Chemistry
How Buffer Capacity Varies with pH and Concentration
Quick fact
A buffer has maximum capacity when its pH equals its pKa, and the capacity decreases by 50% for every unit of pH away from the pKa. Also, doubling the total concentration of the buffer components doubles the buffer capacity.
Why this is interesting
Why does a tiny amount of acid completely change the pH of water, but barely affect a buffer? And why does the same buffer suddenly lose its power after a certain point?
Read the full explanation
Understanding How Buffer Capacity Varies with pH and Concentration
A buffer works by having a weak acid and its conjugate base in solution. When you add strong acid (H+), the conjugate base neutralizes it; when you add strong base (OH-), the weak acid neutralizes it. The buffer capacity is how much acid or base you can add before the pH changes significantly. Think of it like a sponge: a small sponge soaks up a little water, a large sponge soaks up more. Similarly, a buffer with more 'absorbing particles' (higher concentration of acid and conjugate base) can handle more added H+ or OH-. But the sponge also works best when it is partially saturated—if it's already full of water (all conjugate base) or bone dry (all acid), it can't absorb well. In buffer terms, this means the ratio of [base]/[acid] should be close to 1, which is when pH ≈ pKa. As you move away from that pH, the buffer becomes less effective, and eventually the pH changes drastically.
A deeper explanation
Buffer capacity (β) is defined as the moles of strong acid or base needed to change the pH by 1 unit. Mathematically, it depends on two factors: the total concentration of buffer species (C = [acid] + [base]) and the fraction of each species present. The formula is β = 2.303 C [H+] Ka / ([H+] + Ka)^2. When [H+] = Ka (pH = pKa), the denominator is (2Ka)^2, and the fraction [H+]Ka/([H+]+Ka)^2 equals 1/4, giving βmax = 2.303 C / 4. So capacity is directly proportional to total concentration: double the concentration, double the capacity. As pH moves away from pKa, the fraction drops. For example, at pH = pKa + 1, the fraction becomes about 0.09, roughly 36% of the maximum. At pH = pKa + 2, it's about 0.0099, only about 4% of maximum. This is why buffers are most effective within ±1 pH unit of their pKa. The mechanism is that when the ratio of base to acid is near 1, both components are plentiful enough to neutralize added acid or base. But if you are far from pKa, one component is very scarce, so adding even a small amount of strong acid (if base is scarce) or strong base (if acid is scarce) will consume the limited species and cause a large pH shift.