The results of our thermogravimetric experiments on the decompositions of dolomite crystals and powders and some data reported in the literature were used for the determination of the E parameter of the Arrhenius equation by the third-law method and estimation of the self-cooling effect on the results of these determinations. The experimental values of the E parameters, obtained under different conditions by the third-law method, are in excellent agreement with the theoretically predicted values based on the mechanism of congruent decomposition of CaMg(CO3)(2) into gaseous CO2, CaO and MgO with the simultaneous condensation of low-volatility CaO and MgO molecules. The second important result of this study is the first quantitative comparison of absolute rates of decomposition of powder samples and single crystals. Based on these results, a simple procedure was proposed for the determination of the E parameter by the third-law method from the data obtained for powder samples. It consists in the evaluation of the absolute decomposition rate of a powder sample (reduced to the unit of the outer surface area of a pellet formed by the powder sample in a cylindrical crucible). The value received is lowered by the empirical factor and then used for the calculation of the E parameter by the third-law method. The value of this factor (2.8 +/- 0.4) does not depend on the temperature, residual pressure of air in the reactor, grain size and mass of a powder sample. This procedure permits to expand the application of the third-law method to the determination of decomposition kinetics for many solids available only in the powder form.