Chemical Education Today

www.JCE.DivCHED.org • Vol. 82 No. 6 June 2005 • Journal of Chemical Education 827

Commentary

Let’s Drive “Driving Force” Out of Chemistryby Norman C. Craig

One does not have to read far in chemistry textbooks orpapers on thermodynamics to encounter “driving force” beinginvoked to account for spontaneous change. “Driving force” isan idea that sounds significant even though this terminologyis misleading and empty of useful meaning in chemistry. “Driv-ing” and “force” are concepts from Newtonian mechanics (andmotor vehicles) and thereby suggest that Newtonian mechan-ics explains spontaneous change. A defender of the use of “driv-ing force” might ask, “Isn’t a ball driven downward by the forceof gravity, and doesn’t a ball come to rest on a table top be-cause the energy of the ball is thereby minimized?” The ball-on-tabletop outcome is not consistent with basic Newtonianmechanics, in which forces act conservatively. In basic New-tonian mechanics the ball would bounce forever on a perfectlyelastic surface. Being at the top of the drop is as accessible asbeing on the surface in this perpetual motion.

The reason that the ball comes to rest on a tabletop liesoutside basic Newtonian mechanics. The new equilibrium statearises because the compact, Newtonian energy of the fallingball is dispersed into random thermal energy of the moleculesin the tabletop (to simplify a bit by neglecting the heat capac-ity of the ball and the air) by frictional processes. To apply thecentral concept of thermodynamics, the ball comes to rest be-cause the entropy of the “universe” is higher for the ball-on-tabletop state than for the levitated ball. Energy has beentransformed but conserved, whereas entropy, which measuresthe dispersal of energy, has been maximized. An increase inentropy is not suggested by “driving force”. To the contrary,“driving force” reinforces the false notion that energy minimi-zation is a reason for the final state. “Driving force” also sug-gests a mechanical outcome, as is, for example, characteristic ofthe predictable Newtonian circulation of the Moon aroundEarth. The outcome of chemical change is a consequence ofstatistics; that is, the final state is the most probable state.

Those who use arguments of energy-minimization ver-sus entropy-maximization—their number is legion in chem-istry—might say that energy minimization is half of the storyand thus would not be uncomfortable with the “driving force”terminology. Such advocates might be unconcerned about themixed units in the interpretation of �H versus �S. �H hasenergy units; �S has units of energy divided by Kelvins. Howcan �H and �S with different units be regarded as compet-ing and coexisting in one expression? �H and �S coexist inthe Gibbs energy1 expression, �GT � �H � T�S, in whichthe �S term has been multiplied by T to give this term en-ergy units. “Aha,” says the advocate of the �S-versus-�H com-petition, “The units are all energy, thereby confirming thecentral importance of energy and its minimization.” How-ever, we might as well have divided the Gibbs energy expres-sion by T and have obtained �G/T � �H/T � �S. Now,

the expression has been cast in entropy units. Which formu-lation is more fundamental and more informative?

What energy is T�S in the expression �G � �H � T�S?What entropies are �G/T and �H/T in the expression�G/T � �H/T � �S ? In the first expression, T�S is theenergy (qrev, heat term) traded with the surroundings whenthe same net process takes place along a special, reversiblepath. It is the unavoidable energy trade with the thermal sur-roundings under the most favorable (reversible) conditions.For a chemical reaction the reversible path is typically quitedifferent from the irreversible path. One possible reversiblepath consists of embedding the chemical reaction in anelectrochemical cell. Another, abstract reversible path involvesremoving stoichiometric amounts of reactants through species-specific selective membranes and introducing stoichiometricamounts of products through other selective membranes(��i�id�i). ��G is the maximum useful work, such as elec-trical work, available from the net process carried out alongthe reversible path under special constraints. These constraintsconsist of the same temperature and same pressure at the be-ginning and the end of the process, often misleadingly calledconstant temperature and pressure. �G is also an index ofspontaneity, but this index applies only for the same initialand final temperature and pressure and for no work otherthan PV work.2 Thus, with the Gibbs function formulationwe seem to be comfortably in the world of energies with en-tropy conveniently on the sidelines.

