CHE-32

Raoult flash (binary)

yi P = xi Pi^sat. Ideal liquid, ideal vapour, isothermal flash snapshot.

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VLERaoult

Governing equation

y_i P=x_i P_i^{\mathrm{sat}}

$x_1 \in \left[0.01, 0.99\right]$

where

x_1: Liquid mole frac. 1 (—)
P_1^{\mathrm{sat}}: Sat. pressure 1 (kPa)
P_2^{\mathrm{sat}}: Sat. pressure 2 (kPa)
P: System pressure (kPa)
y_1: Vapour mole frac. 1 (—)
P_{\mathrm{bub}}: Bubble pressure (kPa)

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

y_i P=x_i P_i^{\mathrm{sat}}

$x_1 \in \left[0.01, 0.99\right]$

$x_1 = 0.01$ $y_1 = 0.011$

Along the curve

②

Domain of the variable — blue

x_1_{\min} = 0.01,\quad x_1_{\max} = 0.99

$x_1 \in \left[0.01, 0.99\right]$

$x_1 = 0.01$ $x_1 = 0.01$

Along the curve

③

Response curve — green

y_i P=x_i P_i^{\mathrm{sat}}

$x_1 \in \left[0.01, 0.99\right]$

$x_1 = 0.01$ $y_1 = 0.011$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}y_1}{\mathrm{d}x_1}

$x_1 \in \left[0.01, 0.99\right]$

$x_1 = 0.016$ $y_1^{\prime} = 1.143$

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-32 — Raoult flash (binary)) is the form associated with Raoult. Working symbols: $x_1$ , $P_1^{\mathrm{sat}}$ , $P_2^{\mathrm{sat}}$ , $P$ $\rightarrow$ $y_1$ , $P_{\mathrm{bub}}$ . Raoult's law is the ideal-solution limit of VLE. A binary bubble-point is Σ xi Pi^sat = P.

Purpose

Purpose: compute

y_1

P_{\mathrm{bub}}

from

x_1

P_1^{\mathrm{sat}}

P_2^{\mathrm{sat}}

P

in Chemical engineering via

y_i P=x_i P_i^{\mathrm{sat}}

yi P = xi Pi^sat. Ideal liquid, ideal vapour, isothermal flash snapshot. 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

x_1 = 0.400\,\mathrm{—}

P_1^{\mathrm{sat}} = 80.000\,\mathrm{kPa}

P_2^{\mathrm{sat}} = 40.000\,\mathrm{kPa}

P = 70.000\,\mathrm{kPa}

, the governing relation

y_i P=x_i P_i^{\mathrm{sat}}

yields

y_1 = 0.457\,\mathrm{—}

P_{\mathrm{bub}} = 56.0\,\mathrm{kPa}

. A drum, a liquid tick, a vapour tick. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Liquid mole frac. 1 x_10.4 —Sat. pressure 1 P_1^{\mathrm{sat}}80 kPaSat. pressure 2 P_2^{\mathrm{sat}}40 kPaSystem pressure P70 kPa

Outputs

Vapour mole frac. 1 y_10.457 —
Bubble pressure P_{\mathrm{bub}}56.0 kPa

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Narration of this film

A drum, a liquid tick, a vapour tick.

Raoult's law is the ideal-solution limit of VLE. A binary bubble-point is Σ xi Pi^sat = P.

Reading speed

Watch on YouTube