rate in a closed system with only one reaction. This is an unfortunate mistake that has confused many students over the years. According to the law of mass action the forward reaction rate can be written as and the backward reaction rate as The rate at which substance A is produced is thus and since, at equilibrium, the concentration of A is constant we get or, rearranged Ideal tank reactor/continuously stirred tank reactor The continuously mixed tank reactor is an open system with an influent stream of reactants and an effluent stream of products. A lake can be regarded as a tank reactor, and lakes with long turnover times (e.g. with low flux-to-volume ratios) can for many purposes be regarded as continuously stirred (e.g. homogeneous in all respects). The mass balance then becomes where Q0 and Q denote the volumetric flow in and out of the system respectively and CA,0 and CA the concentration of A in the inflow and outflow respective. In an open system we can never reach a chemical equilibrium. We can, however, reach a steady state where all state variables (temperature, concentrations, etc.) remain constant (). Example Consider a bathtub in which there is some bathing salt dissolved. We now fill in more water, keeping the bottom plug in. What happens? Since there is no reaction, and since there is no outflow . The mass balance becomes or Using a mass balance for total volume, however, it is evident that and that . Thus we get Note that there is no reaction and hence no reaction rate or rate law involved, and yet . We can thus draw the conclusion that reaction rate can not be defined in a general manner using . One must first write down a mass balance before a link between and the reaction rate can be found. Many textbooks, however, define reaction rate as without mentioning that this definition implicitly assumes that the system is closed, has a constant volume and that there is only one reaction. Ideal plug flow reactor (PFR) The idealized plug flow reactor is an open system resembling a tube with no mixing in the direction of flow but perfect mixing perpendicular to the direction of flow, often used for systems like rivers and water pipes if the flow is turbulent. When a mass balance is made for a tube, one first considers an infinitesimal part of