A mathematical model of gas detonation of fuel-enriched mixtures of hydrocarbons with oxygen has been formulated, which makes it possible to numerically study the equilibrium flows of detonation products in the presence of free carbon condensation. Reference data for graphite were used to describe the thermodynamic properties of carbon condensate. The calculations are compared with the known results of experimental studies in which, when detonating an acetylene-oxygen mixture in a pipe closed at one end, it is possible to obtain nanoscale particles from a carbon material with special properties. It is assumed that the melting point of such a material is lower than that of graphite and is about 3100 K. Only with such an adjustment of the melting temperature, the best agreement (with an accuracy of about 3 %) was obtained between the calculated and experimental dependence of the detonation front velocity on the molar fraction of acetylene in the mixture.