13. How To Measure Disorder   Previous PageNext Page

In many reactions the contributions of enthalpy and entropy (disorder) reinforce one another, as in the arrow diagram at the upper right. In such a reaction heat is released and disorder is created, both of which favor the spontaneous reaction. We will see examples of such reactions shortly.

In other reactions enthalpy and entropy may work against one another, as at the lower right. In this particular example, heat is given off, thereby favoring the reaction; but order increases (the -TDS arrow points up), thus hindering the reaction.

The enthalpy effect dominates in this case and the reaction still is spontaneous, but this need not always be true. The examples we cited at the beginning of the chapter to show the fallacy of deciding spontaneity on the basis of enthalpy alone were in this category.

How do the changes in enthalpy and entropy compare when ammonium chloride dissolves in water? Which effect predominates? Re-call from Chapter 12 that heat is absorbed: DH0 = +3.62 kcal mole-1.This by itself works against the dissolving process.

But the molar entropy increases from 22.6 e.u. to 40.2 e.u., an increase in disorder per mole of 17.6 e.u., or cal deg-1.

If DS = +17.6 cal deg-1 mole-1, then at room temperature or 298°K:


TDS = 298° (+17.6 cal deg-1 mole-1) = 5245 cal mole-1
TDS = 5.25 kcal mole-1

The free energy change per mole then can be calculated:

D G = DH - TDS = +3.62 kcal - 5.25 kcal = -1.63 kcal

Enthalpy applies 3.62 kcal worth of opposition to the dissolving of ammonium chloride in water, but entropy, or disorder, favors the dissolving process by 5.25 kcal. The net effect is that NH4Cl dissolves with an overall free energy drive of 1.63 kcal mole-l. The key to chemical spontaneity is not what enthalpy or entropy may do individually, but what happens to the free energy during the process. The results are easier to understand, however, if we realize that two components are involved, H and S.

It obviously is unnecessary to tabulate free energies if heats of formation and third-law entropies are available, but standard free energies of formation of compounds from their elements are so useful that they normally are included in tables of the type given in appendix. Let us use these tabulated values for some reactions that will illustrate how free energy behaves.

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