Enthalpy and Entropy Values Deduced from Gibbs Free Energy Measurements
High Temperature Science
An overlooked feature of second-law enthalpy and entropy values is illustrated using recent data for the dissociation of As4(g). Evaluation of a measure-of-fit, δ, for an experimental set of equilibrium constant-temperature values at values of ΔH298 and ΔS298 other than those minimizing δ2 gives contours of constant δ that are long, very narrow ellipses. The value of δ at the contour corresponding to a 95% probability that the true values for ΔH298 and ΔS298 fall within this contour is calculated assuming a normal error distribution. Within an uncertainty of a few hundred calories in the enthalpy the values of ΔH298 and ΔS298 fall along a segment of a best-fit line that covers 8 kcal or more in ΔH298. The best-fit line for each set has a slope equal to the reciprocal of the average value of 1/T for the set and an intercept simply- related to ΔG at this average temperature. Thus the most certain result of an experimental set of ΔG-T values is the value of ΔG at this average temperature, i.e., the determination of a best-fit line. Similar results follow from a conventional, linear least-squares analysis if the correlation coefficient as well as the standard deviations between ΔH298 and ΔS298 are calculated and properly Interpreted. The best-fit line feature leads naturally to a correlation between second law ΔH298 and ΔS298 values from different sets that are equally free of systematic errors, It is shown that the best-fit-line feature is very pronounced whenever the range (standard deviation) in the experimental values of 1/T is small compared to the average value. It Is therefore most likely characteristic of many ΔG-T sets.
Brebrick, Robert F., "Enthalpy and Entropy Values Deduced from Gibbs Free Energy Measurements" (1976). Mechanical Engineering Faculty Research and Publications. 298.