We use ALMA observations of four sub-millimetre galaxies ( SMGs ) at z \sim 2 - 3 to investigate the spatially resolved properties of the inter-stellar medium ( ISM ) at scales of 1–5 kpc ( 0.1–0.6 ^ { \prime \prime } ) . The velocity fields of our sources , traced by the ^ { 12 } CO ( J =3-2 ) emission , are consistent with disk rotation to first order , implying average dynamical masses of \sim 3 \times 10 ^ { 11 } M _ { \odot } within two half-light radii . Through a Bayesian approach we investigate the uncertainties inherent to dynamically constraining total gas masses . We explore the covariance between the stellar mass-to-light ratio and CO-to-H _ { 2 } conversion factor , \alpha _ { CO } , finding values of \alpha _ { CO } = 1.1 ^ { +0.8 } _ { -0.7 } for dark matter fractions of 15 % . We show that the resolved spatial distribution of the gas and dust continuum can be uncorrelated to the stellar emission , challenging energy balance assumptions in global SED fitting . Through a stacking analysis of the resolved radial profiles of the CO ( 3-2 ) , stellar and dust continuum emission in SMG samples , we find that the cool molecular gas emission in these sources ( radii \sim 5–14 kpc ) is clearly more extended than the rest-frame \sim 250 \mu m dust continuum by a factor > 2 . We propose that assuming a constant dust-to-gas ratio , this apparent difference in sizes can be explained by temperature and optical-depth gradients alone . Our results suggest that caution must be exercised when extrapolating morphological properties of dust continuum observations to conclusions about the molecular gas phase of the ISM .