Question

Solubility of ${As}_{2}{S}_{3}$ in aqueous solution is S $mol {L}^{-1}$. Its solubility product is $108{S}^{n}$. What will be the value of n?

Answer 1

Hint: Solubility is the property of a solid, liquid, or a gaseous chemical substance called solute to dissolve in a solid, liquid, or a gaseous solvent. The equilibrium constant for solubility is called the solubility product.

Complete step by step answer:
Solubility can be defined as the maximum amount of substance that can dissolve in a given amount of solvent at a specified temperature. The solubility product is kind of an equilibrium constant whose value depends upon the temperature. It is denoted by ${k}_{sp}$.
Let us now look at the question given to us.
${As}_{2}{S}_{3}$ dissociates to form 2 moles of ${As}^{3+}$ and 3 moles of ${S}^{2-}$.
${ As }_{ 2 }{ S }_{ 3 }\quad \longrightarrow \quad 2{ As }^{ 3+ }\quad +\quad 3{ S }^{ 2- }\quad$.
The solubility product is given as, ${k}_{sp} = {[aA]}^{a}{[bB]}^{b}$, where, A and B are the products of the reaction, and a and b are the stoichiometric coefficients.
Therefore, the solubility product of ${As}_{2}{S}_{3}$ is given as, ${k}_{sp} = {[2{As}^{3+}]}^{2}{[3{S}^{2-}]}^{3}$. -----(1)
Given, the solubility product=$108{S}^{n}$ and the solubility = $Smol {L}^{-1}$. Now, substituting these values in equation (1), we get,
$108{ S }^{ n }\quad =\quad { [2S] }^{ 2 }{ [3S] }^{ 3 }$
$\implies 108{ S }^{ n }\quad =\quad 4{ S }^{ 3 }\quad \times \quad 27{ S }^{ 3 }$
$\implies 108{ S }^{ n }\quad =\quad 108{ S }^{ 5 }$
Now, applying the property of bases and exponents i.e., if the bases are equal then the powers will also be equal, we get, n=5.

Therefore, the value of n is 5.

Note: When calculating the solubility product, we don't consider the concentrations of the solids as their concentrations do not change the expression, any change in their concentration is significant and therefore, is omitted.