What volume of `0.1M` sodium formate solution should be added to 50 mL of `0.05` M formic acid to produce a buffer solution of `pH= 4.0`? `(pK_(a)` of fomic acid `= 3.80)`

Options

A. `39.0mL`
B. `39.62mL`
C. `40 mL`
D. `40.62mL`

Answer

B

Explanation

Let V mL of `0.1M` HCOONa be mixed to 50 mL of `0.05M HCOOH`
`[:' [ ] = ("Total millimole")/("Total volume")]`
`:.` In mixture, `[HCOONa]= (0.1xxV)/((V+50))`
`[HCOOH]= (50xx0.05)/((V+50))`
`:' pH= -log K_(a)+log ([Sal t])/([Acid])`
`:. 4.0=3.80+log ((0.1xxV)//(V+50))/(2.5//(V+50))`
`:. v= 39.62mL`