In my high school textbook, they have stated that diffusion is a process in which water moves along a free energy gradient. I cannot understand how water potential may be related to the Gibbs free energy or the entropy and enthalpy of the system(as Gibbs free energy depends on both of them).

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    $\begingroup$ Your two sentences are not mutually consistent, they describe different problems. What your textbook is referring to is a definition of diffusion within the framework of non-equilibrium thermodynamics. On the other hand the relation between "water chemical potential" and "Gibbs free energy" is very simple: $\mu_i=\left( \frac{\partial G}{\partial n_i} \right)_{p,T}$ $\endgroup$
    – Buck Thorn
    Mar 12, 2021 at 7:55

1 Answer 1


It is not very clear, if mechanical or chemical potential is meant. but it does not matter much, as the former is the part of the latter.

At higher position in gravitational potential context, water has higher both mechanical and chemical potentials.

The former is defined as the rate of increase of mechanical potential energy with component mass. $$V = \frac{\mathrm{d}U}{\mathrm{d}m}$$

The latter as the rate of increase of Gibbs energy with water molar mass.

$$\mu_i = \left(\frac{\partial G}{\partial n_i}\right)_{T,p,n_j \ne n_i}$$

Note that $V$ is the part of $\mu$, if mutually recalculated to either mass or molar amount.

Water staying at higher gravitational potential has higher Gibbs energy and chemical potential.

Similarly, in solution with solute concentration gradient, water in more diluted solution has higher Gibbs energy and chemical potential. therefore it diffuses ( = has non-zero net flow ) from more to less diluted solution.

Comment feedback:

Adding of solute may both increase or decrease the entropy.

What is important is the change of the Gibbs energy during dissolution, if it is a spontaneous process or not. If the enthalpy of dissolution increases the entropy of neighborhood enough, the Gibbs energy change can be still negative even if the system entropy decreases.

Leveling concentrations decreases the Gibbs energy of the system, what means decrease of the total entropy of system + neighborhood.

  • $\begingroup$ So in the physical context of adding solute, we are decreasing the entropy of the system which water tries to regain by going towards a more dilute solute. This makes it a spontaneous process. Am I correct? $\endgroup$
    – Sayak Roy
    Mar 12, 2021 at 9:37
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    $\begingroup$ See the answer update. $\endgroup$
    – Poutnik
    Mar 12, 2021 at 11:16
  • $\begingroup$ @Poutnik "Adding of solute may both increase or decrease the entropy." and " if it is a spontaneous process or not" If I add sugar to water and it spontaneously dissolves, then entropy increases right? but if we keep on adding sugar to the point we have to stir it and heat to make it spontaneous (in other words provide an external agent), is it correct to tell that the entropy has decreased? if not could you tell an example $\endgroup$ Mar 12, 2021 at 12:02
  • $\begingroup$ There is relation of spontaineity and the total entropy increase. Total entropy may increase even if the system entropy decrease. That happens if dissoving decreases thge system entropy, but is exothermic, and the heat increases the neighborhood entropy more, than the system entropy decreased. $\endgroup$
    – Poutnik
    Mar 12, 2021 at 12:27
  • $\begingroup$ dissolving usually increases entropy, but there are exceptions. $\endgroup$
    – Poutnik
    Mar 12, 2021 at 12:29

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