A hydrogen electrode placed in a solution containing sodium acetate and acetic acid in the ratio of `x:y` and `y:x`, ahs electrode potential values of `-1.5` and `-0.5V`, respectively. What is the `pK_(a)` value of acetic acid?

Explanation

`E_(1) (H_(2)) = - 0.059pH_(1) =- 0.059[pK_(a) + log(x//y)] …(i)`
`E_(2)(H_(2)) =- 0.059pH_(2) =- 0.059[pK_(a) + log (y//x)] …(ii)`
Add equaitons (i) and (ii), we get
`E_(1) + E_(2) =- 0.059 [pK_(a) + log (x//u)] - 0.059 [pK_(a) + log (y//x)]`
`=- 2xx 0.059pK`
`pK_(a) = (-(E_(1)+E_(2)))/(2xx0.059)=(-(-1.5-0.5))/(2xx0.059) = (0.1)/(0.059) = 16.94`