[joyb]

The question being:
"The pKa of methanoic acid is 3.8. Methanoic acid/methanoate is going to be used as a buffer for a reaction. The unbuffered reaction at pH 4.5 results in a decrease in the pH of 2.5 units. What is the minimum concentration of the buffer needed to prevent the pH falling below 4.25?"

All I have calculated is that without buffer present, [H⁺] will increase by 9.97x10^-3M whereas in the presence of buffer [H⁺] will only increase by 2.46x10^-5M, so the buffer must accept 9.95x10^-3M protons. However I'm not sure how to use this to find the concentration of buffer, as every time a proton is accepted the position of equilibrium will shift.

[Borek]

Assume all H⁺ is consumed be the methanoate protonation, it will be a simple plug into the Henderson-Hasselbalch equation.

[joyb]

So is the minimum concentration of buffer 9.95x10^-3M? Or am I oversimplifying it now?

[Borek]

You are oversimplifying. You want the buffer pH to change (after methanoate being protonated) by no more than 0.25 pH unit. Express the initial buffer pH using C_HA and C_A^- (these will be your unknowns). Protonation means both concentrations change - and knowing how much H⁺ was produced, you can calculate new concentrations of HA an A^- after protonation (express them using your unknowns and amount of H⁺ - to simplify calculations you can assume 1L of solution). You know buffer with these new concentrations must have pH of 4.25 - that gives you another equation. Two equations in two unknowns, just solve.