CHE-09

CSTR conversion (first order)

X = τ k / (1 + τ k) for irreversible first-order liquid.

Reading speed

ReactorsCSTR

Governing equation

X=\dfrac{\tau k}{1+\tau k}

$\tau \in \left[1, 600\right]$

where

\tau: Space time (s)
k: Rate constant (1/s)
X: Conversion (—)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

X=\dfrac{\tau k}{1+\tau k}

$\tau \in \left[1, 600\right]$

$\tau = 1$ $X = 0.02$

Along the curve

②

Domain of the variable — blue

\tau_{\min} = 1,\quad \tau_{\max} = 600

$\tau \in \left[1, 600\right]$

$\tau = 1$ $\tau = 1$

Along the curve

③

Response curve — green

X=\dfrac{\tau k}{1+\tau k}

$\tau \in \left[1, 600\right]$

$\tau = 1$ $X = 0.02$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}X}{\mathrm{d}\tau}

$\tau \in \left[1, 600\right]$

$\tau = 4.767$ $X^{\prime} = 0.017$

Along the curve

Lecture brief

Historical brief

From CSTR/PFR mole balances and Arrhenius rates to McCabe–Thiele stages and NTU exchangers, chemical engineering is conservation plus equilibrium. The lab is that design arithmetic. This sheet (CHE-09 — CSTR conversion (first order)) is the form associated with CSTR. Working symbols: $\tau$ , $k$ $\rightarrow$ $X$ . Mass balance: F_in − F_out + r V = 0. τ = V/v0.

Purpose

Purpose: compute

X

from

\tau

k

in Chemical engineering via

X=\dfrac{\tau k}{1+\tau k}

X = τ k / (1 + τ k) for irreversible first-order liquid. Use it when a real chemical engineering question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\tau = 60.000\,\mathrm{s}

k = 0.020\,\mathrm{1/s}

, the governing relation

X=\dfrac{\tau k}{1+\tau k}

yields

X = 0.545\,\mathrm{—}

. A stirred tank, inlet and outlet arrows, a conversion. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Space time \tau60 sRate constant k0.02 1/s

Outputs

Conversion X0.545 —

Reading speed

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Narration of this film

A stirred tank, inlet and outlet arrows, a conversion.

Mass balance: F_in − F_out + r V = 0. τ = V/v0.

Reading speed

Watch on YouTube