You have 0.2M solutions of formic acid and sodium formate (pKa 3.75). If you would like to make 1L of a 0.2M formate buffer at a pH of 4.5, then how many mL of formic acid will you need to add

151mL of the 0.2M formic acid

Explanation:

Using H-H equation for Formate buffer:

pH = pKa + log [Formate] / [Formic acid]

4.5 = 3.75 + log [Formate] / [Formic acid]

0.75 = log [Formate] / [Formic acid]

5.6234 = [Formate] / [Formic acid] (1)

That means you need to add 5.6234times more Formate than formic acid.

As both solutions have the same concentration we can write:

1L = [Formate] + [Formic acid] (2)

5.6234 = 1 - [Formic acid] / [Formic acid]

5.6234[Formic acid] = 1 - [Formic acid]

6.6234[Formic acid] = 1

[Formic acid] = 151mL of the 0.2M