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At steady state, the rate of reaction is constant within the CSTR, so that the total moles reacted per time equals reaction rate times volume:

where and are the inlet and outlet molar flow rates of reactant , is rate of reaction (mol/L s) of and is reactor volume. This equation may be expressed in terms of residence time , conversion and inlet concentration of , :

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The rate expression is a function of reactant concentrations and the rate constant :

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The rate constant increases with temperature according to the Arrhenius equation:

where is the pre-exponential factor, is the activation energy of the reaction, is the gas constant and is absolute temperature. Energy released from exothermic reactions causes the reactor contents (and the reactor effluent) to have a higher temperature than the inlet:

where is the total molar flow rate at the inlet or outlet, is the molar heat capacity of the mixture within the reactor, is temperature at the inlet and is the heat of reaction.