Convective instability driven by surface tension is analyzed in an initially quiescent water absorbing ammonia gas with heat transfer using the linear stability analysis. The propagation theory is adapted to find the critical conditions of the onset of Marangoni convection. In this theory, the solutal penetration depth is chosen as the length scale factor. The results show that the liquid layer becomes more stable with decreasing the Schmidt number and increasing the Lewis number. It is also found that there is a critical Biot number to make the liquid layer be most unstable, and there is a linear relationship between the thor-mal Marangoni number and the solutal Marangoni number.