# Why Gibbs free energy is zero at equilibrium? – Free Energy Equation

Gibbs’ free energy is only a rough approximation, which is not the same as the exact value, which is usually computed in such a way that the Gibbs’ equation is a simple sum. The exact values for that exact equation are still unclear, so Gibbs’ free energy is a rough approximation. Gibbs’ free energy is one dimensionless number, and so even a good approximation would not be quite correct. This is the only reason for the discrepancy with Maxwell’s equation.

It’s true that Gibbs’ equation has a few extra terms (there are an extra four energy terms in the calculation, see above). Still, the number of energy terms is so small that they don’t add up to anything noticeable, compared to Maxwell’s equation. For example, the number of energy terms in Gibbs’ equations isn’t a factor of 100. For example, it’s roughly the same as the number of different combinations of energy terms in Maxwell’s equation for example. So the difference between Gibbs’ numbers and Maxwell’s isn’t that large.

In fact, given a small set of energy terms, a few hundred of them do a pretty good job of representing the entire range of possible energy states. It is possible to think of Gibbs’ equation as representing a single potential energy state with lots of particles, while Maxwell’s equation represents a single energy state that has no particles, since it can only have one potential energy state (it’s a potential energy state with no particles).