A hydrogen electrode placed in a solution containing sodium acetate and acetic acid in the ratio of `x:y` and `y:x` has an electrode potential value `E_(1)` and `E_(2)` volts, respectively, at `25^(@)C`. The `pK_(a)` value of acetic acid is

Options

A. `(-(E_(1)+E_(2)))/(2xx0.059)`
B. `(E_(1)+E_(2))/(2xx0.059)`
C. `(E_(2)-E_(1))/(2xx0.059)`
D. `(-(E_(1)+E_(1)))/(0.059)`

Answer

a

Explanation

`Pt|H_(2)|"Sodium acetate"+CH_(3)COOH(x:y)`
`pH` of acidic buffer `=pK_(a)+log((Sal t)/(Aci d))`
`:. pH_(1)=pK_(a)+log.(y)/(x)`
`:. E_(1)=-0.059pH_(1)`
`E_(2)=-0.059pH_(2)`
`(E_(1)+E_(2))=-0.059(pK_(a)+log.(y)/(y))-0.059(pK_(a)+log.(y)/(x))`
Solve `pK_(a)=(-(E_(1)+E_(2)))/(2xx0.059)`