What is buffer capacity?

Buffer capacity is expressed by beta and measures the ability of a solution to resist changes in pH. It indicates how many moles per liter of strong acid or base are required to change the pH by one unit. A high capacity means that the pH will be barely affected when adding acid or base. A low capacity leads to a significant change in pH.

How to calculate buffer capacity?

There are two methods. If you have measured values, divide the amount of strong acid or base added per liter by the resulting pH change: β = n / dpH. If you know the composition of the buffer, use the Van Slyke equation. Multiply the total concentration of the buffer by 2.303, then multiply that by the product of Ka and the hydrogen ion concentration, and divide it by the square of (Ka plus the hydrogen ion concentration). Both methods are implemented in this tool, as well as a third method to calculate buffer capacity directly from concentrations of two components.

At what pH is buffer capacity highest?

It is highest at the pKa of the weak acid, when equal amounts of acid and conjugate base are present; there the Van Slyke ratio equals one fourth so that the maximum capacity is β = 2.303 x C/4, which is about 0.576 times the total concentration. When a pH unit away from the pKa, the capacity has fallen to about one third.

What is the unit of buffer capacity?

It is expressed in moles per liter and pH unit, or mol/L per pH or mol L−1 pH−1. If the capacity is β = 0.058, this means that each liter of solution can absorb 0.058 mole of strong acid or base for a change in pH by one unit. Some textbooks refer to β as dimensionless to balance out the concentration factor, but the numerical values are equal.

How can you increase buffer capacity?

Either the total concentration can be increased or the pH used brought closer to the pKa. Since the concentration is linear, doubling the buffer solution doubles its capacity. Near the limits of the effective range, the effect of adjusting the pH is much greater. Thus it is usually better to choose a buffer system whose pKa matches the desired pH than simply to dilute an inappropriate system more strongly.

Can this tool process phosphate or other polybasic buffers?

This tool can only handle one acid/base combination at a time. Since phosphates have three pKa's and carbonates two, each stage of ionization in an actual polybasic buffer will contribute a Van Slyke term. One performs the procedure for the stage corresponding to the pH used, then repeats it for other stages that are approximately within a pH unit, adding up the capacities of the individual terms.

Buffer Capacity Calculator

Set up your buffer

How do you want to work out the capacity?

Pick how you want to reach the buffer capacity: from the buffer's composition, from a measured pH change, or from the concentrations of the weak acid and its conjugate base.

Buffer composition (pKa, total concentration, pH)

Measured pH change after adding acid or base

From the two components: [HA] and [A-]

Buffer system

Common laboratory buffer systems with their pKa at 25 C. Pick Custom to type your own pKa.

Total buffer concentration (C)

Working pH

Include the water term (beta_water)

Water itself buffers a little. The term matters below about pH 3 and above about pH 11, and is negligible near neutral.

Buffer capacity, beta (mol/L per pH)

Plan a dose: how much acid or base can I add?

Turn a capacity into a working answer: how many millimoles of strong acid or base your batch will absorb for a pH drift you can live with.

Buffer capacity, beta

Share of this buffer's peak capacity: %

Peak capacity, reached at pH = pKa

Ratio [A-] / [HA]

Conjugate base [A-] in the mix: M

Weak acid [HA] in the mix: M

One litre of this buffer soaks up about 0.0576 mol of strong acid or base for every pH unit it moves. That is 100 of the most this concentration could ever manage, which it would hit at pH 4.76.

Capacity falls away fast on either side of the pKa. Outside roughly pH 3.76 to 5.76 you are better off choosing a different buffer system than adding more of this one.

pKa in use

Useful range starts at pH

Useful range ends at pH

How buffer capacity behaves

How the buffer splits between acid and base

A buffer works best when the two halves are close to equal. Push the split past about 10:1 either way and one partner runs out long before the other, which is what puts the edges on the useful range.

What the number means: buffer capacity carries units of mol per litre per pH unit. A capacity of 0.058 means a litre of that buffer swallows 0.058 mol of strong acid before the pH slips by one full unit.

Some textbooks call beta unitless because they define it against a concentration that has already been divided through. The number is the same; only the bookkeeping differs.

Two ways to get more capacity: capacity scales straight with concentration, so doubling the buffer doubles beta at any pH.

Moving the pH is a different story. Capacity depends on pH through a curve, not a line, so shifting a pH unit away from the pKa costs far more than a small change in concentration ever gains.

Where this model stops: it covers one monoprotic acid-base pair at 25 C, with Kw = 1.0e-14 and no correction for ionic strength or temperature.

Phosphate, citrate and carbonate have more than one pKa, so their real capacity is the sum of a term per ionisation step. Run each step separately and add the results. Tris in particular shifts its pKa by roughly 0.03 per degree, so a buffer mixed on the bench and used in a cold room will not be at the pH you set.

Buffer capacity answers the practical question of how much strong acid or base a solution can absorb without its pH changing significantly. It is denoted by the symbol β and has units of amount of substance per litre per unit pH.

