# How do you measure the chemical potential?

It is clear how to measure thermodynamics quantities such as temperature, pressure, energy, particle number and volume. But I have no idea how to measure chemical potential.

Could someone please provide some examples of how one could measure the chemical potential?

• en.wikipedia.org/wiki/Chemical_potential read the discovery part might be of help – Aditya Garg Feb 28 at 19:57
• You said you can measure energy, but can you really? Please describe how you would measure, say, internal energy U. You certainly can't measure it directly. And all you can do indirectly is measure the change in U. The same goes for H, S, and G. And, since G is the basis for chemical potential, you can determine chemical potential indirectly relative to a reference state (at least for an ideal gas). Is this adequate? – Chet Miller Feb 28 at 23:43

You can measure it indirectly by using other extensive quantities and applying thermodynamic relations (see https://en.wikipedia.org/wiki/Table_of_thermodynamic_equations). For instance, you could use $$\mu = (\frac{\partial G}{\partial N})_{p,T}$$
The general procedure to measure difference in the chemical potential is to compare it to some standard reference. Two standard references are in common use: ideal-gas state and ideal solution. In both cases the chemical potential of the reference state is $$\mu_i = \mu_i^0 + RT \ln x_i$$ where $$x_i$$ is the mol fraction of the component and $$\mu_i^0$$ is the chemical potential of the pure component at the same temperature and pressure. One then calculates the departure of the chemical potential from the reference state using auxiliary properties such as activity coefficients, fugacity coefficients, etc.