The conductivity of sodium Chloride at `298K` has been determine at different concentrations and the results are given below `:`
`{:(Concentration(M):,0.001,0.010,0.020,0.050,0.100),(10^(2)xxk(Sm^(-1)):,1.237,11.85,23.15,55.53,1.06.74):}`
Calculate `wedge_(m)` for all concentrations and draw a plot between `wedge_(m)` and `c^(1//2)`. Find the value of `wedge_(m)^(@)`.

Explanation

`Lambda_(m)` at different concentrations may be calculated as :
`Lambda_m = (kappa xx 1000)/(M)`
At 0.001 M , `kappa = 1.237 xx 10^(-2) S m^(-1) = 1.237 xx 10^(-4) S cm^(-1)`
`Lambda_(m) = (1.237 xx 10^(-4) xx 1000)/(0.001) = 123.7 S cm^(2) mol^(-1)`
At 0.010 M , `kappa = 11.85 xx 10^(-2) S m^(-1) = 11.85 xx 10^(-4) S cm^(-1)`
`therefore " " Lambda_(m) = (11.85 xx 10^(-4) xx 1000)/(0.010) = 118.5 S cm^(2) mol^(-1)`
At 0.020 M , `kappa = 23.15 xx 10^(-2) S m^(-1) = 23.15 xx 10^(-4) S cm^(-1)`
`therefore " " Lambda_(m) = (23.15 xx 10^(-4) xx 1000)/(0.020) = 115.75 S cm^(2) mol^(-1)`
At `0.50 M , kappa = 55.53 xx 10^(-2) S m^(-1) = 55.53 xx 10^(-4) S cm^(-1)`
`therefore " " Lambda_(m) = (55.53 xx 10^(-2) xx 1000)/(0.050) = 111.06 S cm^(2) mol^(-1)`
At 0.100 M , `kappa = 106.74 xx 10^(-2) S m^(-1) = 106.74 xx 10^(-4) S cm^(-1)`
`therefore " " Lambda_(m) = (106.74 xx 10^(-4) xx 1000)/(0.1) = 106.74 S cm^(2) mol^(-1)`
The values of `Lambda_(m)` and `C^(1/2)` at different concentrations are : `{:( Lambda (Scm ^(2) mol^(-1)) , 123.7 , 118.5 , 115.75 , 111.06 , 106.74) ,(C^(1/2) "("M^(1/2)")" , 0.0316 , 0.10 , 0.141 , 0.224 , 0.316):}`

The extrapolation of the straight line to zero concentration (intercept) gives the value of `Lambda_(m) = 124.5 S cm^(2) mol^(-1)`