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Size a continuous stirred-tank reactor (CSTR) for a first-order reaction: V = F·X / (k·C₀·(1−X)). Enter molar flow, rate constant, inlet concentration, and target conversion for the required volume in litres.
Size a first-order CSTR from flow, conversion, and rate constant.
V = F·X / (k·C₀·(1−X)) [first-order CSTR, litres]
Assumes steady state, perfect mixing, constant density, and first-order kinetics −r = k·C. Real designs add safety factors (typically 10–25%).
| Symbol | Meaning |
|---|---|
| F | Molar flow rate (mol/s) |
| k | First-order rate constant (1/s) |
| C₀ | Inlet concentration (mol/L) |
| X | Target fractional conversion (0–1 exclusive) |
F = 2 mol/s, k = 0.5 /s, C₀ = 1 mol/L, X = 0.8 → V = 1.6/(0.5×0.2) = 16 L.
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The (1−X) term: pushing the last reactant percent needs disproportionately more residence time — classic CSTR behavior.
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Content updated: September 2026