13. How To Measure Disorder   Previous PageNext Page

For a reaction with the same initial and final temperature, the changes in enthalpy, entropy, and free energy are related by the expression


This expression says that, at constant temperature, the change in free energy, DG, is the change in enthalpy, DH, minus the change in entropy multiplied by the absolute temperature, TDS. It is not too difficult to prove that a spontaneous reaction is one in which the overall free energy decreases, regardless of what happens to the enthalpy and entropy individually.

Spontaneity is a combined effect of both H and S, and the above equation is the proper way of combining them. This equation is easier to understand with the aid of arrow diagrams, as at the right. An upward pointing arrow represents an increase in free energy, enthalpy, and order, or a positive value for DG, DH, and (-TDS). This is the nonspontaneous direction. Conversely, an arrow pointing downward symbolizes a decrease in free energy or enthalpy, and an increase in disorder. These correspond to negative values for DG, DH, and (-TDS), and are in the direction of spontaneity. The DG arrow is the sum of the DH and the (-TDS) arrows, and if the DG arrow points downward, the reaction is spontaneous.

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