A buffer can absorb only so much. From buffer additions you saw that once one partner is used up, the pH changes fast. Two choices decide how well a buffer works: which acid, and how much of it.
Key idea
Choose a weak acid whose $\text{p}K_a$ is within about 1 unit of the pH you want (ideally close to it). Its capacity, the amount of acid or base it can absorb before the pH shifts a lot, grows with the amounts of HA and $\mathrm{A^-}$ present, and is largest when they are equal.
Why it works
A buffer works only while both partners are present in useful amounts. At pH = pKa they are equal, so it can absorb acid and base equally well. At $\text{p}K_a \pm 1$, one partner is ten times the other, so the buffer is lopsided. And the pH depends only on the ratio, but how much it can absorb depends on the moles: a 0.01 M buffer and a 1 M buffer can have the same pH, yet the first is used up by 1/100 as much acid.
Worked examples
Worked example: Choosing a pair
You need a buffer at pH 9.0. Which pair is best: acetic acid/acetate ($\text{p}K_a$ 4.74), $\mathrm{H_2PO_4^-/HPO_4^{2-}}$ (7.21) or $\mathrm{NH_4^+/NH_3}$ (9.25)?
- Pick the $\text{p}K_a$ closest to 9.0: 9.25.
- Ratio needed: $10^{9.0 - 9.25} = 0.56$, comfortably between 0.1 and 10.
Answer: $\mathrm{NH_4^+/NH_3}$.
Worked example: Same pH, different capacity
Two acetate buffers both have pH 4.74: buffer A is $0.010\ \text{M}$ in each partner, buffer B is $0.50\ \text{M}$ in each. To a liter of each, add $0.0050\ \text{mol}$ HCl.
- A: acetate $0.010 - 0.005 = 0.005$, acid $0.015\ \text{mol}$; $$\text{pH} = 4.74 + \log\dfrac{0.005}{0.015} = 4.74 - 0.48 = 4.26$$
- B: acetate $0.495$, acid $0.505\ \text{mol}$; $\text{pH} = 4.74 + \log\dfrac{0.495}{0.505} = 4.73$.
Answer: A drops by about half a unit; B barely moves.
Capacity is not unlimited even at its best. A buffer with 0.10 mol of each partner can absorb a little less than 0.10 mol of strong acid before its base is gone, and before that point the pH has already moved a full unit (when the ratio reaches 1 : 10).
- Pick $\text{p}K_a$ near the target pH.
- Use enough acid and base for the amounts you expect to add.
- Keep the ratio between about 0.1 and 10.
Common mistake
Thinking a buffer's capacity depends only on its pH. Two buffers at the same pH can differ a hundredfold in how much acid they absorb. Check: compare the moles of each partner with the moles of acid or base you plan to add.