Van't Hoff analysis of K degrees (T): how good...or bad?
Binding constant data K degrees (T) are commonly subjected to van't Hoff analysis to extract estimates of DeltaH degrees, DeltaS degrees, and DeltaCP degrees for the process in question. When such analyses employ unweighted least-squares fitting of lnK degrees to an appropriate function of the temperature T, they are tacitly assuming constant relative error in K degrees. When this assumption is correct, the statistical errors in DeltaG degrees, DeltaH degrees, DeltaS degrees, DeltaCP degrees, and the T-derivative of DeltaCP degrees (if determined) are all independent of the actual values of K degrees and can be computed from knowledge of just the T values at which K degrees is known and the percent error in K degrees. All of these statistical errors except that for the highest-order constant are functions of T, so they must normally be calculated using a form of the error propagation equation that is not widely known. However, this computation can be bypassed by defining DeltaH degrees as a polynomial in (T-T0), the coefficients of which thus become DeltaH degrees, DeltaCP degrees, and 1/2 dDeltaCP degrees/dT at T=T0. The errors in the key quantities can then be computed by just repeating the fit for different T0. Procedures for doing this are described for a representative data analysis program. Results of such calculations show that expanding the T range from 10-40 to 5-45 degrees C gives significant improvement in the precision of all quantities. DeltaG degrees is typically determined with standard error a factor of approximately 30 smaller than that for DeltaH degrees. Accordingly, the error in TDeltaS degrees is nearly identical to that in DeltaH degrees. For 4% error in K degrees, the T-derivative in DeltaCP degrees cannot be determined unless it is approximately 10 cal mol-1 K-2 or greater; and DeltaCP degrees must be approximately 50 cal mol-1 K-1. Since all errors scale with the data error and inversely with the square root of the number of data points, the present results for 4% error cover any other relative error and number of points, for the same approximate T structure of the data.
Tellinghuisen
Joel
J
Department of Chemistry, Vanderbilt University, Nashville, TN 37235, United States. joel.tellinghuisen@vanderbilt.edu
D002151:Calorimetry; D008956:Models, Chemical; D015233:Models, Statistical; D011506:Proteins / Q000737:chemistry*; D013816:Thermodynamics
D011506:Proteins