The molar conductivity of a conductivity cell filled with 10 moles of 20 mL NaCl solution is ${\Lambda _{m1}}$ and that of 20 moles another identical cell heaving 80 mL NaCl solution is ${\Lambda _{m2}}$. The conductivities exhibited by these two cells are same. The relationship between ${\Lambda _{m2}}$ and ${\Lambda _{m1}}$ is
Solution
$$\Lambda_{\mathrm{m}_{1}}=\frac{\mathrm{k}_{1} \times 1000}{\mathrm{M}_{1}}=\frac{\mathrm{k} \times 1000}{\frac{10}{0.02}}$$
<br/><br/>
$\Lambda_{\mathrm{m}_{2}}=\frac{\mathrm{k}_{2} \times 1000}{\frac{20}{0.08}}$
<br/><br/>
It is given that $\mathrm{k}_{1}=\mathrm{k}_{2}$
<br/><br/>
$$
\mathrm{k}_{1}=\frac{\Lambda_{\mathrm{m}_{1}}}{2} \quad \quad \mathrm{k}_{2}=\frac{\Lambda_{\mathrm{m}_{2}}}{4}
$$
<br/><br/>
Applying the given condition on conductivity.
<br/><br/>
$$
\begin{gathered}
\frac{\Lambda_{\mathrm{m}_{1}}}{2}=\frac{\Lambda_{\mathrm{m}_{2}}}{4} \\
\Lambda_{\mathrm{m}_{2}}=2 \Lambda_{\mathrm{m}_{1}}
\end{gathered}
$$
About this question
Subject: Chemistry · Chapter: Electrochemistry · Topic: Electrochemical Cells
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