Chemical Reactor Conversion Calculator
Calculate the required volume of a continuous stirred-tank reactor (CSTR) to achieve a target conversion for first- or second-order reactions. Essential for chemical process design and scale-up.
Last updated: September 2026
Formula below · 2 sources (aiche.org, Wikipedia) · Updated Sep 2026
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About this calculator
A continuous stirred-tank reactor (CSTR) operates at steady state with perfect mixing, so the whole vessel runs at the exit concentration C = C₀(1 − X). The CSTR design equation V = v₀·C₀·X / (−r) then gives: first order (−r = kC): V = v₀ × X / (k × (1 − X)); second order (−r = kC²): V = v₀ × X / (k × C₀ × (1 − X)²), where v₀ is the volumetric flow rate, X the fractional conversion, k the rate constant and C₀ the inlet concentration. The calculator converts the flow from L/min to L/s (÷ 60), so k must be per second (s⁻¹ for first order, L/(mol·s) for second order) and the volume comes out in litres. The residence time τ = V / v₀ is the average time a fluid element spends in the reactor. Higher desired conversion always requires a larger reactor, and the relationship becomes strongly nonlinear as conversion approaches 100%, making the last few percent very expensive. A plug-flow reactor needs less volume (first order: V = v₀·ln(1/(1 − X))/k).
How to use
Example: first-order reaction with k = 0.05 s⁻¹, flow rate 10 L/min, desired conversion X = 80%. Step 1: v₀ = 10 / 60 = 0.1667 L/s. Step 2: V = v₀ × X / (k × (1 − X)) = 0.1667 × 0.80 / (0.05 × 0.20) = 0.1333 / 0.01 = 13.33 L, a residence time of 80 s. For a second-order reaction with k = 0.05 L/(mol·s) and C₀ = 2 mol/L at the same flow and conversion: V = 0.1667 × 0.80 / (0.05 × 2 × 0.04) = 33.3 L. At the defaults (100 L/min, first order) the volume is 133.33 L.
Frequently asked questions
What is the difference between a CSTR and a plug flow reactor for achieving high conversion?
A plug flow reactor (PFR) assumes no axial mixing — fluid moves like a plug from inlet to outlet, with concentration changing along the reactor length. A CSTR assumes perfect back-mixing, so the entire vessel operates at the exit (lowest) concentration. Because CSTRs always operate at the lowest driving force, they require a larger volume than a PFR for the same conversion and kinetics. For high conversions (>90%), a PFR is significantly more efficient, while CSTRs are preferred when isothermal operation and easy control are prioritized.
How does reaction order affect the required reactor volume for a given conversion?
Reaction order determines how strongly the reaction rate depends on reactant concentration. For first-order reactions (r = k·C) the CSTR volume scales with X/(1 − X). For second-order reactions (r = k·C²) it scales with X/(1 − X)², so the rate drops off much faster as conversion increases and much larger volumes are needed for high conversion. Higher-order reactions are therefore more sensitive to conversion targets, making the choice of operating conditions and reactor type especially critical in process design.
Why does CSTR volume increase dramatically as desired conversion approaches 100%?
In a CSTR, the reaction rate throughout the vessel equals the rate at the exit concentration, which is the lowest concentration in the system. As conversion approaches 100%, exit concentration approaches zero, and the reaction rate approaches zero. To compensate for this vanishingly slow rate and still process the incoming feed, an enormous reactor volume is required. This is why industrial CSTRs rarely target conversions above 90–95% in a single stage; instead, multiple CSTRs in series or a combination with a PFR is used to approach complete conversion more economically.