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 hArr CH_(3)COO^(-) + H^(+) " " c = 0.1` M
`rArr [H^(+)] = c alpha`
` 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` si added , the solution will behave just like an acidic Buffer solution . Using , Henderson equation :
`pH = pK_(a) +log_(10).(["salt"])/(["acid"])rArr [H^(+)] = K_(a) (["acid"])/(["salt"]) " or " ["salt"] = K_(a) "[acid]"/([H^(+)])`
Now, `[H^(+)]_("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))/(1.41 xx 10^(-4)) = 0.0142 M`
`rArr` moles of salt, sodium acetate ` = 0.0142 ( -= 14.2 "mmoles) per " 1.0 L 1` is required . (`V = 1.0 L`)