Deep convective clouds can efficiently transport trace gases from the planetary boundary layer to the upper troposphere. Once there, some gases will contribute to new particle formation and growth, eventually producing aerosols that are large enough to influence cloud properties, the radiative budget of the Earth, and climate. The magnitude and exact pathways of the convective transport of many organic and inorganic compounds are, however, still unclear. This dissertation presents a framework to study vertical transport of gas mixtures by deep convective clouds. The method consists of a chemical box model that is driven by cloud air parcel trajectory data generated by large-eddy simulation. This combination allows us to examine detailed gas-cloud interactions as well as complex systems of gas-phase chemical reactions. A large ensemble of simulated cloud trajectories was used to identify and characterize convective up- and downdrafts in the Amazon region. The analysis showed that air parcels starting close to the surface (at 0.5 km) experienced a substantially larger probability of reaching the upper troposphere (above 10 km) than parcels starting at the top of the boundary layer. Furthermore, the framework was used to estimate the vertical transport of isoprene, isoprene oxidation products, ammonia, and several non-reactive trace gases. We found that a typical Amazonian deep convective cloud can transport around 30% of the boundary layer isoprene to the cloud outflow if the efficiency of the gas uptake on ice is high and there is no lightning within the cloud. If the efficiency of gas uptake on ice is low and lightning within the cloud is extensive, all isoprene will be oxidized. Several low-volatility isoprene oxidation products will then have relatively high concentrations in the outflow, which potentially could lead to new particle formation and growth. Another result was that up to 10% of the boundary layer ammonia can reach the cloud outflow, where it in some environments can nucleate synergistically with nitric and sulfuric acid. A key uncertainty in our estimates is the efficiency of gas uptake by ice particles.