How this instrument works
A buffer resists changes in pH by having both a weak acid and its conjugate base on hand to soak up whatever acid or base gets added. Buffer capacity, symbol β, quantifies exactly how much resistance is available: it's defined as the moles of strong acid or base per liter needed to shift the pH by one unit. A buffer with high β barely budges when you dose it with acid; one with low β swings wildly from the same dose.
The Van Slyke equation, published by biochemist Donald D. Van Slyke in 1922, gives buffer capacity as a closed-form function of total buffer concentration C, the acid dissociation constant Ka, and the current pH: β = 2.303 × C × (Ka[H+]) ⁄ (Ka + [H+])². Every quantity you'd expect to matter shows up: more total buffer (bigger C) means more capacity everywhere, and the shape of the Ka-dependent term means capacity isn't flat across all pH values — it has a distinct peak.
That peak sits exactly at pH = pKa. At that point the buffer holds equal concentrations of weak acid and conjugate base, which is precisely the condition where it has the most 'headroom' in both directions — room to neutralize added acid by converting base to acid, and room to neutralize added base by converting acid to base. Move the pH more than about one unit away from pKa in either direction and capacity falls off fast, which is the practical reason buffers are chosen so their pKa sits close to the pH you actually need to hold.
- Enter the total buffer concentration, C, in mol/L — the combined concentration of the weak acid and its conjugate base.
- Enter the acid dissociation constant, Ka, for the weak acid in the buffer.
- Enter the solution's pH.
- Read the buffer capacity, β, in mol per liter per pH unit — the moles of strong acid or base per liter needed to shift the pH by one unit at that point.
Worked example — an acetic acid buffer at its own pKa
A 0.1 mol/L acetic acid/acetate buffer has Ka = 1.78 × 10⁻⁵, which corresponds to a pKa of 4.75. Running the Van Slyke equation at pH 4.75 — right at the buffer's own pKa — gives β ≈ 0.0576 mol/(L·pH unit), the maximum buffer capacity this particular buffer can achieve at any pH. That's the textbook result: capacity peaks exactly where pH equals pKa.
Move the same buffer to pH 6, more than a full pH unit away from its pKa of 4.75, and capacity drops to about 0.0116 mol/(L·pH unit) — roughly a fifth of its peak value, even though the total concentration C hasn't changed at all. This is the practical lesson buffer capacity teaches: picking a buffer isn't just about picking any weak acid, it's about picking one whose pKa sits close to the pH you actually need to protect.
Questions
What is buffer capacity?
Buffer capacity (β) measures how much strong acid or base a buffer solution can absorb before its pH shifts by a meaningful amount — formally, the moles of strong acid or base per liter of buffer needed to change the pH by exactly one unit. A high buffer capacity means the solution is very resistant to pH change; a low one means even a small addition of acid or base swings the pH noticeably.
Why does buffer capacity peak when pH equals pKa?
At pH = pKa, the Henderson-Hasselbalch equation says the weak acid and its conjugate base are present in exactly equal concentrations. That balance gives the buffer maximum flexibility in both directions: plenty of conjugate base available to neutralize added acid, and plenty of weak acid available to neutralize added base. Move away from that 1:1 ratio in either direction and one of those two reserves starts running low, which is exactly what the Van Slyke equation's peaked, symmetric shape around pH = pKa captures mathematically.
How do I choose a buffer for a target pH?
Pick a weak acid whose pKa sits as close as possible to the pH you need to maintain — ideally within about one pH unit. Because buffer capacity falls off sharply more than a unit away from pKa, a mismatched buffer (say, a pKa of 4.75 asked to hold pH 7) will offer only weak resistance and drift more easily than a well-matched one. Reference tables of common buffer systems (acetate, phosphate, tris, carbonate, and others) are organized by their pKa values for exactly this reason.
Does increasing the total buffer concentration always increase capacity?
Yes, at a fixed pH — buffer capacity scales linearly with total concentration C in the Van Slyke equation, so doubling the concentration of both the weak acid and its conjugate base doubles the buffer capacity at every pH. This is why concentrated buffers resist pH swings so much better than dilute ones, even when the ratio of acid to base (and therefore the pH itself) is identical.
Is buffer capacity the same thing as pH?
No — they're related but distinct. pH tells you how acidic or basic a solution currently is; buffer capacity tells you how strongly that pH resists being pushed around by an added acid or base. Two solutions can share the exact same pH while having very different buffer capacities, depending on their total buffer concentration and how close that pH sits to the buffer's pKa.