  The composition of gas and solids in protoplanetary discs sets the
composition of planets that form out of them. Recent chemical models have shown
that the composition of gas and dust in discs evolves on Myr time-scales, with
volatile species disappearing from the gas phase. However, discs evolve due to
gas accretion and radial drift of dust on time-scales similar to these chemical
time-scales. Here we present the first model coupling the chemical evolution in
the disc mid-planes with the evolution of discs due to accretion and radial
drift of dust. Our models show that transport will always overcome the
depletion of CO$_2$ from the gas phase, and can also overcome the depletion of
CO and CH$_4$ unless both transport is slow (viscous $\alpha \lesssim 10^{-3}$)
and the ionization rate is high ($\zeta \approx 10^{-17}$). Including radial
drift further enhances the abundances of volatile species because they are
carried in on the surface of grains before evaporating left at their ice lines.
Due to large differences in the abundances within 10 au for models with and
without efficient radial drift, we argue that composition can be used to
constrain models of planet formation via pebble accretion.
