A big irrengular shaped vessel contained waer the sp conductance of which was `2.56 xx 10^(-5) mho cm^(-1) 500g` of `NaCI` was then added to the water and the specific conductance after the addition of `NaCI` was found to be `3.10 xx 10^(-5) mho cm^(-1)`. find the capacity of the vessel if it is fulfilled with water `(lambda_(oo)NaCI = 149.9)`

Explanation

Let the volume of the vessel be V cc.
Number of equivalent of NaCl `= ("wt. in grams")/("eq. weight")`
`= (500)/(58.5) = 8.547`
`therefore` volume of water (cc) containing 1 eq. of NaCl `= (V)/(8.547)`
The sp. cond. of the NaCl solution (only due to presence of `Na^(+)` and `Cl^(-)` ions)
`= 3.10 xx 10^(-5) - 2.56 xx 10^(-5)`
`= 0.54 xx 10^(-5)`
`therefore Lambda_(NaCl) = 0.54 xx 10^(-5) xx (V)/(8.547)`
Sicne the vessel is big, the resulting solution may be supposed to be dilute.
`therefore Lambda_(NaCl) = Lambda_(NaCl)^(@)`
`0.54 xx 10^(-5) xx(V)/(8.547) = 149.9`
`V = 2.37 xx 10^(8)` cc.