CHE-43

Kc from extents

1:1:1:1 pedagogical Kc.

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GoverningKc from extents

Governing equation

K_c=c_C^c c_D^d/(c_A^a c_B^b)

$cC \in \left[0.001, 2\right]$

where

cA: cA (mol/L)
cB: cB (mol/L)
cC: cC (mol/L)
cD: cD (mol/L)
Kc: Kc from extents (—)

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

K_c=c_C^c c_D^d/(c_A^a c_B^b)

$cC \in \left[0.001, 2\right]$

$cC = 0.001$ $Kc = 0.001$

Along the curve

②

Domain of the variable — blue

cC_{\min} = 0.001,\quad cC_{\max} = 2

$cC \in \left[0.001, 2\right]$

$cC = 0.001$ $cC = 0.001$

Along the curve

③

Response curve — green

K_c=c_C^c c_D^d/(c_A^a c_B^b)

$cC \in \left[0.001, 2\right]$

$cC = 0.001$ $Kc = 0.001$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}Kc}{\mathrm{d}cC}

$cC \in \left[0.001, 2\right]$

$cC = 0.014$ $Kc^{\prime} = 1.25$

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-43 — Kc from extents) is the form associated with Kc from extents. Working symbols: $cA$ , $cB$ , $cC$ , $cD$ $\rightarrow$ $Kc$ . 1:1:1:1 pedagogical Kc. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

Kc

from

cA

cB

cC

cD

in Chemical engineering via

K_c=c_C^c c_D^d/(c_A^a c_B^b)

1:1:1:1 pedagogical Kc. 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

cA = 0.400\,\mathrm{mol/L}

cB = 0.400\,\mathrm{mol/L}

cC = 0.200\,\mathrm{mol/L}

cD = 0.200\,\mathrm{mol/L}

, the governing relation

K_c=c_C^c c_D^d/(c_A^a c_B^b)

yields

Kc = 0.250\,\mathrm{—}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

cA cA0.4 mol/LcB cB0.4 mol/LcC cC0.2 mol/LcD cD0.2 mol/L

Outputs

Kc from extents Kc0.250 —

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

1:1:1:1 pedagogical Kc. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube