Effects of self-heating during the thermal decomposition of di-t-butyl peroxide. Anomalous reaction orders and activation energies, and their correction

Abstract

Self-heating accompanying an exothermic reaction that has a positive activation energy enhances the reaction rate. This means that measured reaction orders and rate constants (and hence the effective activation energy) are no longer the true, isothermal values. Theories have been formulated to assess the magnitude of the discrepancies and the way in which they are controlled by conditions. Now it is possible to write down an approximate, but very precise, algebraic expression for the proportionate errors (ΔE/E and Δn/n) in terms of the measured, centre-temperature excesses that are generated within a spherically shaped reacting mass. This is an important development because the sphere has only recently yielded to satisfactory analytical interpretations of self-heating and criticality, yet its finite dimensions make it the shape, amongst class A geometries, that is an archetype for most practical cases.

The objective in the present study is thus to show whether or not the theoretical predictions for anomalous orders and activation energies are quantitatively satisfactory.

The subject for experimental investigation is di-t-butyl peroxide. Its thermal decomposition is studied over the temperature range 420–510 K at low pressures of the pure vapour (< 10 Torr) in a spherical vessel (1 dm³). Pressure increases are monitored continuously by transducer and internal temperature changes measured by a very fine thermocouple.

At the lowest temperature, decomposition remains virtually isothermal; we observe a first-order dependence of initial rate on initial pressure, and we measure an overall isothermal activation energy consistent with reported values. At higher temperatures, approaching but still below those at which ignition occurs (T_a < 460 K), self-heating accompanies reaction and centre-temperature excesses of up to 15 K are measured. They are quasi-steady maxima, achieved within 2 s of entry of reactant to the vessel; there is a subsequent decline, and from ca. 20 s on the reaction is virtually isothermal. Reaction times, characterized by successive ‘quarter-lives’, are considerably shorter during the first interval than the subsequent isothermal periods. Where self-heating occurs, enhanced reaction orders are measured, rising as (ΔT₀)_max increases, and in carefully chosen circumstances curvature of a log (dp/dt)₀ against log p₀ plot is seen. The same is true for effective activation energies, and we show a curved Arrhenius plot (In k against 1/T_a). The measured activation energy can easily exceed the isothermal value by 50% because of self-heating. The anomalous reaction orders and activation energies predicted from theory are in very good agreement with the experimental values. We show that retrospective correction of kinetic data, influenced by self-heating, can be very successful.