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.

Explanation

Both `NH_(4)^(+)` and `CH_(3)COO^(-)` ion of `CH_(3)COONH_(4)` shows hydrolysis as:
`{:(CH_(3)COO^(-)NH_(4)^(+)+H_(2)OhArrCH_(3),COOH+,NH_(4)OH),(1,0,0),((1-h),h,h):}`
Given `pK_(a)CH_(3)COOH=4.76`
`:. -log K_(a)=4.76` or `K_(a)=1.74xx10^(-5)`
`pK_(b)NH_(4)OH=4.75`
`:. -log K_(b)=4.75 or K_(b)=1.78xx10^(-5)`
`K_(H) for CH_(3)COONH_(4)`
`=(K_(w))/(K_(a)xxK_(b))=(10^(-14))/(1.74xx10^(-5)xx1.78xx10^(-5))`
`=3.23xx10^(-5)`
Also h for `CH_(3)COONH_(4)=sqrt(K_(H))`
`=sqrt(3.23xx10^(-5))=5.68xx10^(-3)`
Now for dissociation of `CH_(3)COOH`
`CH_(3)COOHhArr CH_(3)COO^(-)+H^(+)`
`K_(a)=([CH_(3)COO^(-)][H^(+)])/([CH_(3)COOH])=(C(1-h)[H^(+)])/(Ch)`
`[H^(+)]=K_(a)xx(h)/((1-h))=K_(a)xxsqrt(K_(H))`
`=K_(a)xxsqrt((K_(w))/(K_(a)xxK_(b)))=sqrt((K_(w)xxK_(a))/(K_(b)))`
`=sqrt((10^(-14)xx1.74xx10^(-5))/(1.78xx10^(-5)))`
`[H^(+)]=9.88xx10^(-8)`
or `pH= 7.005`
(pH and h are independent of initial conc. of salt)