For application in geothermobarometry it is essential to estimate the errors associated with the derived enthalpies and entropies. The least squares logic itself provides an estimate of the uncertainties for the values of enthalpy and entropy through the covariance matrix. This approach was used by Powell & Holland (1985) and Holland & Powell (1985, 1990). However this approach does not seem to be appropriate for the procedure used here. The resulting errors which the covariance matrix delivers are dependent on the input parameters. The closer the input parameters are to a final result, the smaller will be the calculated errors using the covariance matrix. In the iterative approach used here, the input data were already relatively close to the final result, making errors calculated from the covariance matrix meaningless.
To get at least some idea about the confidence of the extracted ΔfH° and S° values, errors were estimated using a Monte Carlo simulation, with a variance assigned to each input parameter of the final iteration. Values within this selected range had to be still feasible with respect to the experimental results for each mineral reaction and the calorimetric results. Values within this range were then selected randomly using a gaussian distribution. With these randomly chosen input parameters the regression was calculated again. This procedure was repeated 1000 times, every time using a new randomly chosen set of input parameters. Results were then averaged and the standard deviation (σ) calculated. It is clear that while the resulting errors reflect the assigned variance of the input parameters, it at least gives some level of confidence for the extracted ΔfH° and S°.