# How to find the pH value from the molarity

If you can work with logarithms, the pH value calculation is much easier: The pH value is defined as the negative decadic logarithm of the proton concentration:

pH = - log [H.+]

And of course the following also applies:

pOH = - log [OH-]

As simple as that? No! Your math teacher will rightly say: A logarithm can only be calculated from dimensionless numbers. And the concentration has the dimension mol / l.
The symbol [H+] it is Not about the concentration of protons, but about theirs Activitya. This means corrected, dimensionlesse concentration values.

a = f · c

a is the activity of a substance c his concentration. f is the correction factor. It applies

0< f < 1

The following example shows how this is noticeable in pH value measurements. If you take one of the weighed-in one-molar solution of hydrochloric acid, you do not measure the calculated pH value 0 with the correctly calibrated glass electrode, which is sensitive for protons, but only about 0.1. The solution seems to contain fewer protons than the weighed-in hydrochloric acid, even though HCl, as a strong acid, should be completely dissociated. However, the protons and the chloride ions influence each other so strongly that, when measured and chemically reacted, it appears that the acid is weaker than one molar. The whole thing still depends on the temperature. For hydrochloric acid with a temperature of 25 C, the following applies precisely:

 Activity 1 corresponds to the molarity 1.184 mol / L (pH value = 0.0)

or

 The molarity 1 mol / L corresponds to the activity 0.8446 (pH value = 0.073)

A solution with proton activity 1 therefore contains 1 mol of independently behaving protons per liter. You have to know that if you want to build a standard hydrogen electrode, for example.
(The same applies, of course, to alkalis such as caustic soda.)
Note: To make the whole thing even more confusing, the activity is given the dimension mol / l in some books. So, pay close attention!

The more dilute the solutions become, the more the values ​​of concentration and activity converge, because the interaction between the ions of the acid then decreases.
For calibration, solutions are prepared that actually show the desired pH value. To do this, however, you have to use buffer solutions with precisely defined proton concentrations ("Calibration buffer"). So: Never use a dilute hydrochloric acid or sodium hydroxide solution to calibrate the glass electrodes.

Finally, a note: In pure water, the activities can be set equal to the concentrations. It is different in salt solutions containing ions and other electrolytes such as acid or base solutions. Then the concentrations have to be corrected using activity coefficients. These can be found listed in special tables.

Important NOTE
The activity term derived here applies in principle to all electrochemical concentration data, e.g. B. for conductivity measurements or for potential calculation with the help of the Nernst equation.

Further texts on the subject of `` water ''