Chemical Education Today
Commentary
Let’s Drive “Driving Force” Out of Chemistry by Norman C. Craig
One does not have to read far in chemistry textbooks or papers on thermodynamics to encounter “driving force” being invoked to account for spontaneous change. “Driving force” is an idea that sounds significant even though this terminology is misleading and empty of useful meaning in chemistry. “Driving” and “force” are concepts from Newtonian mechanics (and motor vehicles) and thereby suggest that Newtonian mechanics explains spontaneous change. A defender of the use of “driving force” might ask, “Isn’t a ball driven downward by the force of gravity, and doesn’t a ball come to rest on a table top because the energy of the ball is thereby minimized?” The ballon-tabletop outcome is not consistent with basic Newtonian mechanics, in which forces act conservatively. In basic Newtonian mechanics the ball would bounce forever on a perfectly elastic surface. Being at the top of the drop is as accessible as being on the surface in this perpetual motion. The reason that the ball comes to rest on a tabletop lies outside basic Newtonian mechanics. The new equilibrium state arises because the compact, Newtonian energy of the falling ball is dispersed into random thermal energy of the molecules in the tabletop (to simplify a bit by neglecting the heat capacity of the ball and the air) by frictional processes. To apply the central concept of thermodynamics, the ball comes to rest because the entropy of the “universe” is higher for the ball-ontabletop state than for the levitated ball. Energy has been transformed but conserved, whereas entropy, which measures the dispersal of energy, has been maximized. An increase in entropy is not suggested by “driving force”. To the contrary, “driving force” reinforces the false notion that energy minimization is a reason for the final state. “Driving force” also suggests a mechanical outcome, as is, for example, characteristic of the predictable Newtonian circulation of the Moon around Earth. The outcome of chemical change is a consequence of statistics; that is, the final state is the most probable state. Those who use arguments of energy-minimization versus entropy-maximization—their number is legion in chemistry—might say that energy minimization is half of the story and thus would not be uncomfortable with the “driving force” terminology. Such advocates might be unconcerned about the mixed units in the interpretation of H versus S. H has energy units; S has units of energy divided by Kelvins. How can H and S with different units be regarded as competing and coexisting in one expression? H and S coexist in the Gibbs energy1 expression, GT H TS, in which the S term has been multiplied by T to give this term energy units. “Aha,” says the advocate of the S-versus-H competition, “The units are all energy, thereby confirming the central importance of energy and its minimization.” However, we might as well have divided the Gibbs energy expression by T and have obtained G/T H/T S. Now,
www.JCE.DivCHED.org
•
“Driving force” is an idea that sounds significant even though this terminology is misleading and empty of useful meaning in chemistry.
the expression has been cast in entropy units. Which formulation is more fundamental and more informative? What energy is TS in the expression G H TS? What entropies are G/T and H/T in the expression G/T H/T S ? In the first expression, TS is the energy (qrev, heat term) traded with the surroundings when the same net process takes place along a special, reversible path. It is the unavoidable energy trade with the thermal surroundings under the most favorable (reversible) conditions. For a chemical reaction the reversible path is typically quite different from the irreversible path. One possible reversible path consists of embedding the chemical reaction in an electrochemical cell. Another, abstract reversible path involves removing stoichiometric amounts of reactants through speciesspecific selective membranes and introducing stoichiometric amounts of products through other selective membranes (iidi). G is the maximum useful work, such as electrical work, available from the net process carried out along the reversible path under special constraints. These constraints consist of the same temperature and same pressure at the beginning and the end of the process, often misleadingly called constant temperature and pressure. G is also an index of spontaneity, but this index applies only for the same initial and final temperature and pressure and for no work other than PV work.2 Thus, with the Gibbs function formulation we seem to be comfortably in the world of energies with entropy conveniently on the sidelines. We now consider the alternative equation (expressed in entropy units) G/T H/T S and change the signs to give G/T H/T S. Of course, S is the entropy change in the system. The term H/T is easily identified as the entropy change occurring in the thermal surroundings as a consequence of the transfer of the energy, H, to the thermal surroundings in an ordinary, irreversible process with T and P the same at the beginning and end of the process. The sum of the two entropy terms gives G/T, which is the total entropy change, Stot, or what is often called the entropy change of the universe. Indeed, we might have started with Stot Ssurr Ssys, where “tot” is for the total entropy change, “surr” is for the surroundings in thermal contact with the system, and “sys” is for the system. This last expression is a direct consequence of the second law, in which the “change
Vol. 82 No. 6 June 2005
•
Journal of Chemical Education
827
Chemical Education Today
Commentary in” (entropy) function is used throughout. We see that the significance of the H term is not in telling about energy decrease in the system. Its significance is in telling us about entropy increase in the thermal surroundings. We also see that the change in the Gibbs energy is Stot disguised in energy units with a change in sign. Of course, we do not expect entropy to be conserved. Thus, the Gibbs energy is not conserved, as would be a proper energy. What are the advantages of the entropy formulation? It is a direct application of the action (change) law of thermodynamics. This entropy formulation avoids suggesting that a “driving force” contributes spontaneity to a process. Because entropy is an expression of probabilities, any suggestion that a Newtonian determinism explains chemical change is avoided. We do not regard the quantities H and S, which have different units and which are evaluated for different paths, as competing when accounting for spontaneous change. We do not use a derived function, GT,P, expressed in misleading energy units. The all-important entropy function is brought to the foreground, and the energy function recedes into the background where it belongs when considering spontaneity. The insightful way to discuss spontaneity in chemical change is with entropy analyses, in which Stot Ssurr Ssys and its extensions are used. This formulation applies to assessing spontaneity in many processes, such as electrochemical cells, heat engines, and osmosis, to which the Gibbs energy formulation does not apply. Entropy analyses have been exemplified in several places (1–5). Entropy analyses are appearing with greater frequency in general chemistry textbooks such as in the Moore, Stanitski, and Jurs text (6) and in the Zumdahl and Zumdahl text (7). Barrow was an early advocate 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 and now bristle when I encounter it. Let us instead do all we can to help students become at home with entropy and its direct applications.
828
Journal of Chemical Education
•
Notes 1. The Gibbs energy, G, is often called the “Gibbs free energy”. This usage is imprecise and misleading. Only under the special conditions of the same temperature and pressure at the beginning and end of a reaction is G the free (available) energy, namely, work available other than the obligatory PV work. For work other 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 for processes, 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 spontaneity. GT,P Uel is, where Uel is the change in amount of electrical energy produced, because GT,P Uel = TStot (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 Molecular Science, 2nd ed.; Thomson, Brooks/Cole: Belmont, CA, 2005; Chapter 18. 7. Zumdahl, S. S.; Zumdahl, S. A. Chemistry, 6th ed.; Houghton Mifflin: Boston, MA, 2003; Chapter 16. 8. Barrow, G. M. Physical Chemistry, 5th ed.; WCB/McGrawHill: New York, 1996; Chapter 4.
Norman C. Craig is an emeritus member of the Department of Chemistry, Oberlin College, Oberlin, OH 44074;
[email protected] Vol. 82 No. 6 June 2005
•
www.JCE.DivCHED.org
