A hydrogen electrode placed in a solution containing `CH_(3)COOK` and `CH_(3)COOH` in the ration `a:b` and `b:a` has electrode potential values of `-1.59` and `+1.0V,` respectively. Calculate `pK_(a)` of `CH_(3)COOH.`

Explanation

Mixture of `CH_(3)COOHK(` salt of `W_(A)//S_(B))` and `CH_(3)COOH(W_(A))`
forms acidic buffer solution whose `pH` is
`pH_(aci dic buffer)=pK_(a)+log.([Sa l t])/([Aci d])`
`:. E_(1(H_(2)))=-0.059pH_(1)=-0.059[pK_(a)+log.(a)/(b)],,,(i)`
`E_(2(H_(2)))=-0.059pH_(2)=-0.059[Pk_(a)+log.(b)/(a)],,,(ii)`
Adding Eqs. `(i)` and `(ii)`, we get
`E_(1)+E_(2)=-0.059[pK_(a)+log.(a)/(b)]-0.059[pK_(a)+log.(b)/(a)]`
`=-2xx0.059pK_(a)`
`:. pK_(a)=(-(E_(1)+E_(2)))/(2xx0.059)=(-(-1.59+1.0))/(2xx0.059)`
`=(0.059)/(2xx0.059)=5`
`:. pK_(a)=5`