Buffer Capacity Calculator
This calculator works out the buffer capacity (beta) of a weak acid and conjugate base buffer using the Van Slyke equation, the standard measure of how many moles of strong acid or base a buffer can absorb per litre before its pH shifts by one unit. It matters because buffers only work well within a range around their pKa, and this figure tells you how much punishment a given recipe can take before it stops resisting pH change. You enter the pKa, either directly or by picking a common buffer system such as acetic acid/acetate, phosphate or Tris, the total buffer concentration in mol/L, and the solution pH, set directly or from a conjugate base to acid ratio. Results show the buffer capacity in mol/L per pH unit, the solution pH, its distance from the pKa, and the maximum capacity at pH equal to pKa. A breakdown below shows the Henderson-Hasselbalch ratio, the acid and base concentrations, the percentage split between them, and whether your pH sits inside the effective buffering range of pKa plus or minus one unit. Use it to check whether a recipe is strong enough for planned additions of acid or base, or how fast capacity falls as pH drifts from pKa. These figures assume a simple monoprotic buffer at standard conditions and are indicative for teaching and planning, so verify performance experimentally for critical work.
1. Buffer Parameters
2. Solution pH
Calculation Breakdown
Henderson-Hasselbalch
How Buffer Capacity Is Calculated
Buffer capacity (beta, also written as beta) quantifies how effectively a buffer resists pH changes. It was first defined by Van Slyke (1922) as the ratio of the small amount of strong base (or acid) added to the resulting pH change:
For a simple weak acid (HA) / conjugate base (A-) buffer, the Van Slyke equation gives:
Where C is the total molar concentration of the buffer (C = [HA] + [A-]), Ka is the acid dissociation constant (Ka = 10^(-pKa)), and [H+] is the hydrogen ion concentration (= 10^(-pH)).
Henderson-Hasselbalch Equation
The Henderson-Hasselbalch equation relates solution pH, pKa, and the ratio of conjugate base to weak acid:
Rearranged: [A-] / [HA] = 10^(pH - pKa). The individual concentrations are:
- [A-] = C x 10^(pH - pKa) / (1 + 10^(pH - pKa))
- [HA] = C / (1 + 10^(pH - pKa))
Maximum Buffer Capacity
Buffer capacity is greatest when pH = pKa, meaning [A-] = [HA] (equal concentrations of acid and conjugate base). At this point the Van Slyke equation simplifies to:
For example, a 0.1 mol/L acetate buffer at pH 4.76 (its pKa) has a maximum beta of approximately 0.0576 mol/L per pH unit. Moving the pH one unit away from the pKa reduces beta to about 23% of its maximum value.
Effective Buffer Range
A buffer is considered effective within the range of pKa plus or minus 1 pH unit. Within this range, both acid and base components are present in concentrations above about 9% of the total, providing meaningful resistance to pH change in both directions. Common laboratory buffers are chosen so that the desired working pH falls within this range.
Worked Example (Default Values)
Using a 0.1 mol/L acetic acid / acetate buffer at pH 4.76 (the pKa of acetic acid):
- pKa = 4.76, so Ka = 10^(-4.76) = 1.738 x 10^(-5) mol/L
- [H+] = 10^(-4.76) = 1.738 x 10^(-5) mol/L
- Because pH = pKa, Ka = [H+], so Ka x [H+] = (1.738 x 10^(-5))^2 = 3.021 x 10^(-10)
- (Ka + [H+])^2 = (2 x 1.738 x 10^(-5))^2 = (3.476 x 10^(-5))^2 = 1.208 x 10^(-9)
- beta = 2.303 x 0.1 x 3.021 x 10^(-10) / 1.208 x 10^(-9) = 0.2303 x 0.25 = 0.0576 mol/L/pH unit
This matches the simplified maximum formula: 2.303 x 0.1 / 4 = 0.0576. This is the highest possible buffer capacity for a 0.1 mol/L acetate buffer, achieved at pH = pKa = 4.76.
Common Buffer Systems
| Buffer System | pKa | Useful pH Range | Common Use |
|---|---|---|---|
| Acetic acid / Acetate | 4.76 | 3.8 to 5.8 | Food chemistry, electrochemistry |
| Citric acid / Citrate (pKa2) | 4.76 | 3.0 to 6.2 | Food, pharmaceuticals |
| MES | 6.15 | 5.5 to 6.7 | Biochemistry |
| Phosphate (H2PO4- / HPO4-2) | 7.21 | 6.2 to 8.2 | Biochemistry, cell culture |
| HEPES | 7.55 | 6.8 to 8.2 | Cell biology, molecular biology |
| Tris | 8.06 | 7.0 to 9.0 | Molecular biology, electrophoresis |
| Ammonium / Ammonia | 9.25 | 8.3 to 10.3 | Analytical chemistry |
| Carbonate (HCO3- / CO3-2) | 10.33 | 9.3 to 11.3 | Biochemistry, photography |
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Sources and method: Van Slyke DD (1922) "On the measurement of buffer values and on the relationship of buffer value to the dissociation constant of the buffer and the concentration and reaction of the buffer solution." Journal of Biological Chemistry 52:525-570. Henderson-Hasselbalch equation as used in analytical and biochemistry curricula. Standard thermodynamic values at 25 degrees Celsius.
This calculator uses the Van Slyke equation for a simple monoprotic weak acid buffer. Polyprotic acids, mixed buffers, and ionic strength effects are not included. Results are approximate and suitable for teaching and preliminary experimental planning. Always verify buffer performance experimentally for critical applications.