Calculate CSTR reactor volume, reaction rate, conversion, or reactant molar flow rate from any 3 known values and units in mol/s and L.
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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.
V_R = \frac{F_{A0}X}{-r_A}-r_A = \frac{F_{A0}X}{V_R}X = \frac{(-r_A)V_R}{F_{A0}}F_{A0} = \frac{(-r_A)V_R}{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 positive value
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. A result above 1 means the entered values imply more than 100% conversion, so you should check the inputs.
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 3.78541 |
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).
V_R = \frac{F_{A0}X}{-r_A}V_R = \frac{4(0.75)}{0.20} = 15\text{ 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 = \frac{(-r_A)V_R}{F_{A0}}X = \frac{0.05(80)}{10} = 0.40The 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.