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Question: The ionization constant of a weak electrolyte is \[25 \times {10^ - }^6\] while the equivalent condu...

The ionization constant of a weak electrolyte is 25×10−625 \times {10^ - }^6 while the equivalent conductance of its 0.01 M0.01{\text{ }}M solution is19.6 S  cm2eq−119.6{\text{ }}S\;c{m^2}e{q^{ - 1}}. The equivalent conductance of the electrolyte at infinite dilution (in S  cm2eq−1S\;c{m^2}e{q^{ - 1}}) will be
A. 250
B. 196
C. 392
D. 384

Explanation

Solution

In this question, the ionization constant of a weak electrolyte and the equivalent conductance of its 0.01 M0.01{\text{ }}M solution is given. Students need to find the equivalent conductance of the electrolyte at infinite dilution. Firstly, Students need to calculate the degree of dissociation in this question. Then proceed the question further with the formulas of dissociation.

Formula used:
Degree of dissociation,α=equivalent conductance at concentration Cequivalent conductance at infinite dilution=KC{\text{Degree of dissociation,}}\alpha = \dfrac{{{\text{equivalent conductance at concentration C}}}}{{{\text{equivalent conductance at infinite dilution}}}} = \sqrt {\dfrac{K}{C}}

Complete step by step answer:
The degree of dissociation for a weak electrolyte is directly proportional to the inverse square root of the concentration as shown below:
Degree of dissociation,α=equivalent conductance at concentration Cequivalent conductance at infinite dilution=KC ⇒α=25×10−610−2 ⇒α=5×10−2  {\text{Degree of dissociation,}}\alpha = \dfrac{{{\text{equivalent conductance at concentration C}}}}{{{\text{equivalent conductance at infinite dilution}}}} = \sqrt {\dfrac{K}{C}} \\\ \Rightarrow \alpha = \dfrac{{\sqrt {25 \times {{10}^{ - 6}}} }}{{\sqrt {{{10}^{ - 2}}} }} \\\ \Rightarrow \alpha = 5 \times {10^{ - 2}} \\\
Now, the equivalent conductance of the electrolyte at infinite dilution will be
∧∞eq=∧eqα ⇒∧∞eq=19.65×10−2=392  { \wedge ^\infty }_{eq} = \dfrac{{{ \wedge ^{}}_{eq}}}{\alpha } \\\ \Rightarrow { \wedge ^\infty }_{eq} = \dfrac{{19.6}}{{5 \times {{10}^{ - 2}}}} = 392 \\\
Hence, from the above explanation we can see that the equivalent conductance of the electrolyte at infinite dilution is 392.

So, the correct answer is Option C.

Additional information:
Degree of dissociation is defined as the equivalent conductance at concentration C to the equivalent conductance at infinite solution. In the formula, KC\sqrt {\dfrac{K}{C}} , K is the ionisation constant and C is the concentration.

Note: Students usually make calculation mistakes in these types of problems. So, it is advised to do the calculations properly. Also, students should by heart the formulas beforehand while proceeding to the answer. This will give students the confidence to solve the questions easily. Moreover, it is very important to read the question thoroughly so that they can understand what values are given and what exactly they need to find out.