CHE-35

Conversion of A

X = (FA0 − FA)/FA0 = 1 − C/C0 at constant density.

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BalancesLevenspiel

Governing equation

X=\dfrac{F_{A0}-F_A}{F_{A0}}=1-\dfrac{C}{C_0}

$C \in \left[0.1, 2000\right]$

where

C_0: Inlet conc. (mol/m³)
C: Outlet conc. (mol/m³)
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{F_{A0}-F_A}{F_{A0}}=1-\dfrac{C}{C_0}

$C \in \left[0.1, 2000\right]$

$C = 0.1$ $X = 0.999$

Along the curve

②

Domain of the variable — blue

C_{\min} = 0.1,\quad C_{\max} = 2000

$C \in \left[0.1, 2000\right]$

$C = 0.1$ $C = 0.1$

Along the curve

③

Response curve — green

X=\dfrac{F_{A0}-F_A}{F_{A0}}=1-\dfrac{C}{C_0}

$C \in \left[0.1, 2000\right]$

$C = 0.1$ $X = 0.999$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}X}{\mathrm{d}C}

$C \in \left[0.1, 2000\right]$

$C = 12.68$ $X^{\prime} = -0.01$

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-35 — Conversion of A) is the form associated with Levenspiel. Working symbols: $C_0$ , $C$ $\rightarrow$ $X$ . Conversion is the fraction of a limiting reactant that has been consumed. It is the natural extent variable of reactor design.

Purpose

Purpose: compute

X

from

C_0

C

in Chemical engineering via

X=\dfrac{F_{A0}-F_A}{F_{A0}}=1-\dfrac{C}{C_0}

X = (FA0 − FA)/FA0 = 1 − C/C0 at constant density. 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

C_0 = 100.000\,\mathrm{mol/m^{3}}

C = 20.000\,\mathrm{mol/m^{3}}

, the governing relation

X=\dfrac{F_{A0}-F_A}{F_{A0}}=1-\dfrac{C}{C_0}

yields

X = 0.800\,\mathrm{—}

. An inlet bar, an outlet bar, an X tick. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Inlet conc. C_0100 mol/m³Outlet conc. C20 mol/m³

Outputs

Conversion X0.800 —

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Narration of this film

An inlet bar, an outlet bar, an X tick.

Conversion is the fraction of a limiting reactant that has been consumed. It is the natural extent variable of reactor design.

Reading speed

Watch on YouTube