  $\textit{In situ}$ 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.
