An approximate model of chemical equilibrium in heterogeneous mixtures of a combustible gas with chemically inert solid or liquid particles has been suggested. It includes explicit algebraic formulas for the calculation of the molar mass of the gas, internal energy, and heat capacities of gas-particles mixture, and ordinary differential equations for the description of isentropic compression and adiabatic index of the system. The model can be also useful for the rough estimations of thermodynamic parameters of gaseous mixtures with particles of soot. As an example of a possible application of the suggested model of chemical equilibrium, parameters of stationary one-dimensional detonation wave in gas-particles mixtures are calculated. The algorithm of estimation of detonation cell size in such heterogeneous mixtures is presented. Detonation wave parameters and cell size in the stoichiometric hydrogen-oxygen mixture with particles of W, Al2O3, and SiO2 have been calculated. The results of the calculations of detonation parameters and cell sizes are used for analysis of the method of multi-front detonation wave suppression by particles injection before the leading shock front of the wave. The minimal total mass of the particles and characteristic size of the cloud, which are necessary for detonation suppression, have been calculated. It is shown that such suppression is more effective if the particles have high heat capacity, low melting point, and high heat of melting. Among the particles under consideration, the particles of Al2O3 are the best for the detonation wave suppression.