution is (K_sp of PbSO₄ is 1.25 × 10^–9)

Moderate

A

1.25 $\times$ 10^-7 M
B

1.25 $\times$ 10^-9 M
C

1.25 $\times$ 10^-10 M
D

0.1 M

Solution

Solubility of PbSO₄ get suppressed in 0.01 M Na₂SO₄ solution due to common-ion effect and the following equilibrium gets established.
$\large PbS{O_4}\left( s \right) \rightleftharpoons \mathop {PbS{O_4}\left( {aq} \right)}\limits_{S'} \xrightarrow{{}}\mathop {P{b^{ + 2}}\left( {aq} \right)}\limits_{S'} + \mathop {SO_4^{ - 2}\left( {aq} \right)}\limits_{S' + 0.01}$
$\large N{a_2}S{O_4}\xrightarrow{{}}\mathop {2N{a^ + }\left( {aq} \right)}\limits_{2 \times \left( {0.01} \right)} + \mathop {SO_4^{ - 2}\left( {aq} \right)}\limits_{0.01 + S'}$
K_sp = (S') x (S' + 0.01)
K_sp $≅$ S' x 0.01
⇒ 1.25 x 10^-9 = S' x 10^-2
⇒ S' = 1.25 x 10^-7

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