Question

The molar conductivity of a conductivity cell filled with $10$ moles of $20mLNaCl$ solution is ${\Lambda }_{m1}$ and that of $20$ moles another identical cell heaving $80mLNaCl$ solution is ${\Lambda }_{m2}$, The conductivities exhibited by these two cells are same. The relationship between ${\Lambda }_{m2}$ and ${\Lambda }_{m1}$ is

• A. ${\Lambda }_{m2}=2{\Lambda }_{m1}$
• B. ${\Lambda }_{m2}={\Lambda }_{m1}/2$
• C. ${\Lambda }_{m2}={\Lambda }_{m1}$
• D. ${\Lambda }_{m2}=4{\Lambda }_{m1}$

Answer 1

Answer: (A)

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