Question

The conductivity of saturated solution of $BaS{O_4}$​ is $3.06 \times {10^{ - 6}}\,mho\,c{m^{ - 1}}$ and its equivalent conductance is $1.53\,\,mho\,c{m^2}e{q^{ - 1}}$ . The ${K_{sp}}$​ for ​$BaS{O_4}$ will be:
A) $4 \times {10^{ - 12}}M$
B) $4 \times {10^{ - 6}}M$
C) $4 \times {10^{ - 12}}{M^2}$
D) $1 \times {10^{ - 12}}{M^2}$

Answer 1

Hint In order to answer this question you must be aware of the concepts of conductivity and equivalent conductance. Firstly, use the formula of equivalent conductance and after enlisting all the values put the correct values in the formula and then you will be able to find the solubility. By using the equation of the reaction, find the Solubility product ${K_{sp}}$ in terms of solubility and then put the value of solubility to find ${K_{sp}}$ . Take care of the units.

Complete step by step answer:
Step 1: In this step, we will write the reaction:
$BaS{O_4}\, \rightleftarrows \,B{a^{2 + }}\, + \,S{O_4}^{2 - }$
Step 2: In this step, we will use the formula of equivalent conductance to find the solubility:
Given quantities are:
Conductivity = $3.06 \times {10^{ - 6}}\,mho\,c{m^{ - 1}}$
Equivalent Conductance = $1.53\,\,mho\,c{m^2}e{q^{ - 1}}$
Equivalent Conductance = ${\lambda _{eq}}\, = \,$ $\frac{{{\lambda _c} \times 1000}}{s}$
$1.53\,\, = \,\,\frac{{3.06 \times {{10}^{ - 6}} \times 1000}}{s}$
$s\,\, = \,\,2 \times {10^{ - 3}}\,mol\,{L^{ - 1}}$
Step 3: In this step, we will use the reaction to find the solubility product:
${K_{sp}}\,\, = \,\,[B{a^{2 + }}] \times [S{O_4}^{2 - }]\,\, = \,\,{s^2}$
Here, ${K_{sp}}$ is the Solubility product of the reaction and s is the solubility.
${K_{sp}}\,\, = \,\,{(2 \times {10^{ - 3}})^2}\,\, = \,\,4 \times {10^{ - 6}}$
${K_{sp}}\,\, = $ $4 \times {10^{ - 6}}M$
Here, we got our required answer.
Therefore, option (B) is correct.

Note:Solubility is the ability of a substance to dissolve. In the process of dissolving something, there is a solute and a solvent. The solute is the substance that is being dissolved and the solvent is the substance that is doing the dissolving. With this concept, we can understand solubility on a more specific level. Solubility is known to be the maximum amount of solute that can be dissolved in a solvent at equilibrium. Equilibrium is when the concentrations of products and reactants have become equal after the reaction has taken place.