Question

The `pK_(a)` of `CH_(3)COOH` and `pK_(a)` of `nH_(4)OH` is `4.76` and `4.75`, respectively. Calculate the hydrolysis constant of ammonium acetate `(CH_(3)COONH_(4))` at `298K` and also the drgree of hydrolysis and `pH` of its (a) `0.01M` and (b) `0.04M` solutions.

Answer 1

a. `CH_(3)COONH_(4)` is a salt of `W_(A)//W_(B)`.
`K_(a) = "antilog" (-4.76) = "antilog" [(-4-0.76 +1-1) = bar(5).24)]`
`= 1.74 xx 10^(-5)`
`K_(b) = "antilog" (-4.75) = "antilog" [(-4 - 0.75 +1 - 1)= bar(5).25] = 1.77 xx 10^(-5)`
`K_(h) = (K_(w))/(K_(a)K_(b)) = (10^(-14))/(1.74 xx 10^(-5)xx1.77xx10^(-5))`
`= 3.25 xx 10^(-5)`
Since `K(h)` is small, and `(1-h) ~~1`.
`:. h = (K_(h))^(1//2) = (3.25 xx 10^(-5))^(1//2) = 5.7 xx 10^(-3)`
b. `pH = (1)/(2) (pK_(w) +pK_(a) - pK_(b))`
`=(1)/(2) (14 +4.76 - 4.75) = 7.005`
It has been already shown that the dergee of hydrolysis `(h)` and the `pH` are independent of concentration and thus `pH` of `0.01M` and `0.04M` solutions of `CH_(3)COONH_(4)` is same, i.e., `pH = 7.005`.