# Maximum Useful Work

Submitted by ChemPRIME Staff on Thu, 12/16/2010 - 15:23

The Gibbs free energyGibbs energy: a thermodynamic function corresponding to the tendency for spontaneous change in a system; represented by the symbol G. has another very useful property. When a spontaneousCapable of proceeding without an outside source of energy; refers to a reaction in which the products are thermodynamically favored (product-favored reaction). chemical reactionA process in which one or more substances, the reactant or reactants, change into one or more different substances, the products; chemical change involves rearrangement, combination, or separation of atoms. Also called chemical change. occurs, the decrease in free energy,–ΔG corresponds to the maximum possible quantity of useful workA mechanical process in which energy is transferred to or from an object, changing the state of motion of the object., wmax, which can be obtained. Symbolically,

–ΔG = wmax

For a reaction which is not spontaneous ΔG is positive and wmax is negative. This means that work must be done on the system (through some outside intervention) to force the nonspontaneous reaction to occur. The minimum work that must be done is given by ΔG. As an example of the utility of this interpretation of ΔG, consider the recovery of Al from Al2O3 oreNaturally occurring minerals from which metals and other substances can be extracted commercially.:

Al2O3 → 2 Al + 3/2O2      ΔGm°(298 K) = 1576.4 kJ mol–1

The positive ΔG tells us that at least 1576.4 kJ of work must be done on 1 mol Al2O3 to effect this change. In a modern aluminum manufacturing plant this work is supplied electrically, and the electricity is often provided by burning coal. Assuming coal to be mainly carbon, we can write

C(s) + O2(g) → CO2(g)      ΔGm°(298 K) = –394.4 kJ mol–1

Thus 1 mol C can do almost exactly one-quarter the work required to decompose 1 mol Al2O3 and we must burn at least 4 mol C to process each 1 mol Al2O3 ore. (In practice the aluminum smelting process is only 17 percent efficient, so it is necessary to burn nearly 6 times the theoretical 4 mol C.)

In the context we have just described, free energy is energy that is available to do useful work, not energy that we can get for nothing. When a spontaneous process occurs and there is a free energy decrease, it is the availability of useful energy which decreases. According to the first law of thermodynamicsA formal statement that energy can neither be created nor destroyed; as applied to chemical systems, the change in internal energy is equal to the heat energy transfer into the system plus the work energy transfer into the system., energy cannot be consumed in any process, but according to the second law, free (or available) energy is always consumed in a spontaneous process.

When we talk about consuming energy resources by burning fossil fuels, it is the availability of energy that is used up. The energy originally stored in a fuel is converted to heatEnergy transferred as a result of a temperature difference; a form of energy stored in the movement of atomic-sized particles. energy and dispersed to the surroundings. Once this has happened its usefulness is lost. There is no way of abstracting this energy from the surroundings and using it to lift a weightA measure of the gravitational force on an object; directly proportional to mass. or do other useful work, because that would correspond to the reversal of a spontaneous process. The second law thus adds a very important qualification to the first law. While the first law tells us that we cannot destroy energy, the second law tells as that we cannot recycle it either.