$\textit{In situ}$ environmental transmission electron microscopy (ETEM) is a powerful tool for observing structural modifications taking place in heterogeneous catalysts under reaction conditions. However, to strengthen the link between catalyst structure and functionality, an $\textit{operando}$ measurement must be performed in which reaction kinetics and catalyst structure are simultaneously determined... To determine chemical kinetics for gas-phase catalysis, it is necessary to develop a reliable chemical engineering model to describe catalysis as well as heat and mass transport processes within the ETEM cell. Here, we establish a finite element model to determine the gas and temperature profiles during catalysis in an open-cell operando ETEM experiment. The model is applied to a $SiO_2$-supported Ru catalyst performing CO oxidation. Good agreement is achieved between simulated compositions and those measured experimentally across a temperature range of 25 - 350 {\deg}C. In general, for lower conversions, the simulations show that the temperature and gas are relatively homogeneous within the hot zone of the TEM holder where the catalyst is located. The uniformity of gas and temperature indicates that the ETEM reactor system behavior approximates that of a continuously stirred tank reactor. The large degree of gas-phase uniformity also allows one to estimate the catalytic conversion of reactants in the cell to within 10 percent using electron energy-loss spectroscopy. Moreover, the findings indicate that for reactant conversions below 30 percent, one can reliably evaluate the steady-state reaction rate of catalyst nanoparticles that are imaged on the TEM grid. (read more)