A numerical model for a drop convective cloud with detailed microphysics, chemistry, and radiation is presented. The condensation and coagulation processes are described with the help of a kinetic equation. The coagulation is calculated using a modification of the well-known Kowetz-Alund method. The chemical model includes about 150 gas-phase reactions (with a detailed description of transformations in the oxygen, nitrogen, hydrogen, chlorine, sulfur, methane, and ethane cycles) and about 110 aqueous-phase reactions (including both the interphase and aqueous-phase steady-state reactions) that account for diffusion and gas absorption on the cloud drop surfaces. The photodissociation rates in the radiative transfer module are calculated using the delta-Eddington scheme. The results of numerical experiments indicate that convective clouds in the troposphere tend to decrease the concentrations of highly soluble species due to their capture by the cloud drops and further precipitation scavenging. The vertical transport in convective clouds significantly affects the concentrations of slightly soluble gases. The radiative processes in clouds have a profound impact on the concentrations of short-lived gaseous species. It is also shown that the aqueous-phase chemistry calculations must include not only the chemical reactions but also the species redistribution over drop sizes during condensation-evaporation and coagulation processes.