Buffer pH Calculator

Buffer solutions are like shock absorbers in chemistry. When small amounts of strong acids or bases are added to pure water, the pH will jump up or down by several units. However, if you add the same amount to a buffer solution, the pH will only change slightly.

This calculator uses this relationship both ways. If you provide the contents of a container, it will give information about pH, acid to base ratio, working range and buffer capacity. If you specify a desired pH, it will show a recipe that gives the concentration of each component as well as how much of each to weigh out based on the volume specified.

Henderson-Hasselbalch equation

A buffer solution contains both a weak acid and its conjugate base in the same solution. As the weak acid is constantly giving off protons and the conjugate base is constantly taking up protons, the pH stabilizes at the point where these two processes are in equilibrium.

If you rearrange the dissociation equation of an acid and take the logarithm, you get a formula that is always used in buffer calculations.

The pKa is a property of the acid itself. What you can control is only the logarithm and that's not an absolute value but depends completely on the ratio of both components.

From this we can deduce some results that are worth noting. If both concentrations are halved the ratio does not change so the pH will remain the same but the capacity is halved. A diluted buffer solution may give correct readings on a meter, but it will fail immediately once stressed.

If the components are identical:

When both concentrations are equal, the ratio is 1. Since the log of 1 is zero, the whole term disappears and the pH equals exactly pKa.

This is the optimal point. Half of the buffer will be used to neutralize added acid while the other half can be used to neutralize added base, resulting in a symmetrical and maximum buffering capacity. When selecting a buffer system one should always start here and select a system whose pKa is closest to the desired pH.

Basic buffers work through the pOH:

There are also buffers that consist of a weak base and its conjugate acid. Ammonia and ammonium chloride is a typical example. The principle is the same but it is usually expressed in terms of the pOH scale.

These formulas are just different representations of the same equation. For conjugate acid-base pairs, pKa and pKb always add up to a constant (14 at 25 °C). So this calculator will convert the entered pKb value into the pKa value for the conjugate acid and display that value. This allows basic and acidic buffer solutions to be compared on the same scale.

How to use this calculator:

Begin with the calculation method dropdown field at the top. The first three options are for retrieving the pH of an existing buffer solution while the other two options are used to design a buffer solution.

The buffer system drop-down menu contains a variety of common buffers for laboratory use at 25 °C so that in most cases no manual input is required. If the desired system is not listed or you wish to enter the original Ka or Kb value instead of the pKa, select Custom.

Determination of buffer capacity:

Buffer capacity is a measure of how much a buffer solution can withstand being stressed. It answers the direct question: How much strong base does it take to change the pH of this solution by one unit?

The value can be directly calculated using the van Slyke equation. The calculator displays the amount of strong base in millimoles per litre or per unit pH.

At the pKa, the average will be maximized and the capacity is about 0.576 times the total concentration of buffer. Thus a buffer with 100 mM at its pKa can take up about 58 mmol strong base per liter before the pH changes fully by one unit.

If the pH deviates by one unit from the pKa, this value falls to about a third of its peak. If it deviates by two units, it falls to about one twentieth. This is the real reason for the rule of thumb that you should move in the range of plus/minus one unit around the pKa-value and outside this range the calculator gives a warning.

Choice of buffer system

First the pKa value is adjusted to match the desired pH, then other factors are taken into account. The systems listed in the drop-down menu were selected this way and all apply for 25°C.

Chemical properties not directly related to pKa are also important. Phosphates can precipitate divalent metals and inhibit some enzymes. Tris varies strongly with temperature and reacts with aldehydes. Borates form complexes with sugars.

The "good" buffers that are in the middle of the list between MES and CAPS were developed in the 1960s to avoid such side effects when working with biology.

How the ratio changes the pH level:

Because this relationship is logarithmic, the pH will change only slightly even if the composition changes dramatically. This is a key property of buffers.

If you read the few lines in the middle, it becomes clear that the rule "pKa plus or minus one unit" appears to be natural. At the edge of this range, one of the components is already reduced to about nine percent of the total amount and quickly runs out under stress.

Example of a formulation:

You need to prepare 500 mL of a 100 mM phosphate buffer solution with pH 7.40, using sodium dihydrogen phosphate as the acid form and disodium hydrogen phosphate as the base form.

The relevant constants are for the second dissociation stage of phosphoric acid with a pKa2 value of 7.20. The required ratios can be directly derived from the formula.

If the total concentration is 100 mM, then according to this ratio, the concentration of the basic form will be 61.3 mM and that of the acidic form will be 38.7 mM. Multiply each of these concentrations by 0.5 L and then by the corresponding molar mass to obtain the masses to weigh in the lab. Sodium dihydrogen phosphate weighs about 2.32 g (119.98 g/mol) while disodium hydrogen phosphate weighs about 4.35 g (141.96 g/mol).

Dissolve both substances in about 400mL of water and check the pH with a calibrated meter. If necessary, make small adjustments using acid or base then top up to the 500mL mark. It is important that you adjust the pH before final dilution, not after.

Summary of inputs:

The results are based on the assumption of a dilute aqueous solution at 25 °C with an activity coefficient of 1 and neglect small changes in pKa due to ionic strength. The actual buffer substances may also change depending on temperature. Consider the output as a starting point for formulation, and verify the final pH using a calibrated meter.