Electrochemical CO2 reduction (CO2R) using renewable electricity is a key pathway toward synthesizing fuels and chemicals. In this study, multi-physics modeling is used to interpret experimental data obtained for CO2R to CO using Ag catalysts in a membrane electrode assembly. The one-dimensional model is validated using measured CO2 crossover and product formation rates. The kinetics of CO formation are described by Marcus–Hush–Chidsey kinetics, which enables accurate prediction of the experimental data by accounting for the reorganization of the solvent during CO2R. The results show how the performance is dictated by competing phenomena including ion formation and transport, CO2 solubility, and water management. The model shows that increasing the ion-exchange capacity of the membrane and surface area of the catalyst increases CO formation rates by >100 mA cm–2 without negatively impacting CO2 utilization. Here we provide insights into how to manage the trade-off between productivity and CO2 utilization in CO2 electrolyzers. The design of CO2 electrolyzers is complicated by coupled transport and reaction phenomena. Here the authors develop a continuum model incorporating physical phenomena across multiple scales to predict the activity and selectivity of CO2 electrolysis, along with the loss of CO2 due to crossover in membrane electrode assemblies.