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Can someone explain to me why does the chemical potential becomes smaller when the temperature increases?

I'd like a mathematical and also an explanation via intuition.

Thanks

Qmechanic
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imbAF
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1 Answers1

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Mathematical: the chemical potential $\mu$ is the molar Gibbs free energy $G\equiv H-TS$, where $H$ is the enthalpy, $T$ is the temperature, and $S$ is the entropy. Entropy is always positive, so $\mu$ decreases with increasing $T$.

Intuitive: Nature prefers both strong bonding (enthalpy minimization) and many possibilities (entropy maximization). At higher temperature, more energy is available from our surroundings, making the enthalpy benefit $\Delta H$ we gain from bond formation less important. Therefore, we'd expect the Gibbs free energy—which governs how Nature spontaneously proceeds at constant temperature and pressure—to decrease with increasing temperature to decrease the relative magnitude of $H$.

See also this answer, which shows graphically the steadily decreasing chemical potential of the solid, liquid, and gas phases of a material with increasing temperature.

Chemomechanics
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  • But if chemical potential is the same as molar gibbs free energy, then why we have 2 different names for the same thing? From what i know, the chemical potential is the energy change of a system when we remove or add a particle from it, or is it not ? – imbAF May 24 '21 at 21:55
  • Yes, with the appropriate parameters held constant; see here, for example. Nothing usual about having multiple technical terms for a concept, especially when it was defined and investigated simultaneously in multiple fields. – Chemomechanics May 24 '21 at 22:00
  • What is the effect od enthalpy? I assume it is increasing as temerature becomes higher. – ytlu May 26 '21 at 12:45
  • The heat capacity at constant pressure mediates how the enthalpy changes with temperature. – Chemomechanics May 26 '21 at 16:16