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)`

Explanation

`pH=pK_(a) + log.(["Salt"])/(["Acid"]) :. 4=3.8+ log.(["Salt"])/(["Acid"]) or log.(["Salt"])/(["Acid"]) = 0.2 or (["Salt"])/(["Acid"])=1.5849`
or `("No. of moles of salt")/("No. of moles of acid")=1.5849` (`:'` Volume is same for both)
No. of moles of acid present `=(0.05)/(1000)xx50=2.5xx10^(-3)`
`:.` No. of moles of salt `=1.5849 xx 2.5xx10^(-3)=3.962xx10^(-3)`
Hence, volume of 0.1 M sodium formate required `=(1000)/(0.1) xx 3.962xx10^(-3)=39.62 ml`