MHT CET · Chemistry · Electrochemistry

Which among the following statements is true for conductivity?

A It is inversely proportional to resistivity.
B It is inversely proportional to molar conductivity.
C It is directly proportional to resistivity.
D It is directly proportional to resistance.

Verified Solution

Answer & Solution

Correct Answer

(A) It is inversely proportional to resistivity.

Step-by-step Solution

Detailed explanation

Specific conductance/ Conductivity (k): -
It is defined as the reciprocal of specific resistance, or resistivity, \(\mathrm{k}=\frac{1}{\rho}\)
\(
\begin{aligned}
& \mathrm{R}=\rho \frac{\ell}{\mathrm{A}} \\
& \frac{1}{\rho}=\frac{1}{\mathrm{R}} \cdot \frac{\ell}{\mathrm{A}} \\
& \mathrm{k}=\mathrm{G} \times \mathrm{G}^*
\end{aligned}
\)
Specific conductance \(=\) Conductance \(\times\) Cell constant
Hence specific conductivity of a solution is defined as the conductance offered by \(1 \mathrm{~cm}^3\) of electrolytic solution.
Unit of \(\mathrm{k}\) is ohm \({ }^{-1} \mathrm{~cm}^{-1}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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