Question

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

$=3.1\times 10^{-5}-2.56\times 10^{-5}=0.54\times 10^{-5}oh{m}^{-1}c{m}^{-1}$

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

${\Lambda }_{NaCl}^{\circ }=149.9oh{m}^{-1}c{m}^{2}e{q}^{-1}$

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

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