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A continuous stirred-tank reactor (CSTR) is a vessel that is stirred continuously while reactants flow in and product flows out at the same rate, so the liquid inside is treated as having one uniform composition equal to the outlet stream. It is also called a backmix or mixed flow reactor. A batch reactor has no inflow or outflow, and a plug flow reactor has no mixing along its length.
Short answer
In an ideal CSTR, steady-state conversion depends only on the rate constant k and the mean residence time τ = V/v (reactor volume divided by volumetric flow). For a first-order reaction A → B, the outlet concentration is [A] = [A]0/(1 + kτ) and conversion is X = kτ/(1 + kτ) (LibreTexts, NYU CHEM-UA 652, read 2026-11-08). Real lab reactors only approximate this, and the gap is measurable.
Definition and scope
The ideal CSTR rests on three assumptions in the NYU course notes: the contents are perfectly mixed and uniform everywhere, the reactor has reached steady state after start-up, and the volume is constant because outlet flow equals inlet flow. Wikipedia’s treatment adds constant density, isothermal operation and a single irreversible nth-order reaction as the usual textbook idealisation.
Because the vessel composition equals the outlet composition, incoming reagent is diluted immediately to the (usually low) exit concentration. That dilution is both the CSTR’s main advantage, since it is less sensitive to changes in feed composition, and its main cost for most reaction orders.
How a CSTR is analysed in practice
The starting point is a mole balance on species j: dNj/dt = Fj0 − Fj + V rj. At steady state the left side is zero, which gives v([j]0 − [j]) + V rj = 0 (NYU CHEM-UA 652). Substituting a rate law and solving for the outlet concentration gives closed forms for low reaction orders; higher orders are solved numerically.
Outlet concentration by reaction order, with worked values
| Reaction order | Outlet concentration C (ideal CSTR) | Worked example (computed from the formula) |
|---|---|---|
| Zeroth | C = C0 − kτ | C0 = 1, kτ = 0.5 gives C = 0.5 (valid while kτ ≤ C0) |
| First | C = C0/(1 + kτ) | kτ = 4 gives C = 0.2 C0, so conversion X = 0.8 |
| Second | C = (−1 + √(1 + 4kτC0))/(2kτ) | C0 = 1, kτ = 4 gives C ≈ 0.39, so about 61% converted |
The formulas are from Wikipedia’s “Continuous stirred-tank reactor” article (read 2026-11-08); the worked values are arithmetic on those formulas with arbitrary units and are illustrations, not measured data. They show a useful pattern: with the same kτ = 4, a first-order reaction reaches 80% conversion but a second-order one with C0 = 1 reaches only about 61%.
Types and related concepts
CSTR versus batch and plug flow reactors
For reactions of non-zero order, a CSTR needs a larger volume than a plug flow reactor (PFR) for the same conversion at the same residence time, because the reaction runs at the low outlet concentration throughout. For zeroth-order reactions the total volume does not depend on how many reactors are used. An infinite series of ideal CSTRs is hydraulically equivalent to an ideal PFR, which is why staged CSTR cascades are used to approach plug flow behaviour (Wikipedia). Where a reaction produces an intermediate B that is the desired product, CSTRs are typically avoided in favour of batch or plug flow operation.
Related CASRAI guides
Continuous flow chemistry at small scale is covered in microreactors, which are flow reactors with a different mixing regime. A stirred-tank bioreactor uses the same stirred-vessel configuration for cell or enzyme work. Stirring and heating of small vessels at the bench is described in the hot plate stirrer guide, and a laboratory diffusion setup in the diffusion cell guide.
Where it matters for laboratories
The University of Utah chemical engineering laboratory describes its teaching CSTR as a jacketed glass reactor with fluid circulated through the jacket, and with mixer speed and pump rates under computer control. Its equipment description states that ideal reactors do not exist in laboratories and that perfect mixing should not be assumed. Wikipedia likewise notes that perfect mixing is a theoretical concept that is not achievable in practice.
Checklist: ideal assumption versus real laboratory reactor
| Ideal assumption | What the sources say about the real reactor |
|---|---|
| Perfect mixing | Not achievable in practice; dead space and short-circuiting shorten the effective residence time (Wikipedia) |
| Steady state | Reached only after start-up; outlet flow must equal inlet flow (NYU notes; Utah description: Qf = Qe at steady state) |
| Uniform contents | Non-ideality is characterised by dead-zone volumes and bypass flow, calculated from a residence-time distribution (RTD) measured with an inert tracer (Utah description) |
| Known instrument settings | Calibrations are done before experiments (Utah description) |
Sources: University of Utah chemical engineering CSTR equipment description (my.che.utah.edu/~tony/chen4903/equipment/R_CSTR), read 2026-11-08.
Common misunderstandings
- A CSTR is not a stirred batch vessel. A batch reactor has no flow in or out and its composition changes with time; a CSTR operates at steady state with continuous flow.
- Perfect mixing is not real. It is a modelling assumption. A tracer experiment can show how far a given vessel departs from it.
- Residence time is not reaction time in a batch sense. τ = V/v is a mean; individual molecules spend different times in the vessel, which is the reason the RTD is measured.
- More stirring does not remove the volume penalty. The larger volume versus a PFR for non-zero-order reactions follows from the uniform low outlet concentration, not from poor mixing.
FAQ
What is another name for a CSTR?
Vat reactor, backmix reactor or mixed flow reactor (Wikipedia).
What does the residence time τ mean?
τ = V/v, the reactor volume divided by the volumetric flow rate (NYU CHEM-UA 652).
How do I calculate conversion for a first-order reaction in an ideal CSTR?
X = kτ/(1 + kτ). With kτ = 4, X = 0.8.
Why is a CSTR larger than a PFR for the same conversion?
For reactions that are not zeroth order, the whole vessel runs at the outlet concentration, which lowers the rate compared with a plug flow reactor (Wikipedia).
Sources
- LibreTexts, NYU CHEM-UA 652, “1.23 Continuously stirred tank reactors”, chem.libretexts.org, read 2026-11-08.
- Wikipedia, “Continuous stirred-tank reactor”, en.wikipedia.org/wiki/Continuous_stirred-tank_reactor, read 2026-11-08 (secondary source).
- University of Utah Chemical Engineering, CSTR equipment description, my.che.utah.edu/~tony/chen4903/equipment/R_CSTR, read 2026-11-08.
