The theme of this chapter has been the use of free energy and potential as a measure of the drive toward chemical change.

The free energy change per mole of molecules or electrons is the "pressure" on these molecules or electrons to move: from one solid, liquid, or gas phase to another for molecules; or from one atom, ion, or molecule to another for electrons.

An important concept adapted from gravitation is the idea that the free energy involved in a chemical change can be described as the product of a potential for change times the amount of substance that undergoes the change.

The kinetic energy that a ball gains in rolling down a hill of height h is E = mgh. This is the product of the mass of the ball, m, and the gravitational potential, gh.

The total free energy released by a chemical reaction is the energy change per mole times the number of moles of reaction that occur.

The free energy released during the transfer of electrons in an oxidation-reduction process is the free energy change per mole of electrons times the number of moles of electrons transferred.

As long as a higher potential exists for a starting state than for a final state, the shift from the initial state to the other is spontaneous, and the energy released can be harnessed to drive some other process.

Water running downhill can turn a mill wheel or generate electricity. Burning gasoline can push a piston or heat a room. And electrons moving from zinc to silver can send a telegraph message or lay down a track of silver on a printed circuit board for a computer.

When a potential gradient has "run down," and no difference in potential exists between two states, then the system is at equilibrium.

No more drive toward change exists, and no more useful energy or work can be obtained from the system. This is the situation when all of the water has run to the bottom of the hill, a solution is in equilibrium with solid or vapor, or a battery has run down.