Question

A big irregular shaped vessel contained water, the conductivity of which was $2.56 \times 10^{-5} \,S\, cm ^{-1} .500\, g$ of $NaCl$ was then added to the water and the conductivity after the addition of $NaCl$, was found to be $3.10 \times 10^{-5} \,S\, cm ^{-1}$. The capacity of the vessel if it is fully filled with water $\left(\Lambda_{m}^{\circ}\right.$ of $\left. NaCl =149.9\right)$ is

• A. $4587.9 \times 10^{2}\, L$
• B. $3.4752 \times 10^{5}\, L$
• C. $5467.5 \times 10^{2}\, L$
• D. $2.3725 \times 10^{5} \,L$

Answer 1

Answer: (D)

Let us suppose the volume of vessel is $V \,mL $ Volume containing $1$ equivalent

$=\frac{\text { Volume }}{\text { Mass/equivalent mass }}$

$=\frac{V}{500 / 58.5}=\frac{V}{8.547}$

Specific conductance of $NaCl =$ Specific conductance of $NaCl$ solution - specific conductance of water

$=3.1 \times 10^{-5}-2.56 \times 10^{-5}=0.54 \times 10^{-5} ohm ^{-1} cm ^{-1}$

$\Lambda=\kappa \times$ Volume containing 1 equivalent of electrolyte

$\Lambda_{ NaCl }^{\circ}=149.9 \, ohm ^{-1} \, cm ^{2} eq ^{-1}$

$149.9=0.54 \times 10^{-5} \times \frac{V}{8.547}$

$V=\frac{149.9 \times 8.547}{0.54 \times 10^{-5}}=237258.39\, L =2.3725 \times 10^{5} \,L$