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)`

Answer

`V = 2.34 xx 10^(8) c c`

Explanation

Let the volume of the vessel be V cc
Number of equivalent of `NaCl`
`=(500)/(58.5) = 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 xx10^(-5) =0.54 xx 10^(-5)`
`:. Lamda_("NaCl") =0.54 xx 10^(-5) xx(V)/(8.547)`
Since the vessel is big, the resulting solution may be supposed to be dilute.
`:. Lamda_("Nacl") = Lamda_("Nacl")^(@)`
`0.54 xx 10^(-5) xx (V)/(8.547) = 149.9`
`V = 2.47 xx 10^(8) "cc"`.