ENV-22

Guldberg–Waage mass action

K = [C]^c [D]^d / ([A]^a [B]^b) at equilibrium.

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KineticsGuldberg–Waage 1864

Governing equation

K=\dfrac{[C]^c[D]^d}{[A]^a[B]^b}

where

[A]: Species A (mol/L)
[B]: Species B (mol/L)
[C]: Species C (mol/L)
[D]: Species D (mol/L)
a: Stoich. a (—)
b: Stoich. b (—)
c: Stoich. c (—)
d: Stoich. d (—)
K: Equilibrium constant (—)

Lecture brief

Historical brief

Streeter–Phelps (1925) oxygen sag, settling theory and Guldberg–Waage kinetics made water and air quality a rate problem. The lab computes sag, overflow and a snapshot of reactor mass balance. This sheet (ENV-22 — Guldberg–Waage mass action) is the form associated with Guldberg–Waage 1864. Working symbols: $[A]$ , $[B]$ , $[C]$ , $[D]$ , $a$ , $b$ , $c$ , $d$ $\rightarrow$ $K$ . The rate of an elementary reaction is proportional to the active masses of the reactants — the origin of K.

Purpose

Purpose: compute

K

from

[A]

[B]

[C]

[D]

a

b

c

d

in Environmental via

K=\dfrac{[C]^c[D]^d}{[A]^a[B]^b}

K = [C]^c [D]^d / ([A]^a [B]^b) at equilibrium. Use it when a real environmental question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

[A] = 0.200\,\mathrm{mol/L}

[B] = 0.100\,\mathrm{mol/L}

[C] = 0.400\,\mathrm{mol/L}

[D] = 0.300\,\mathrm{mol/L}

a = 1.000\,\mathrm{—}

b = 1.000\,\mathrm{—}

c = 1.000\,\mathrm{—}

d = 1.000\,\mathrm{—}

, the governing relation

K=\dfrac{[C]^c[D]^d}{[A]^a[B]^b}

yields

K = 6.0000\,\mathrm{—}

. Four concentration bars, a K ratio. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Species A [A]0.2 mol/LSpecies B [B]0.1 mol/LSpecies C [C]0.4 mol/LSpecies D [D]0.3 mol/LStoich. a a1 —Stoich. b b1 —Stoich. c c1 —Stoich. d d1 —

Outputs

Equilibrium constant K6.0000 —

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Narration of this film

Four concentration bars, a K ratio.

The rate of an elementary reaction is proportional to the active masses of the reactants — the origin of K.

Reading speed

Watch on YouTube