What is the `pH` of the solution when `0.20 mol` of `HCI` is added to `1L` of a solution containing
a. `1M` each of acetic acid and acetate ion.
b. `0.1M`each of aceta acid and acetate ion.
Assume the total volume is `1L. K_(a)` for acetic acid is `1.8 xx 10^(-5)`.

Explanation

Intially [ Acetic acid ] = 1 M
[ Acetate ] = 1 M
Now `0.2` mole of HCl are added to it .
`{: (,HCl,+,CH_(3)COO^(-) , to , CH_(3)COOH , + , Cl^(-)),("mole before reaction", 0.2 , ,1 ,,1,,0),("Mole after reaction " ,0 , , 0.8, ,1.2 ,,0.2):}`
` :. ` New `[ CH_(3)COOH] = 1.2 , " " [ CH_(3)COO^(-)] = 0.8 `
` :. pH = - log 1 .8 xx 10^(-5) + log. (0.8)/(1.2) = 4.5686`
(b) In II case intially [ Acetic acid ] = `0.1` M
[ Acetate ] = 0.1 M
Now `0.2 ` mole of HCl are added to it
`{: (,HCl,+,CH_(3)COO^(-) , to , CH_(3)COOH , + , Cl^(-)),("mole before reaction", 0.2 , ,0.1 ,,0.1,,0),("Mole after reaction " ,0.1 , , 0, ,0.2 ,,0.1):}`
` :. [ H^(+)] ` from free HCl ` = 0.1 = 10^(-1)`
` :. pH = 1 `
Note `CH_(3)COOH` no doubt gives `H^(+)` but being wak acid as well as in presence HCl does not dissociate appreciably and thus , `H^(+)` from `CH_(3)COOH` may be neglected .