Correlation and prediction of solubility and standard entropy of solution of gases in liquids by means of analysis of variance and/or principal components analysis

Abstract

Various mathematical-statistical models (analysis of variance, principle components analysis and a hybrid model) are applied to 322 data on the standard entropy of solution of 15 gases in 40 solvents, and 464 data on the solubility of 20 gases in 45 solvents. The average standard deviations of (prediction-future observation) are calculated for the missing values in the two data sets, for all models. It is shown that ▪ first decreases and then increases with increasing complexity of the model ( i.e., increasing number of parameters). The model with the smallest ▪ is the best one for the prediction of missing values. By means of these optimal models 278 missing values of the standard entropy of solution, and 436 missing values of the solubility are calculated, together with their individual values of ▪ For the standard entropy of solution the estimation M̂ of the observations y and their standard deviations are also tabulated, as M̂ is judged to be more trustworthy than y (the standard deviation of the fit is mainly experimental error, rather than model error). For the solubility data the reverse situation occurs: the standard deviation of the fit is mainly model error, and thus the observations y are more trustworthy than the model estimates M̂. The average standard deviation of the estimated values of the standard entropy of solution is 0.6 cal.mole −1.K. −1 for missing values and 0.4 cal.mole −1.K −1 when an observation exists. The average standard deviation of estimates of missing values of the solubility is 35%. For comparison: the experimental error in recent accurate work is 1 cal.mole −1.K −1 for the standard entropy of solution and 1% for the solubility.