The initial ∼60% of an isothermal vacuum dehydration of goethite can commonly be approximated by first order kinetics. Also, natural goethites contain small amounts of an Fe(CO
3)OH component in apparent solid solution. The
18O/
16O of CO
2 evolved from the Fe(CO
3)OH during isothermal vacuum dehydrations is related to the
18O/
16O of the goethite by an apparent fractionation factor (
αapp) that is, in turn, correlated with a first order rate constant, |
m|. A kinetic exchange model predicts that
αapp should decrease as |
m| increases for a range of |
m| that corresponds to relatively slow rates of dehydration. This pattern has been observed in published results. In contrast, for rapid rates of dehydration,
αapp is predicted to increase with increasing |
m|. Isothermal vacuum dehydrations of two natural goethites had unusually large values of |
m| and provided serendipitous tests of this rapid-rate prediction. For these experiments, the measured values of
αapp were consistent with patterns of variation predicted by the model. This allowed an estimate of the activation energy (
E2) of a model parameter,
K2, which is the rate constant for oxygen
isotope exchange between CO
2 and H
2O during the solid-state goethite to hematite phase transition. The estimated value of
E2 is only ∼9 kJ/mol. Heterogeneous catalysis tends to decrease the activation energies of gas reactions. Consequently, the inferred value of
E2 suggests that goethite and/or hematite catalyze oxygen
isotope exchange between CO
2 and H
2O during the solid-state phase change.
Yield, δ13C, and δ18O values are routinely measured for increments of CO2 evolved from the Fe(CO3)OH component during isothermal vacuum dehydration of goethite. Model-predicted values of αapp can be combined with plateau δ18O values of the evolved CO2 to estimate the δ18O of the goethite with a less than optimal, but potentially useful, precision of about ±0.8‰. Therefore, a single analytical procedure (incremental dehydration) applied to one aliquot of a sample could provide not only δ13C and mole fractions (X) of the Fe(CO3)OH component, but also hydrogen yield, δD, and the approximate δ18O value of the goethite. Recovery of multiple types of geochemical data from a single aliquot would be particularly useful if the amount of sample available for analysis were limited. Also, the method could be used to estimate the δ18O value of goethite in mixtures of minerals not amenable to selective dissolution – e.g., goethite admixed with hematite.
