Optimal methods for estimating kinetic isotope effects from different forms of the Rayleigh distillation equation

Abstract The interpretation of stable isotope values hinges on precise, accurate estimates of kinetic isotope effects (α), which are equal to 1 k/ 2 k, where 1 k and 2 k are the reaction rate constants for the two isotopes. Kinetic isotope effects are commonly determined by monitoring the reactant concentration ( C ) and isotope ratio ( R ) relative to their initial values ( C 1 and R 1 , respectively). Values of α are estimated from the C and R values by using the Rayleigh distillation equation (RDE). (A) (R/R 1 )=(C/C 1 ) 1/α−1 We conducted simulation experiments to evaluate the precision of the many different published approaches of estimating α from linearized versions of the RDE and reached the following conclusions: (a) kinetic isotope effects estimated from the slope of the line ln( R ) vs. ln( C ) were accurate and precise; (b) regressing ln( R i / R j ) on ln( C i / C j ), where all i datapoints were compared to all preceding datapoints j resulted in inflated 95% confidence intervals; (c) forcing the regression of ln( R / R 1 ) on ln( C / C 1 ) through the origin resulted in 95% confidence intervals for α that covered the true value less than 90% of the time; and (d) regression methods that compensate for errors in both x and y values need to be used with caution. When combining multiple datasets, values of α were sensitive to the form of the equation and the level of error. If all datasets had the same level of error, the optimal estimate of α was achieved by a linear regression with dummy variables. However, when the three datasets had different levels of error, the optimal estimate of α and much narrower 95% confidence intervals were obtained by using the Pitman estimator. Our study demonstrates that some of the other methods jeopardize the accuracy and precision of empirically determined kinetic isotope effects, thus confounding the interpretation of stable isotope values in the environment.