Question

The correct relation between ${K_{sp}}$ and solubility for the salt, $K\,Al{(S{O_4})_2}$ is:
A. $4{s^4}$
B. $27{s^4}$
C. $108{s^5}$
D. none of these

Answer 1

Hint : In order to this question, to know the relation between ${K_{sp}}$ and solubility for the salt, $K\,Al{(S{O_4})_2}$ , we should first write the formula of ${K_{sp}}$ and then put the given values in the formula from the given compound.

Complete Step By Step Answer:
As we know that,
${K_{sp}} = {x^x}{y^y}{s^{(x + y)}}$
For our question-
$K\,Al{(S{O_4})_2} \Rightarrow K^+ \;+\; Al^{+3}\; 2SO_4{-2}$

| $K\,Al{(S{O_4})_2}$| $K^+$| $Al^{+3}$| $2SO_4{-2}$
---|---|---|---|---
Initial| -| -| -| -
At Equilibrium| -| s| s| 2s

${K_{sp}} = [K^+] \; [Al^{+3}] \; [SO_4^{-2}]^2$
$\Rightarrow {K_{sp}} =(s)(s)(2s)^2 = 4s^4$
The solubility product is a kind of equilibrium constant and its value depends on temperature. ${K_{sp}}$ usually increases with an increase in temperature due to increased solubility. Solubility is defined as a property of a substance called solute to get dissolved in a solvent in order to form a solution.
Hence, the correct option is (A).

Note :
${K_{sp}}$ usually increases with an increase in temperature due to increased solubility. Solubility is defined as a property of a substance called solute to get dissolved in a solvent in order to form a solution.