A big irregular shaped vessel contained water, the conductivity of which was `2.56xx10^(-5)` `cm^(-1)` . 500 g of NaCl was then added to the water and the conductivity after the addition of NaCl, was found to be `3.10xx10^(-5)` S `cm^(-5)` !. The capacity of the vessel if it is fully filled with water (`Lambda_m^@` of NaCl = 149.9) is

Options

A. `4587.9xx10^(2)` L
B. `3.4752xx10^(5)` L
C. `5467.5xx10^(2)` L
D. `2.3725xx10^(5)` L

Answer

D

Explanation

Let us suppose the volume of vessel is V mL
Volume containing 1 equivalent = `(Volume)/ (Mass//"equivalent" mass)`
`=V/(500//58.5)=V/8.547`
Specific conductance of NaCl - Specific conductance of Naci solution - specific conductance of water
`=3.1xx10^(-5)-2.56xx10^(-5)=0.54xx10^(-5)` `ohm^(-1)cm^(-1)`
`Lambda=kxx Volume` containing 1 equivalent of electrolyte
`Lambda_(NaCI)^@=149.9` `ohm^(-1)cm^(2)eq^(-1)`
`149.9=0.54xx10^(-5)xxV/8.547`
`V=(149.9xx8.547)/(0.54xx10^(-5))=237258.39 L=2.3725xx10^5` L