For the cell (at 1bar `H_(2)` pressure) `Pt`|`H_(2)`(g)| `HX(m_(1))`, `NaX(m_(2))`, `NaCl(m_(3))`|`AgCl`|`Ag`|`Pt`, it is found that the value of `E-E^(@) + RTF^(-1)` ln `[(m_(HX).m_(Cl^(-)))/(m_(X^(-)))]` approaches 0.2814 in the limit of zero concentration. Calcualte `K_(a)` for the acid HX at `25^(@)C` expressing your answer as `10^(-7) K_(a)`

Answer

174

Explanation

`E=E^(@)+RTF^(-1)ln([X^(-)])/(K_(a)[HX][Cl^(-)])impliesE-E^(@)+RTF^(-1)ln([HX][Cl^(-)])/([X^(-)])RTF^(-)ln(1)/(K_(a))`
`impliesl n(1)/(K_(a))=(96500)/(8.315xx298)(0.2814)impliesK_(a)=1.74xx10^(-5)`