The solution to the adiabatic thermal explosion problem of a dusty gas mixture is presented. The same definition of the critical state used for the homogeneous solid is used for the gas mixture. The critical trajectory is defined as the trajectory containing only one inflection point before the maximum temperature is reached in the temperature-concentration domain. In the case of the solid, the inflection point occurred before the maximum temperature. In the case of the dusty gas mixture it was found that the inflection point could occur as well at the maximum temperature. The presence of the gas produces a second critical temperature, and the limiting cases of no gas present or infinite amount of gas present lead to the classical adiabatic solid case or the case of the solid losing heat to the gas as its environment. The solution led to the discovery of three different singular solutions that help in understanding the Various trajectories in the subcritical, critical, or supercritical state.