There are three ways to achieve the same value and this tool performs all three methods. You can predict buffer capacity from volumes when mixing, measure it from two pH measurements or read it directly from concentrations of two components.

Let's start with a definition.

You add a known amount of strong acid or base to a certain volume of buffer and observe how much the pH changes before dividing.

\beta = \frac{n}{\Delta \mathrm{pH}}

where n is the amount of strong base added per liter of buffer solution and the change in pH is the difference between the final pH and initial pH. If 0.010 moles of sodium hydroxide are added to each liter of buffer solution and the pH increases by 0.30, then this concentration is 0.010/0.30 = 0.033 moles per liter per pH unit.

This is also true for acids but the signs are reversed. Adding 0.010 mol of hydrochloric acid corresponds to n = -0.010 and the pH goes down by 0.30. The two minuses cancel out, so the result is again 0.033. This is why definitions are always given relative to a strong base. You can change the pH in both directions while keeping the capacity positive.

This method is honest and reliable but it's retrospective. It describes the pH range that will be reached in an actual titration and to get a result you must first perform an experiment.

Van Slyke Equation - Calculating capacity before mixing

When this change in pH is set to zero, the ratio becomes a derivative. For a single weak acid and its conjugate base there is a closed form for the derivative. Chemists call it the van Slyke buffer value.

\beta = 2.303 \times C \times \frac{K_a\,[\mathrm{H}^+]}{\left(K_a + [\mathrm{H}^+]\right)^2}

C is the total concentration of buffer, so it's the sum of concentrations of acidic and basic form. Ka is the acid dissociation constant, so -pKa of 10. Hydrogen ion concentration is -pH of 10. 2.303 is natural logarithm of 10. pH is a log base 10, that's why this value appears.

Water itself also has some buffering capacity and this is important at the extremes of the scale.

\beta_{\mathrm{water}} = 2.303 \times \left([\mathrm{H}^+] + [\mathrm{OH}^-]\right) \qquad \beta_{\mathrm{total}} = \beta_{\mathrm{buffer}} + \beta_{\mathrm{water}}

At pH below about 3 or above about 11 it is worth considering the contribution of water. In regions close to neutral this contribution is so small that it is barely perceptible which is why this option is disabled by default in this tool.

A simple calculation method when two components are known:

When the Henderson–Hasselbalch equation is substituted into the Van Slyke equation, both pKa and pH are completely eliminated.

\beta = 2.303 \times \frac{[\mathrm{HA}]\,[\mathrm{A}^-]}{[\mathrm{HA}] + [\mathrm{A}^-]}

If you already know how much of a weak acid and its conjugate base are in the flask, that's enough. The pKa helps to pick this combination of components and calculate what pH the mixture will eventually reach, but the capacity itself is only determined by the two concentrations.

Example: Acetic acid buffer solution

The total concentration of acetic acid and sodium acetate is 0.100 mol/L, and the pH is 4.76. This value corresponds exactly to the pKa of the acetate ion. Ka equals 10 to the power of minus 4.76, which gives approximately 1.74e-5. The concentration of hydrogen ions also has this value.

\beta = 2.303 \times 0.100 \times \frac{(1.74\times10^{-5})^2}{(3.48\times10^{-5})^2} = 2.303 \times 0.100 \times 0.25 = 0.0576

At a pKa of half that factor goes down to one quarter so the capacity is 2.303 times C divided by 4 which is the upper limit for any buffer at this concentration and no matter how you adjust the ratio you can't exceed that value.

Let's look at the components in their form. When pH is equal to pKa, buffer species are evenly distributed so both concentrations will be 0.0500 mol/L each. If you multiply 0.0500 by 2.303 and then multiply that by 0.0500 and divide it by 0.100, we get back to 0.0576.

How capacity rapidly decreases as you move away from the pKa.

The pH term in the Van Slyke equation produces a bell curve on a logarithmic scale. It reaches its maximum at the pKa value and then falls symmetrically. This fall is faster than most people expect.

pH minus pKa	[A-] / [HA] ratio	Share of peak capacity	Capacity at C = 0.100 mol/L
0.0	1 : 1	100%	0.0576
0.5	3.16 : 1	73%	0.0420
1.0	10 : 1	33%	0.0190
1.5	31.6 : 1	12%	0.0068
2.0	100 : 1	3.9%	0.0023
3.0	1000 : 1	0.4%	0.00023

When one is only one pH unit away from the pKa, capacity loss has already reached two-thirds of its original value. This forms the basis for a common rule of thumb. Buffers are most effective within about a pH unit on either side of their pKa. When this range is exceeded, it is not worth trying to buffer further; instead, another buffering system should be chosen.

Selection of buffer system according to target pH.

Select the system with a pKa value closest to your desired pH and set the concentration according to the capacity required. The default values for this tool use the pKa at 25 degrees.

