The author replies to Lambert.

Dr. Lambert has presented an interesting, alternative way of teaching the concept of entropy in his article “Disorder—A Cracked Crutch for Entropy Discussions” (1). However, in my view, he has not succeeded in “showing”, as he contends, that molecular disorder should be rejected as a viable model. Furthermore, the disorder model is not at all confusing to students, if presented properly. For example, Richard Feynman clearly and simply says, “We measure disorder by the number of ways that the insides can be arranged, so that from the outside it looks the same…entropy measures the disorder” (2). In a slightly more mathematical manner, Ilya Prigogine says, “Boltzmann identified the number of complexions, P, with the entropy through the relation

S = k log P

in which k represents Boltzmann’s universal constant: an entropy increase expresses growing molecular disorder, as indicated by the increasing number of complexions” (3).

As far as disorder not being a viable model for rubber, the expression for the entropy of a rubber polymer chain may be obtained by means of the random coil model, which is clearly related to the degree of disorder of the chain (4). Furthermore, as Nash says, “partial straightening of chain segments is an ordering process reflected in an entropy decrease” (5). Lambert has not included this point when citing the same reference. I do agree that energy is more “spread out” in relaxed than in stretched rubber chains; however, this leads to an increase in the molecular disorder in the relaxed state.

The Gibbs free energy, ΔG, was selected in the rubber band activity (6) in lieu of the Helmholtz free energy, ΔA, since general chemistry texts do not ordinarily mention the latter. It was noted that the assumption of constant pressure was an approximation. I agree that using ΔA is more rigorous. However, even in applying the Helmholtz equation, the assumption of constant volume is not necessarily true, especially if one notes that rubber bands contract laterally when stretched (4). Regardless of which form of free energy is used, it is clear from the activity that the temperature in the TΔS term is not perfectly constant so that this term is also approximate. Nevertheless, in my view, making these approximations does not invalidate the conclusions the student obtains from performing the activity.

Literature Cited

1. Lambert, F. L. J. Chem. Educ. 2002, 79, 187–192.
2. Feynman, R. P.; Leighton, R. B.; Sands, M. The Feynman Lectures on Physics, Vol. 1; Addison-Wesley: California Institute of Technology, 1977; pp 46-5–46-7.
3. Prigogine, I. From Being to Becoming-Time and Complexity in the Physical Sciences; W. H. Freeman: San Francisco, 1980; pp 9–11.
4. Atkins, P. W. Physical Chemistry, 3rd ed.; W. H. Freeman: New York, 1985; pp 625, 635–636.
5. Nash, L. K. J. Chem. Educ. 1979, 56, 363–368.
6. Hirsch, W. J. Chem. Educ. 2002, 79, 200A–200B.