Calculate the `pH` of a buffer solution prepared by dissolving `10.6 g` of `Na_(2)CO_(3)` in `500 ml` of an aqueous solution containing `80 ml` of `1 M HCl`. `K_(a)` for `HCO_(3)^(-)=6xx10^(-11)`

Options

A. `8.6`
B. `9.6`
C. `11.6`
D. `12.6`

Answer

B

Explanation

`{:(,Na_(2)CO_(3),+,HCl,to,NaCl,+,NaHCO_(3)),("Meq. before",(10.6)/(106)xx1000,,2,,80xx1,,4),("Reaction",=100,,80,,0,,0),("Meq. After",20,,0,,80,,80),("Reaction",1,,2,,2,,2):}`
The reaction has `Na_(2)CO_(3)` and `HCO_(3)^(-)` and thus acts as buffer
`pH= -logK_(a)+log``([CO_(3)^(-2)])/([HCO_(3)^(-)])`
`= -log 6xx10^(-11)+log``(20)/(80)=9.6`