Question

If the solubility product ${K_{sp}}$ of a sparingly soluble salt $M{X_2}$ at ${25^ \circ }C$ is $1.0 \times {10^{ - 11}}$ , then the solubility of the salt in mole $litr{e^{ - 1}}$ at this temperature will be:
(A) $2.46 \times {10^{14}}$
(B) $1.35 \times {10^{ - 4}}$
(C) $2.60 \times {10^{ - 7}}$
(D) $1.20 \times {10^{ - 10}}$

Answer 1

Hint: In this question it is given in the question that, the solubility product of sparingly soluble salt$M{X_2}$ is $1.0 \times {10^{ - 11}}$ at the temperature of ${25^ \circ }C$ then we have to find the solubility of salt in mole $litr{e^{ - 1}}$ . To find this the formula which is used is given in the solution part.

Complete step by step solution:
As we know that the reaction of sparingly soluble salt $M{X_2}$ is as follows,
$M{X_2}\overset {} \leftrightarrows {M^{2 + }}(S) + 2{X^ - }{(2S)^2}$
As from this, the formula which we use to find the solubility of salt in mole $litr{e^{ - 1}}$ is,
${K_{sp}} = 4{S^3}$
Here in the above formula, we have to find the value of $S$ so by rearranging the whole formula as suitable for the question we get,
$S = \sqrt[3]{{\dfrac{{{K_{sp}}}}{4}}}$
The above formula, which we are going to use for the solution of this question. So, by putting all available values in the above formula we get,
$S = \sqrt[3]{{\dfrac{{1 \times {{10}^{ - 11}}}}{4}}}$
By doing further solution of the above equation, we get the result as,
 $S = 1.35 \times {10^{ - 4}}$
As we get the value of solubility of the salt in mole $litr{e^{ - 1}}$ is $1.35 \times {10^{ - 4}}$ .
Therefore, the correct answer is $1.35 \times {10^{ - 4}}$ .

Additional Information :
Solubility is defined as the property of a substance known as solute to get dissolved in a solvent for the formation of a solution. The solubility of ionic compounds that dissociate and form cations and anions in water varies to a great extent. Some compounds are highly soluble and can even absorb moisture from the atmosphere whereas, on the other hand, the others are highly insoluble.

Hence, the correct option is (B)

Note: Salts with very low solubilities are referred to as sparingly soluble salts. A substance's solubility is determined by how much of it can dissolve in $100$ millilitres of water.