We present ALMA Band 9 observations of the C II158 μm emission for a sample of 10 main-sequence galaxies at redshift z ˜ 2, with typical stellar masses (log M⋆/M⊙ ˜ 10.0-10.9) and star formation rates (˜35-115 M⊙ yr-1). Given the strong and well-understood evolution of the interstellar medium from the present to z = 2, we investigate the behaviour of the C II emission and empirically identify its primary driver. We detect C II from six galaxies (four secure and two tentative) and estimate ensemble averages including non-detections. The C II-to-infrared luminosity ratio (C II/LIR) of our sample is similar to that of local main-sequence galaxies (˜2 × 10-3), and ˜10 times higher than that of starbursts. The C II emission has an average spatial extent of 4-7 kpc, consistent with the optical size. Complementing our sample with literature data, we find that the C II luminosity correlates with galaxies' molecular gas mass, with a mean absolute deviation of 0.2 dex and without evident systematics: the C II-to-H2 conversion factor (α _C II ˜ 30 M⊙/L⊙) is largely independent of galaxies' depletion time, metallicity, and redshift. C II seems therefore a convenient tracer to estimate galaxies' molecular gas content regardless of their starburst or main-sequence nature, and extending to metal-poor galaxies at low and high redshifts. The dearth of C II emission reported for z > 6-7 galaxies might suggest either a high star formation efficiency or a small fraction of ultraviolet light from star formation reprocessed by dust.