The onset of buoyancy-driven convection caused by gas absorption through the upper free boundary of an initially quiescent, horizontal liquid layer is analyzed under linear theory. It is well-known that convective motion sets in when the Rayleigh number (Ra) exceeds a certain value. In this study, the critical conditions to mark the onset of convective instability are analyzed using the dominant mode method and frozen-time model for large Ra values. The results are compared with those from the propagation theory and also the amplification theory. The dominant mode method yields the stability criteria, which agree well with those from the propagation theory. Therefore, the latter results are compared with available experimental data. It is shown that the initiated instabilities grow until detected experimentally and the upper free interface often behaves similar to a rigid one.