The gaseous mobile phase has hardly any effect on the thermodynamics of retention, i.e. on the distribution of the analyte between the mobile phase and the stationary phase. The main factors determining retention are the pure-component vapour pressure of the analyte and its (infinite dilution) activity coefficient in the stationary phase. Both parameters are affected by the temperature. The selectivity (a) is solely determined by the ratio of the thermodynamic distribution coefficients and thus also barely affected by the nature of the mobile phase.
Retention times may be affected, because different gases exhibit different diffusion coefficients for the analyte. Diffusion is faster in lighter gases, i.e. faster in hydrogen than in helium, while diffusion in helium is in turn much faster than that in nitrogen. As a result, at the same optimum reduced velocity, the actual optimum velocity is highest in hydrogen (see figure).
Hydrogen also has the lowest viscosity (and nitrogen the highest).
Fundamentally and economically, hydrogen is the best choice, but helium is often preferred for safety reasons. Nitrogen is much-less favourable, but it is both safe and cheap.
For more on GC mobile phases see Module 2.8
