You have 100 mL of 1 M ammonia solution (pK_a=9.25). What volume of 1 M hydrochloric acid is needed to prepare buffer with pH=9.5?

Adding hydrochloric acid to the solution of ammonia (base) we create a conjugate acid NH₄⁺. Ratio of their concentrations at pH 9.5 will be given by the Henderson-Hasselbalch equation.

If all added acid reacts with ammonia, amounts of conjugate acid NH₄⁺ created and base NH₃ left is defined by the stoichiometry of the neutralization reaction:

and

qbq2.3 is equivalent to

where n_a and n_b are number of moles of acid and conjugate base, n_NH3start is number of moles of ammonia at the beginning (0.1 mole - n=CV) and n_HCl is number of moles of acid added. We are using number of moles as it makes calculation much easier - this way we don't have to calculate how the concentrations change due to the dilution once the acid is added to original ammonia solution. We can do that thanks to the fact that in the Henderson-Hasselbalch equation volumes can be canceled out and replaced by mole ratio.

Putting pH=9.5 into the Henderson-Hasselbalch equation we get

Finally we have a set of equations qbq2.4 and qbq2.5. When solved they give n_a=0.036 and n_b=0.064. From qbq2.2 we get that we have to add 0.036 mole of HCl, or 36 mL of 1 M solution.

We can use pH calculator to check the result. Create a solution containing both ammonia and hydrochloric acid. Enter 1 as both concentrations. From the drop down list above pH sign select Ca+Cb+Va+Vb. Enter 36 as acid volume and 100 as base volume. Perfect!

Note: if you need program that will help in buffer calculation, our pH calculator is not suited for the task, however, you can try our Buffer Maker - the buffer calculator. Buffer calculator was specifically designed to help in buffer preparation, so - given pH - it will automatically calculate recipe of any buffer you may need.