Question

At a certain temperature, the solubility of the salt $A_x{B}_y$ is $S$ moles per litre. The general expression solubility product will be:

• A. $K_{sp}=x^y{y}^x{S}^{x+y}$
• B. $K_{sp}={\left(xy\right)}^{x+y}{S}^{x+y}$
• C. $K_{sp}=\left(x^y{y}^x\right)S^{x+y}$
• D. $K_{sp}=\left(x^y{y}^x\right)S^{xy}$

Answer 1

Answer: (A)

$K_{sp}=x^y{y}^x{S}^{x+y}$

Let us consider solubility of any general salt $A_x{B}_y$. Let the solubility is $s$ mol per liter

$AxBy\left(s\right)\leftrightharpoons A^{y+}\left(aq\right)+y{B}^{x-}\left(aq\right)$

xs ys

The solution which contains maximum possible amount of solute in it are called Saturated solution. For saturated solution, at equilibrium

$K=\frac{[A^{y+}{]}^y\times [B^{x-}{]}^x}{\left[A_x{B}_y\right]}=\frac{[xs{]}^y\times [ys{]}^x}{\left[AxBy\right]}$

$K\left[A_x{B}_y\right]=(xs{)}^y\times (ys{)}^x$

As concentraion of solid $A_x{B}_y$ remains constant we can write

$K_{sp}=x^y\times y^x\times s^{(x+y)}$