Non-linear regression analysis to determine Antoine equation constants

AssignmentNon-linear regression analysis to determine Antoine equation constantsW.R. Wilcox, Clarkson University, spring 2004Use Solver to find the best values for A, B and C in the Antoine equation (ln(p) = A - B/(T + C)),i.e., those giving the maximum value of R2. Use the template at the tab below.As initial guesses start with A=10, C=-10, B=100 and with the negative of those values.How do the new values of A, B, C and R2 compare with those from the previous exercise?Using 10, -10 and 10, almost the same, assuming you did previous exercise correctly.Do the values of A, B, C and R2 found by Solver depend on the initial guesses?Sometimes.Why is it better to base the calculations on ln(p) rather than p?ln(p) because p varies over orders of magnitude and one would not expect themagnitude of the error to be the same for all of these. The percent error,on the other hand, is more likely to be about the same (although surely notidentical). Consequently, the error in ln(p) will be less dependent on p.In using least squares on ln(p) we are assuming the percent error isindependent of p. While probably not true, it's much better than assumingthe absolute error is independent of p.

SolutionAnalysis of data on vapor pressure of OxygenFit to Antoine equation (ln(p) = A - B/(T + C)).Where T is absolute temperature and A, B, C are constants to be determined.Solution: Use solver to maximize R2 starting withA =13.6813.68A=10, C=-10, B=100 and with the negative of those valuesC =-4.18-4.18Click on cells to see formulas used.B =780780from solverValues from previous exerciseOriginal DataModified unitsExperimentalCorrelatedDeviation squaredp (torr)T (C)p (Pa)T (K)ln(p)(ln(p)-ln(pavg))2ln(p)(ln(pexp)-ln(pcor))21-222.013351.24.8929.44-2.9361.1385515-217.266756.06.5014.57-1.3962.23393610-215.0133358.27.209.75-0.7763.48629420-212.8266660.47.895.91-0.2165.52770540-210.0533363.28.583.020.4566.07599260-208.1799965.18.991.770.8765.955656100-205.71333267.59.500.671.3566.358257200-201.32666471.910.190.022.1564.603225400-196.35332976.910.880.322.9563.006877760-191.310132581.911.531.463.6462.22962920265089.712.223.614.5558.755977T (C)p (atm)506625102.513.147.935.7454.654111-191.311013250112.213.8312.326.4654.359691-183.522026500123.514.5217.677.1454.488083-170.753039750131.314.9321.247.5454.547601-161.01010.32129.70917.4216-149.720-6.073563322R2 using solver to maximize by varying A, B, C-141.9300.999082699R2 using A, B, C from previous exerciseThe solution (values of A, B, C) depends on the initial values. Some combinations may not give a solution.It is better here to do regression on ln(p) because p varies over 3 orders of magnitude.Using ln(p) gives equal emphasis to minimizing the percent error for both large and small p.If p is used, regression strongly emphasizes large values, so the result will be a poor fitfor small values of p.

average of abovesum of abovesum of above

ln(p) vs T4.8927699845-2.92634447526.5022078969-1.38664091177.1953550775-0.77247359647.888502258-0.20641623648.58164943860.45293539098.98711454670.86580581579.49794017051.351882408710.1910873512.153474213110.88423453162.946547406111.52608841783.637512553112.21923559834.55399087413.13552633025.742684440813.82867351086.455771047514.52182069137.140216315914.92728579947.5416510585

ExperimentalCorrelationTemperature, KVapor pressure, PaAntoine correlation for CO