Buffer system	pKa at 25 C	Useful pH window
Formate	3.75	2.75 to 4.75
Acetate	4.76	3.76 to 5.76
MES	6.21	5.21 to 7.21
Phosphate, second step	7.20	6.20 to 8.20
MOPS	7.31	6.31 to 8.31
HEPES	7.66	6.66 to 8.66
Tris	8.06	7.06 to 9.06
CHES	9.41	8.41 to 10.41
CAPS	10.51	9.51 to 11.51

Concentration is also a means of adjustment and is linear. At any given pH, the capacity doubles when the buffer concentration is doubled. Laboratory buffers are typically in the range 10 to 100 millimoles per liter, which is sufficient to hold the pH without unduly affecting ionic strength or biological systems.

Conversion of capacity to required quantity:

When you take the volume and the allowable change into account, this value becomes concrete. We re-order the definition and multiply it by the volume.

n = \beta \times \Delta \mathrm{pH} \times V

Let's take the above acetic acid buffer solution of 100 mL with a capacity of 0.0576 and an allowable deviation of 0.10 pH units. The amount of strong acid or base that can be absorbed is the result of multiplying 0.0576 by 0.10, which in turn is multiplied by 0.100 liters to get 5.8e-4 moles, or 0.58 millimoles. If you open up the amount planner, this tool will do the calculation for you.

Consider this as a first approximation. This formula assumes that the capacity remains constant over the entire range. For small changes this assumption is acceptable but for larger changes it becomes increasingly unrealistic since the buffer will gradually deviate from its pKa as consumption proceeds.

Aspects that are not considered in this model:

All content here is for monoprotic acid-base systems at 25 degrees with the water ion product fixed to 1.0e-14 and no correction for ionic strength.

For polybasic acids, a Van Slyke term must be calculated for each ionization stage and then added together. Phosphates have three such terms, citrates have three, and carbonates have two. Enter each relevant stage individually into this tool and sum the values of the individual terms.

Temperature and salt affect the pKa value. The pH of Tris changes by about 0.03 units for every temperature change, so the pH of a Tris buffer solution used in lab titrations may not be what was set. Ionic strength also affects the pKa value, so instead of textbook constants, Debye-Hückel corrections are given in strict procedures.

This tool is for educational and planning purposes only. If the pH value is extremely important, measure your prepared buffer solution with calibrated instruments at the actual temperature of use.

Frequently asked questions

What is buffer capacity?: Buffer capacity is expressed by beta and measures the ability of a solution to resist changes in pH. It indicates how many moles per liter of strong acid or base are required to change the pH by one unit. A high capacity means that the pH will be barely affected when adding acid or base. A low capacity leads to a significant change in pH.
How to calculate buffer capacity?: There are two methods. If you have measured values, divide the amount of strong acid or base added per liter by the resulting pH change: β = n / dpH. If you know the composition of the buffer, use the Van Slyke equation. Multiply the total concentration of the buffer by 2.303, then multiply that by the product of Ka and the hydrogen ion concentration, and divide it by the square of (Ka plus the hydrogen ion concentration). Both methods are implemented in this tool, as well as a third method to calculate buffer capacity directly from concentrations of two components.
At what pH is buffer capacity highest?: It is highest at the pKa of the weak acid, when equal amounts of acid and conjugate base are present; there the Van Slyke ratio equals one fourth so that the maximum capacity is β = 2.303 x C/4, which is about 0.576 times the total concentration. When a pH unit away from the pKa, the capacity has fallen to about one third.
What is the unit of buffer capacity?: It is expressed in moles per liter and pH unit, or mol/L per pH or mol L−1 pH−1. If the capacity is β = 0.058, this means that each liter of solution can absorb 0.058 mole of strong acid or base for a change in pH by one unit. Some textbooks refer to β as dimensionless to balance out the concentration factor, but the numerical values are equal.
How can you increase buffer capacity?: Either the total concentration can be increased or the pH used brought closer to the pKa. Since the concentration is linear, doubling the buffer solution doubles its capacity. Near the limits of the effective range, the effect of adjusting the pH is much greater. Thus it is usually better to choose a buffer system whose pKa matches the desired pH than simply to dilute an inappropriate system more strongly.
Can this tool process phosphate or other polybasic buffers?: This tool can only handle one acid/base combination at a time. Since phosphates have three pKa's and carbonates two, each stage of ionization in an actual polybasic buffer will contribute a Van Slyke term. One performs the procedure for the stage corresponding to the pH used, then repeats it for other stages that are approximately within a pH unit, adding up the capacities of the individual terms.

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

Buffer solution - Wikipedia
Encyclopedic treatment of buffer solutions, including buffer capacity and the derivation of the Van Slyke buffer value.
Henderson-Hasselbalch equation - Wikipedia
The relationship between pH, pKa and the ratio of conjugate base to weak acid that sets a buffer's composition.
Henderson, L. J. (1908). Concerning the relationship between the strength of acids and their capacity to preserve neutrality
The original paper linking acid strength to the ability of a solution to hold its pH.
Acid dissociation constant - Wikipedia
Definition of Ka and pKa, the constants that fix where a buffer's capacity peaks.