What volume of `0.1 M HCOONa` solution should be added to `50ml` of `0.05 M` formic acid to produce a buffer solution of `pH=4.0`, `pK_(a)` of formic acid `=3.7`?

Options

A. `50 ml`
B. `40 ml`
C. `30 ml`
D. `60 ml`

Answer

A

Explanation

Let `V` of `0.1 M HCOONa` be mixed to `50 ml` of `0.05 M HCOOH` in mixture
`[HCOONa]=(0.1xxV)/((V+50))`
`[HCOOH]=(50xx0.05)/((V+50))`
`:. pH= -log K_(a)+log``(["Salt"])/([Acid])`
`4.0=3.7+log``((0.1xxV)//(V+50))/(2.5//(V+50))`
`V=50 ml`.