We now consider the alternative equation (expressed inentropy units) �G/T � �H/T � �S and change the signs togive ��G/T � ��H/T �S. Of course, �S is the entropychange in the system. The term ��H/T is easily identified asthe entropy change occurring in the thermal surroundings asa consequence of the transfer of the energy, ��H, to the ther-mal surroundings in an ordinary, irreversible process with Tand P the same at the beginning and end of the process. Thesum of the two entropy terms gives ��G/T, which is the totalentropy change, �Stot, or what is often called the entropychange of the universe. Indeed, we might have started with�Stot � �Ssurr �Ssys, where “tot” is for the total entropychange, “surr” is for the surroundings in thermal contact withthe system, and “sys” is for the system. This last expression isa direct consequence of the second law, in which the “change

“Driving force” is an idea that sounds significant

even though this terminology is misleading and

empty of useful meaning in chemistry.

Chemical Education Today

828 Journal of Chemical Education • Vol. 82 No. 6 June 2005 • www.JCE.DivCHED.org

in” (entropy) function is used throughout. We see that thesignificance of the �H term is not in telling about energy de-crease in the system. Its significance is in telling us about en-tropy increase in the thermal surroundings. We also see thatthe change in the Gibbs energy is �Stot disguised in energyunits with a change in sign. Of course, we do not expect en-tropy to be conserved. Thus, the Gibbs energy is not con-served, as would be a proper energy.

What are the advantages of the entropy formulation? Itis a direct application of the action (change) law of thermo-dynamics. This entropy formulation avoids suggesting that a“driving force” contributes spontaneity to a process. Becauseentropy is an expression of probabilities, any suggestion thata Newtonian determinism explains chemical change isavoided. We do not regard the quantities �H and �S, whichhave different units and which are evaluated for different paths,as competing when accounting for spontaneous change. Wedo not use a derived function, �GT,P, expressed in misleadingenergy units. The all-important entropy function is broughtto the foreground, and the energy function recedes into thebackground where it belongs when considering spontaneity.

The insightful way to discuss spontaneity in chemicalchange is with entropy analyses, in which �Stot � �Ssurr �Ssysand its extensions are used. This formulation applies to as-sessing spontaneity in many processes, such as electrochemicalcells, heat engines, and osmosis, to which the Gibbs energyformulation does not apply. Entropy analyses have been ex-emplified in several places (1–5). Entropy analyses are ap-pearing with greater frequency in general chemistry textbookssuch as in the Moore, Stanitski, and Jurs text (6) and in theZumdahl and Zumdahl text (7). Barrow was an early advo-cate of using �Stot in his physical chemistry textbook (8).

Let’s drive the pretentious, empty phrase “driving force”out of chemistry. I have driven it out of my vocabulary andnow bristle when I encounter it. Let us instead do all we canto help students become at home with entropy and its directapplications.

Notes

1. The Gibbs energy, G, is often called the “Gibbs free en-ergy”. This usage is imprecise and misleading. Only under the spe-cial conditions of the same temperature and pressure at thebeginning and end of a reaction is ��G the free (available) energy,namely, work available other than the obligatory PV work. For workother than PV work the change, �GT,P , is the Gibbs free energy.Never by itself is G a free energy. In addition, �G is defined forprocesses, such as a gas changing pressure at constant temperature,where it is not a free energy.

2. For an electrochemical cell �GT,P is not the index of spon-taneity. �GT,P �Uel is, where �Uel is the change in amount ofelectrical energy produced, because ��GT,P � �Uel = T�Stot (3).

Literature Cited

1. Bent, H. A. The Second Law; Oxford: New York, 1968;J. Chem. Educ. 1962, 39, 491–499; J. Chem. Educ. 1970, 47,337–341; J. Chem. Educ. 1972, 49, 44–46.

2. Craig, N. C. J. Chem. Educ. 1970, 47, 342–346; J. Chem.Educ. 1988, 65, 760–764.

3. Craig, N. C. Entropy Analysis; VCH: New York, 1992.4. Craig, N. C. J. Chem. Educ. 1996, 73, 710–715.5. Davies, W. G. Introduction to Chemical Thermodynamics: A

Non-Calculus Approach; Saunders: Philadelphia, 1972.6. Moore, J. W.; Stanitski, C. L.; Jurs, P. C. Chemistry The Mo-

lecular Science, 2nd ed.; Thomson, Brooks/Cole: Belmont, CA,2005; Chapter 18.

7. Zumdahl, S. S.; Zumdahl, S. A. Chemistry, 6th ed.; HoughtonMifflin: Boston, MA, 2003; Chapter 16.

8. Barrow, G. M. Physical Chemistry, 5th ed.; WCB/McGraw-Hill: New York, 1996; Chapter 4.

Norman C. Craig is an emeritus member of the Departmentof Chemistry, Oberlin College, Oberlin, OH 44074;Norm.Craig@oberlin.edu

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