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Question: The conductivity of saturated solution of \(BaS{O_4}\)​ is \(3.06 \times {10^{ - 6}}\,mho\,c{m^{ - 1...

The conductivity of saturated solution of BaSO4BaS{O_4}​ is 3.06×10−6 mho cm−13.06 \times {10^{ - 6}}\,mho\,c{m^{ - 1}} and its equivalent conductance is 1.53  mho cm2eq−11.53\,\,mho\,c{m^2}e{q^{ - 1}} . The Ksp{K_{sp}}​ for ​BaSO4BaS{O_4} will be:
A) 4×10−12M4 \times {10^{ - 12}}M
B) 4×10−6M4 \times {10^{ - 6}}M
C) 4×10−12M24 \times {10^{ - 12}}{M^2}
D) 1×10−12M21 \times {10^{ - 12}}{M^2}

Explanation

Solution

‌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 Ksp{K_{sp}} in terms of solubility and then put the value of solubility to find Ksp{K_{sp}} . Take care of the units.

Complete answer:
Step 1: In this step, we will write the reaction:
BaSO4 ⇄ Ba2+ + SO42−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 = 3.06×10−6 mho cm−13.06 \times {10^{ - 6}}\,mho\,c{m^{ - 1}} and
Equivalent Conductance = 1.53  mho cm2eq−11.53\,\,mho\,c{m^2}e{q^{ - 1}}
Equivalent Conductance
λeq = {\lambda _{eq}}\, = \, λc×1000s\dfrac{{{\lambda _c} \times 1000}}{s}
1.53  =  3.06×10−6×1000s1.53\,\, = \,\,\dfrac{{3.06 \times {{10}^{ - 6}} \times 1000}}{s}
s  =  2×10−3 mol L−1s\,\, = \,\,2 \times {10^{ - 3}}\,mol\,{L^{ - 1}}
Step 3: In this step, we will use the reaction to find the solubility product:
Ksp  =  [Ba2+]×[SO42−]  =  s2{K_{sp}}\,\, = \,\,[B{a^{2 + }}] \times [S{O_4}^{2 - }]\,\, = \,\,{s^2}
Here, Ksp{K_{sp}} is the Solubility product of the reaction and s is the solubility.
Ksp  =  (2×10−3)2  =  4×10−6{K_{sp}}\,\, = \,\,{(2 \times {10^{ - 3}})^2}\,\, = \,\,4 \times {10^{ - 6}}
Ksp  ={K_{sp}}\,\, = 4×10−6M4 \times {10^{ - 6}}M
Here, we got our required answer.
Therefore the correct option is option B..

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.