Question

The molar conductivity of a conductivity cell filled with $10$ moles of $20\, mL\, NaCl$ solution is $\Lambda_{ m 1}$ and that of $20$ moles another identical cell heaving $80 \, mL \, NaCl$ solution is $\Lambda_{ m 2}$, The conductivities exhibited by these two cells are same The relationship between $\Lambda_{ m 2}$ and $\Lambda_{ m 1}$ is

• A. $\Lambda_{ m 2}=2 \Lambda_{ m 1}$
• B. $\Lambda_{ m 2}=\Lambda_{ m 1} / 2$
• C. $\Lambda_{ m 2}=\Lambda_{ m 1}$
• D. $\Lambda_{ m 2}=4 \Lambda_{ m 1}$

Answer 1

The Correct Option is A

${\Lambda }_m=\kappa \times \frac{1000}{M}$
$\Rightarrow {\Lambda }_m\propto \frac{1}{M}$
$\frac{{\Lambda }_{m_1}}{{\Lambda }_{m_2}}=\frac{M_2}{M_1}=\frac{\frac{20}{80}}{\frac{10}{20}}=\frac{1}{4}\times \frac{2}{1}=\frac{1}{2}$
$\Rightarrow {\Lambda }_{m_2}=2{\Lambda }_{m_1}$