Closed form expressions for the fully developed velocity, temperature and concentration profiles in a vertical channel are found by solving the equations for a cavity in the limit as the aspect ratio tends to infinity. We consider plane, steady, laminar, Boussinesq flow of an ideal gas-vapour mixture. The vertical walls are held at different constant temperatures and compositions, are impermeable to the gas and nonslip. The finite mass transfer effects of interfacial velocity and interdiffusion of enthalpy are included.