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# Batch Reactors at Constant Volume or Constant Pressure

Fractional conversion versus dimensionless time is plotted for an irreversible, gas-phase reaction in two isothermal batch reactors. Both reactors start at the same initial conditions, but one is at constant volume and the other is at constant pressure. Select the final conversion in both reactors with a slider. Use sliders to change the stoichiometric coefficient () and the reaction order. If the reaction order is one or if the stoichiometric coefficient is one, the two curves are identical, so only one curve is seen. In the constant-pressure reactor, the reactant concentration changes because of reaction, but it also changes when the stoichiometric coefficient is not one because of the reactor volume change due to the mole change.

### DETAILS

The reaction is , follows the rate equation .
The mole balance for a constant-volume batch reactor is given by:
, which simplifies to ,
, which simplifies to ,
.
The mole balance for a constant-pressure batch reactor is given by:
,
,
,
,
,
,
where and are the concentrations of the reactant and product (mol/L), and are moles of reactant and product (mol), is reactor volume (L), is the rate constant, is reactor temperature (K), is the ideal gas constant (J/[mol K]), is the pressure inside the reactor (bar), is the reaction order, and is the stoichiometric coefficient of .
For a first-order isothermal reaction, the time to reach a given conversion is the same for constant-pressure and constant-volume reactors. Also, the time is the same for a reaction of any order if there is no change in the number of moles. If the number of moles increases and the reaction order is greater than 1, then it takes longer to reach the same conversion point in the constant-pressure reactor, because the volume increases as the reaction proceeds, thus decreasing the reactant concentration and lowering the reaction rate.
The screencast video at [1] shows how to use this Demonstration.
Reference
[1] Batch Reactors at Constant Volume or Constant Pressure. www.colorado.edu/learncheme/kinetics/BatchReactorConstantPorV.html.

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