10217

# Batch Reactors at Constant Volume or Constant Pressure

This Demonstration compares the time for an irreversible, gas-phase reaction to reach a certain fractional conversion in an isothermal batch reactor operating either at constant volume or at constant pressure. Both reactors start at the same initial conditions. If the reaction involves a mole change and the rate of reaction is not zero or first-order, then the time to reach a certain conversion is different for the two types of reactors; in a constant-pressure reactor, the reactant concentration changes because of the volume change due to the mole change.

### DETAILS

The reaction is , which 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:
,
,
,
,
,
.
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.
= concentration of reactant
= concentration of product
= moles of reactant
= moles of product
= volume of reactor
= rate constant
= temperature of reactor
= ideal gas constant
= pressure inside reactor
= reaction order
= mole change

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