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Liquid mixtures, which have a phase diagram exhibiting a miscibility gap ending in a critical point of solution, have been used as solvents for chemical reactions. The reaction rate in the forward direction has often been observed to slow down as a function of temperature in the critical region. Theories based upon the Gibbs free energy of reaction as the driving force for chemical change have been invoked to explain this behavior. With the assumption that the reaction is proceeding under relaxation conditions, these theories expand the free energy in a Taylor series about the position of equilibrium. Since the free energy is zero at equilibrium, the leading term in the Taylor series is proportional to the first derivative of the free energy with respect to the extent of reaction. To analyze the critical behavior of this derivative, the theories exploit the principle of critical point isomorphism, which is thought to govern all critical phenomena. They find that the derivative goes to zero in the critical region, which accounts for the slowing down observed in the reaction rate. As has been pointed out, however, most experimental rate investigations have been carried out under irreversible conditions as opposed to relaxation conditions [Shen et al. J. Phys. Chem. A 2015, 119, 8784-8791]. Below, we consider a reaction governed by first order kinetics and invoke transition state theory to take into account the irreversible conditions. We express the apparent activation energy in terms of thermodynamic derivatives evaluated under standard conditions as well as the pseudoequilibrium conditions associated with the reactant and the activated complex. We show that these derivatives approach infinity in the critical region. The apparent activation energy follows this behavior, and its divergence accounts for the slowing down of the reaction rate. [ABSTRACT FROM AUTHOR]

Rate constants for the gas-phase reactions of OH radical, NO3radical, and ozone with allyl alcohol (AAL) and allyl isocyanate (AIC) have been measured using relative rate methods at atmospheric pressure in purified air. The experimental Arrhenius expression obtained for the reaction of the OH radical with AAL is (1.68 ± 0.89) × 10−12× exp(1100/T) cm3molecule−1s−1, for T= 282−315 K; the Arrhenius expression for the reaction of OH radical with AIC is (1.94 ± 1.04) × 10−14× exp(2207/T) cm3molecule−1s−1, for T= 282−317 K, where the indicated errors are one least-squares standard deviation. All OH radical reaction rate constants have been measured relative to k(OH + α-pinene) and k(OH + 1,3,5-trimethylbenzene). The rate constant for the gas-phase reaction of OH radical with allyl alcohol-d6isotopomer (AAL-d6) has been measured at T= 298 K, and the value is 5.10 × 10−11cm3molecule−1s−1. The kinetic isotope effect is small, with k(AAL)/k(AAL-d6) = 1.32. Rate constants for the gas-phase reactions of NO3radical with AAL [relative to k(NO3+methacrolein)] and O3[relative to k(O3+ β-pinene)] have been measured, and the values are 7.7 × 10−15cm3molecule−1s−1at T= 298 K and 1.6 × 10−17cm3molecule−1s−1at T= 296 K, respectively. Rate constants for the gas-phase reactions of NO3radical and O3with AIC have been measured, and the values are 9.4 × 10−16cm3molecule−1s−1at T= 299 K and 5.54 × 10−18cm3molecule−1s−1at T= 299 K, respectively. Multireference ab initio calculations at the MRMP2/6-311G(d,p) level have been carried out for reactions of OH radical with AAL and AIC. Results indicate that prereactive hydrogen bonded complexes form in the entrance channels for these reactions. [ABSTRACT FROM AUTHOR]