Thermodynamics and Spontaneity

In the Classroom Thermodynamics and Spontaneity Raymond S. Ochs Department of Pharmaceutical Sciences, St. John’s University, 8000 Utopia Parkway, Jamaica, NY 11439 Despite the importance of thermodynamics as the onstrates that the word is not used as originally defined. foundation of chemistry, most students emerge from in- troductory courses with only a dim understanding of this Spontaneous Processes in Chemistry subject. Generally students recognize that the informa- tion is significant, yet do not assimilate it into later stud- Most current treatments of thermodynamics (e.g., ref ies, especially in applied fields such as biology and bio- 10) explain the first law as the constancy of energy in the chemistry. universe, and the second as the ever-increasing entropy A clear sense of the problem is reflected in a number of the universe. While most derivations have sufficient of other contributions to this Journal (e.g., 1–6). Most (1– rigor, some semantics are missing. We can divide terms 4, 6) recommend increased rigor in derivation of equa- used for scientific description into two classes. One is the tions. This may appeal to students in advanced courses in group of words common to everyday language, such as chemical thermodynamics, but not to most. A few other temperature, heat, and energy. The other is a group of suggestions are to introduce the subject earlier in gen- specialized words, such as enthalpy, entropy, and exer- eral chemistry courses (2) or to provide innovative ways gonic. The specialized words were invented deliberately to visualize reaction changes (3). to avoid confusion with everyday terminology. For example, I suggest that the problem lies at another level en- Clausius proposed that the quantity q/T was a useful one, tirely: the meanings of the terms are not clear. Recently, and named it “entropy” to sound like energy (to which it MacNeal (7) introduced the concept of mathsemantics, the has a parallel) but at the same time to avoid connotations joining of mathematics with a deep understanding of the of existing words. sense (semantics) in which it operates. For example, the Usually, common words pressed into scientific service author argues that not only can we add apples and or- are given a precise and limited meaning. However, one anges (yielding total fruit), but that anything less than term stands out that is almost never defined as a techni- such a synthesis is trivial. Mathematics is hard, not be- cal word, but is invariably used as one: spontaneous. This cause of the actual mathematical part of the problem but is meant in almost every case to signify a change in a because of the semantics. As discussed thoroughly by process (most commonly, a chemical transformation) in a Weinburg (8), the very names we affix to ideas dominate particular direction. Thus, we would say that if a reaction how we think about them. proceeds in a stated direction, it is spontaneous. The re- A similar reorientation would benefit chemical edu- verse reaction, therefore, is not spontaneous. This appears cation. By way of example, the word “spontaneous” is to be the sense of the word; let us accept it as a working widely used in thermodynamics, presumably because the definition and see where it leads. word is familiar and assists understanding of this sub- When the free energy for a reaction (∆G) is negative, ject. In the following, I will provide evidence that this word then the reaction will proceed in the indicated direction, has contributed more to the obfuscation of chemical ideas usually taken as left to right as written on the page. Com- than it has helped elucidate them. bined with the above, we can equate spontaneous with “∆G is negative.” Consider dictionary definitions of the Spontaneous Inflammation word spontaneous (11): Downloaded via UNIV OF SAO PAULO on February 28, 2019 at 17:54:12 (UTC). 1. Proceeding without obvious constraint, i.e., of un- Insight into the historical origins of the word sponta- known cause neous as applied to chemistry can be obtained from a con- See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. 2. Arising from a momentary impulse sideration of an excerpt from J. Thompson’s 1813 Lecture 3. Happening without external influence, i.e., naturally on Inflammation (9): These definitions may appear to justify the chemical When inflammation occurs...without our being able to use of spontaneous. An external agent of unexplained ori- trace its production to the action of any obvious cause, gin is consistent with the notion that classical thermody- it is termed spontaneous inflammation. namics is a formalism independent of mechanisms. In Development of thermodynamics in the 19th century order to gauge how appropriate spontaneous is in its closely followed the spirit of this definition. This system, chemical context, we can substitute the dictionary mean- now called classical thermodynamics, assumes no under- ings into a chemical definition of the word. A most