Choose the value to solve: CSTR reactor volume, exit reaction rate, conversion, or inlet reactant molar flow rate. Enter the other three values with their units.

Steady-state, perfectly mixed CSTR model. Use the reaction rate at reactor exit conditions. Zero results are algebraic limiting cases, not operating-reactor designs.

For 60% conversion, enter 0.60.

Related Calculators

Reactor Volume Formula

This calculator uses the steady-state CSTR design equation in terms of reactant molar flow rate, conversion, reaction rate, and reactor volume.

VR = (FA0X) / (- rA)
- rA = (FA0X) / (VR)
X = ((- rA)VR) / (FA0)
FA0 = ((- rA)VR) / (X)
  • VR = reactor volume
  • FA0 = inlet molar flow rate of reactant A
  • X = conversion, entered as a decimal from 0 to 1
  • -rA = rate of disappearance of reactant A, entered as a nonnegative magnitude at reactor exit conditions

The reactor volume function solves for VR when you know flow rate, conversion, and reaction rate.

The reaction rate function rearranges the same equation to solve for -rA.

The conversion function solves for X. Values implying conversion above 1 are rejected; check the inputs. Zero-denominator cases cannot determine a valid unique result.

The molar flow rate function solves for FA0 when reactor volume, conversion, and reaction rate are known.

Unit Conversions Used in the Reactor Volume Calculation

Quantity Input unit Base unit used Conversion to base unit
Reaction rate mol/(L·s) mol/(L·s) multiply by 1
Reaction rate mol/(m³·s) mol/(L·s) multiply by 0.001
Molar flow rate kmol/s mol/s multiply by 1000
Molar flow rate mol/min mol/s divide by 60
Reactor volume m³ L multiply by 1000
Reactor volume US gal L multiply by 3.785411784

Conversion Values and Meaning

Conversion X Percent conversion Meaning
0.10 10% 10% of reactant A is consumed.
0.50 50% Half of reactant A is consumed.
0.90 90% Most of reactant A is consumed.
1.00 100% Complete conversion in the equation.

Example Reactor Volume Calculations

Example 1: Calculate reactor volume

You have a molar flow rate of 4 mol/s, a conversion of 0.75, and a reaction rate of 0.20 mol/(L·s).

VR = (FA0X) / (- rA)
VR = (4(0.75)) / (0.20) = 15 L

The required reactor volume is 15 L.

Example 2: Calculate conversion

You have a reaction rate of 0.05 mol/(L·s), a reactor volume of 80 L, and a molar flow rate of 10 mol/s.

X = ((- rA)VR) / (FA0)
X = (0.05(80)) / (10) = 0.40

The conversion is 0.40, or 40%.

Reactor Volume Calculator FAQ

Why is the reaction rate entered as a positive value?

For a reactant, the rate of disappearance is written as -rA. The negative sign shows that reactant A is being consumed. In the design equation, -rA is treated as a positive rate value, so you should enter the magnitude only.

What type of reactor does this equation apply to?

This form applies to a continuous stirred tank reactor, or CSTR, when the reaction rate used is the rate at the reactor exit conditions. It is not the plug flow reactor design equation.

What should I enter for conversion?

Enter conversion as a decimal. For example, enter 60% conversion as 0.60. Normal conversion values are between 0 and 1. A value of 1 means 100% conversion.