"Calculate the minimum concentrations of formic acid and sodium formate that are needed to prepare 500.0 mL of a pH 3.80 buffer whose pH will not change by more than 0.10 unit if 1.00 mL of 0.100 M strong acid or strong base is added."
Ka of formic acid = 1.8E-4
pKa of formic acid = 3.74
Henderson-Hasselbalch equation: pH = pKa + log([base]/[acid])
The Attempt at a Solution
So...the initial concentration of H3O+ in the pH 3.80 solution would be 10^-3.80 = 1.58E-4 M. In a 500 mL solution, it is: 500 mL x 1.58E-4 mol / mL = 0.079 mmol H3O+. The thing is, I'm not sure how to apply this.
Alternatively, knowing the pH and pKa of the acid, I can use the Henderson-Hasselbalch equation: 3.80 = 3.74 + log([base]/[acid]). The resulting ratio is 0.871. I am unsure how I would be able to use this to calculate the concentrations of acid and salt (base). If we are adding .100 M strong acid (or base), the resulting pH would be 3.70 (or 3.90), correct? Using 3.70 as the pH in the H-H equation, the resulting ratio is 0.912.
I'm just really lost. Thanks for any help!