To `0.1L` of a decimolar solution of acetic acid, how much dry sodium acetate be added (in moles) so as to decrease the concentration of `H^(o+)` ion to `1//10th` of its previous value? `K_(a) = 2.0 xx 10^(-5)`.

Explanation

`CH_(3)COOH_((aq)) hArr CH_(3)COO^(Theta)(aq) +H^(Theta)(aq)`
`rArr [H^(o+)] = C alpha (C = 0.1M)`
`= sqrt(K_(a)C) = sqrt(2.0 xx 10^(-5) xx 0.1) = 1.41 xx 10^(-3)M`
[Check yourself that approximations are valid]
Note that when salt, `Ch_(3)COONa` is added, the sodium will behave just like an acidic buffer solution.
Using, Henderson's equation:
`pH = pK_(a) + "log"(["salt"])/(["acid"])`
`rArr [H^(o+)] = K_(a) (["acid"])/(["salt"])` or `["salt"] = K_(a) (["acid"])/([H^(o+)])`
Now, `[H^(o+)]_("new") = (1)/(10) xx 1.41 xx 10^(-3)M = 1.41 xx 10^(-4)M`
`rArr ["salt"] = ((2.0 xx 10^(-5))(0.1))/(1.41xx 10^(-4)) = 0.0142M`
`rArr` moles of salt sodium acetate `= 0.0142 ( -=14.2 mmol)` per `1.0L` is required. `(V = 1.0L)`