**Multiple States in an Isothermal Continuous Stirred-Tank Reactor**

The reaction A→B, for which the kinetics are nonlinear, is carried out in an isothermal, continuous stirred-tank reactor (CSTR). Over a range of residence times, as shown in the rate versus reactant concentration plot, the reactor has three steady-state solutions, of which two are stable. The rate versus concentration plot shows the nonlinear rate dependence on concentration (red curve) and the mass balance (blue line). You can vary the reactor residence time in the rate versus concentration plot to determine conditions where either one or three steady states exist. The concentration versus time and the rate versus time plots show the approach to steady state for a user-selected initial reactant concentration in the reactor. These plots are obtained by solving the unsteady-state mass balance, and show that the concentration approaches one of the two stable states (when three steady-state solutions exist), depending on whether the starting concentration is above or below the concentration of the unstable state.

**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).