A hydrogen electrode placed in a buffer solution of `CH_(3)COONa` and `CH_(3)COOH` in the ratios of `x:y` and `y:x` has electrode potential values `E_(1)` volts and `E_(2)` volts, respectively at `25^(@)C` The `pK_(a)` values of acetic acid is `(E_(1)` and `E_(2)` are oxidation potential)

Options

A. `(E_(1)+E_(2))/(0.118)`
B. `(E_(2)-E_(1))/(0.118)`
C. `-(E_(1)+E_(2))/(0.118)`
D. `(E_(1)-E_(1))/(0.118)`

Answer

A

Explanation

`E_(1)=(-0.059)/(1)log[H^(+)]`
or `pH_(1)=E_(1)//0.059=pK_(a)+log((x)/(y))`
`pH_(2)=E_(2)//0.059=pK_(a)+log((y)/(x))`
or `(E_(1)+E_(2))/(0.059)=2pK_(a)` or `pK_(a)=(E_(1)+E_(2))/(0.118)`