For a reaction,
`CH_(3)COOH(aq) hArr H^(+) (aq)+CH_(3)COO^(-)(aq)` or `HAc (aq) hArr H^(+)(aq)+Ac^(-)(aq)`
Evaluate the pH of the solution resulting on addition of `0.05M` acetata ion to `0.05M` acid solution `(K_(a) = 1.8 xx 10^(-5))`

Options

A. `5.72`
B. `3.87`
C. `4.24`
D. `4.74`

Answer

D

Explanation

`{:(,HAc(aq)hArr,H^(+)(aq)+,Ac^(-)(aq)),("Initial conc"(M),0.05,0,0.05),("At equilibrium",0.05-x,x,0.05+x):}`
concentration `(M)`
`K_(a) = ([H^(+)][Ac^(-)])/([HAc]) ([(x)(0.05+x)])/((0.05-x))`
As `K_(a)` is small for a very weak, `x lt lt 0.05`
Hence, `(0.05+x) ~~ (0.05 -x)~~ 0.05`
Thus, `1.8 xx 10^(-5) = ((x)(0.05+x))/((0.05-1)) = (x(0.05))/((0.05)) = x = [H^(+)]`
`1.8 xx 10^(-5)M`
`pH = - log (1.8 xx 10^(-5)) = 4.74`