direct lying mechanism for transformations. Thus, we do not need and hardly controversial statement is given by Pimentel to consider the existence of molecules at all. Since under- and Spratley (12): “The free energy change is negative— standing is enriched when we do consider that molecules the process will occur spontaneously.” Proceeding with the exist, most modern treatments are mixtures of classical substitution, we have: and statistical thermodynamics. Nonetheless, the word 1. The free energy change is negative—the process will spontaneous has remained in current use. Thompson was occur without obvious constraint, i.e., of unknown careful to circumscribe its meaning, which should exclude cause. it from discussions encompassing statistical thermody- 2. The free energy change is negative—the reaction namics. While this distinction may appear picayune, it dem- 952 Journal of Chemical Education • Vol. 73 No. 10 October 1996 In the Classroom products arise from a momentary impulse. free energy and equilibrium. Most students are familiar 3. The free energy change is negative—the process with the equation will happen without external influence, i.e., naturally. ∆G = ∆H –T∆S (1) These statements suggest that the meanings behind where G is free energy, H is enthalpy, T is temperature, spontaneous do not in fact enhance our understanding of and S is entropy. Understanding is usually enhanced by a thermodynamically allowed process. Simply eliminat- considering how the sign of ∆G changes as we vary the ing the word clarifies the meaning: “The free energy terms on the right hand side, especially the temperature change is negative—therefore, the process will occur.” Use at various fixed levels of enthalpy and entropy. Perform- of the word spontaneous leads us to believe that we un- ing such calculations develops a feel for the values for derstand something when we do not. It also causes us to which reactions are possible; to introduce spontaneity at attribute false qualities to reactions, such as an unknow- this point is to cloud the picture more than to clear it. able origin (“without obvious constraint”), a time base Consider how the problem is compounded when we (“momentary impulse”), or inexplicable forces of nature introduce an alternative ∆G, written in terms of changes (“naturally”). in the concentrations of the compounds involved in a reaction. From A Literary Sojourn ∆G = ∆G° + RTlnQ (2) An argument that may be raised against the dictio- where G° is standard free energy, R the gas constant, nary definitions is that virtually everyone has some gut and Q the mass action ratio, we impose the equilibrium understanding of the word spontaneous that allows them restrictions to clearly appreciate it. In order to evaluate that gut un- ∆G = 0; and Q = Keq (3) derstanding let us examine literary specimens in situ. My source of this material is a compilation of 2,000 literary where Keq is the equilibrium constant, and arrive at ∆ ° works on CDROM (13), searched for occurrences of the word G = –RTlnKeq (4) “spontaneous” or “spontaneity”. A few representative quo- This last equation is the important relation between tations, followed by comments, are reproduced below. the equilibrium constant and the standard free energy, But Christmas puddings, brawn, and abundance of but it is also readily misconstrued. It appears to relate spirituous liquors, throwing the mental originality into the free energy change of a reaction to the equilibrium the channel of nightmare, are great preservatives constant. If the state of equilibrium is correctly grasped against a dangerous spontaneity of waking thought. as a limiting condition of no net change in a reaction (at a fixed temperature), then we must face the linguistic con- – George Elliot, Silas Marner sequences that a spontaneous change appears to relate to COMMENT: Originality in thought is a key to the mean- a static (equilibrium) situation. The problem is removed ing here; it has the nuance of being unexpected and un- as soon as the word spontaneous is omitted. predictable. Incidentally, another common problem emerges from Genius is revealed to us, perhaps, with a sudden flash, this simple formulation, which is the confusion of stan- but it has been making its way for a long time under- dard states for actual ones. Equation 4 may seem to im- ground, so that what we take for a spontaneous burst part some special meaning to ∆G°; after all, it appears of genius is nothing but the final effort of a sap which that once the equilibrium constant is known, a specific has been slowly accumulating and which from hence- value must be assigned to ∆G°. This is paradoxical be- forth is all-powerful. cause the values of the standard free energy are entirely arbitrary, having been established by agreement among –Rene Doumic, George Sand chemists that all concentrations should be 1 M and all COMMENT: This implies a time base and the element pressures 1 atm.

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