Question

What will be the molar conductance ’Λ’, if resistivity is x for 0.1 N H₂SO₄?

• A. $\mathrm{\Lambda }=\mathrm{x}\times 1000/0.1$
• B. $\mathrm{\Lambda }=2\times 1000/\mathrm{x}\times 0.1$
• C. $\mathrm{\Lambda }=\mathrm{x}\times 1000/0.5$
• D. $\mathrm{\Lambda }=0.5/1000\mathrm{x}$

Answer 1

The correct option is B

$\mathrm{\Lambda }=2\times 1000/\mathrm{x}\times 0.1$

Explanation for correct option:

(B) $\mathrm{\Lambda }=2\times 1000/\mathrm{x}\times 0.1$

Step 1: Molar conductivity:

• “The conductivity of solutions of different electrolytes in the same solvent and at a given temperature differs due to charge and size of the ions in which they dissociate, the concentration of ions, or ease with which the ions move under a potential gradient.”
• "It, therefore, becomes necessary to define a physically more meaningful quantity called molar conductivity denoted by the symbol ${\mathrm{\Lambda }}_{\mathrm{m}}$."
• It is related to the conductivity of the solution by the equation:

${\mathrm{\Lambda }}_{\mathrm{m}}=\frac{\mathrm{K}}{\mathrm{c}}$, if $\mathrm{K}$ is expressed in $\mathrm{S}{\mathrm{m}}^{-1}$ and the concentration, $\mathrm{c}$ in $\mathrm{mol}{\mathrm{m}}^{-3}$ then the units of ${\mathrm{\Lambda }}_{\mathrm{m}}$ are in $\mathrm{S}{\mathrm{m}}^2{\mathrm{mol}}^{-1}$.

• Or it can also be expressed as, ${\mathrm{\Lambda }}_{\mathrm{m}}\left(\mathrm{S}{\mathrm{cm}}^2{\mathrm{mol}}^{-1}\right)=\frac{\mathrm{K}\left(\mathrm{S}{\mathrm{cm}}^{-1}\right)}{1000\left(\mathrm{L}{\mathrm{m}}^{-3}\right)\times \mathrm{Molarity}\left(\mathrm{mol}{\mathrm{L}}^{-1}\right)}$

Step 2: Given information:

• $\mathrm{K}$ = Specific conductance = 1 / specific resistance = 1 / 1
• M = Molarity = 0.1 / 2

Step 3: Calculation for Molar conductance:

$$\begin{gathered} {\mathrm{\Lambda }}_{\mathrm{m}}=\frac{1000\times (1/\mathrm{x})}{(0.1/2)} \\ {\mathrm{\Lambda }}_{\mathrm{m}}=\frac{2\times 1000}{\mathrm{x}\times 0.1} \end{gathered}$$

Hence, the molar conductance will be, $\mathrm{\Lambda }=2\times 1000/\mathrm{x}\times 0.1$.

Explanation for incorrect options:

The molar conductance is $\mathrm{\Lambda }=2\times 1000/\mathrm{x}\times 0.1$. Thus, options A, C, and D are incorrect.

Hence, the correct option is B i.e. $\mathrm{\Lambda }=2\times 1000/\mathrm{x}\times 0.1$.