# Multiple States in an Isothermal Continuous Stirred-Tank Reactor

An irreversible reaction is carried out in an isothermal, continuous stirred-tank reactor (CSTR). The green curve in the "rate vs. concentration" plot shows the non-linear dependence of the reaction rate (). The blue line is the CSTR mass balance, and the intersections of the green curve and the blue line are the steady-state solutions to the mass balance. When three solutions are obtained, only two are stable. Changing the residence time with the slider changes the steady-state solutions, and at high and low residence times, only one solution exists. The "concentration vs. time" and "rate vs. time" plots show how the concentration and rate approach steady state when the initial reactant concentration in the reactor, which can be changed with the slider, is not the steady-state concentration. When the reactor has three steady-state solutions, if the initial reactant concentration is above the concentration for the middle steady state, then the reactant concentration in the reactor approaches the higher steady-state reactant concentration. Otherwise, it approaches the lower steady-state reactant concentration. The feed concentration to the reactor is 6.0 mol/L.

### DETAILS

Rate equations:
τ = ,
,
,
,
where is residence time (min), is reactor volume (L), is the volumetric flow rate (L/min), is reaction rate (mol/[L min]), is the steady-state rate (mol/[L min]), is the transient rate expression (mol/[L min]), is the concentration of reactant (mol/L), and and are the feed and steady-state concentrations of reactant (mol/L).
Mole balance:
,
,
where is the initial concentration of in the reactor (mol/L).
The screencast video at [1] shows how to use this Demonstration.
Reference
[1] Multiple States in an Isothermal Continuous Stirred-Tank Reactor. www.colorado.edu/learncheme/kinetics/MultipleStatesIsothermalCSTR.html.

### PERMANENT CITATION

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