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Is the statement in the title true? Does the chemical potential of a single pure substance that does not undergo any chemical reactions or phase changes have any physical meaning?

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I would say no. The chemical potential is directly equal to the Fermi energy in some ideal ($T=0$) systems. This chemical potential is dependent on electron mass, number of electrons and volume.

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Yes. Irrespective of the phase or reaction, chemical potential refers to the change in total free energy (Gibbs free energy) with the change in number of particles of the system. Fundamental definition is $\mu = \frac{\partial G}{\partial n}$ where n represents the number of particles in the system and G the total Gibb's free energy. For a pure substance total free energy is the product of the number of moles and molar Gibbs free energy ($G = n G_m$). For a pure system, adding a new particle does not change the environment (meaning dilute the system) and hence the above relation. Hence for such systems the derivative is simply the molar Gibb's free energy ($\mu = G_m$). For ideal gases, one can use fundamental property relation of $dG$ with pressure $P$ to calculate the dependency of $\mu$ with $P$ (under NO phase change even). For ideal gases this reads as $\mu = \mu_0 + RTlog(P/P_0)$. All one can say is that the base chemical potential $\mu_0$ is arbitrary and hence $\Delta \mu$ has real physical meaning. Probably for ideal gases, this may not be evident. But it is very evident for real gases and liquids.

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