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

[C]∈[1×10−6,5][C] \in \left[1\times 10^{-6}, 5\right]

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 (—)

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ENV-22 · phase
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①

Governing law — red

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

[C]∈[1×10−6,5][C] \in \left[1\times 10^{-6}, 5\right]

[C]=1×10−6[C] = 1\times 10^{-6}K=1.5×10−5K = 1.5\times 10^{-5}

②

Domain of the variable — blue

[C]min⁡=1×10−6,[C]max⁡=5[C]_{\min} = 1\times 10^{-6},\quad [C]_{\max} = 5

[C]∈[1×10−6,5][C] \in \left[1\times 10^{-6}, 5\right]

[C]=1×10−6[C] = 1\times 10^{-6}[C]=1×10−6[C] = 1\times 10^{-6}

③

Response curve — green

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

[C]∈[1×10−6,5][C] \in \left[1\times 10^{-6}, 5\right]

[C]=1×10−6[C] = 1\times 10^{-6}K=1.5×10−5K = 1.5\times 10^{-5}

④

Rate of change — amber

dKd[C]\frac{\mathrm{d}K}{\mathrm{d}[C]}

[C]∈[1×10−6,5][C] \in \left[1\times 10^{-6}, 5\right]

[C]=0.031[C] = 0.031K′=15K^{\prime} = 15

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][A], [B][B], [C][C], [D][D], aa, bb, cc, dd →\rightarrow KK. The rate of an elementary reaction is proportional to the active masses of the reactants — the origin of K.

Purpose

Purpose: compute KK from [A][A], [B][B], [C][C], [D][D], aa, bb, cc, dd in Environmental via K=[C]c[D]d[A]a[B]bK=\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 mol/L[A] = 0.200\,\mathrm{mol/L}, [B]=0.100 mol/L[B] = 0.100\,\mathrm{mol/L}, [C]=0.400 mol/L[C] = 0.400\,\mathrm{mol/L}, [D]=0.300 mol/L[D] = 0.300\,\mathrm{mol/L}, a=1.000 —a = 1.000\,\mathrm{—}, b=1.000 —b = 1.000\,\mathrm{—}, c=1.000 —c = 1.000\,\mathrm{—}, d=1.000 —d = 1.000\,\mathrm{—}, the governing relation K=[C]c[D]d[A]a[B]bK=\dfrac{[C]^c[D]^d}{[A]^a[B]^b} yields K=6.0000 —K = 6.0000\,\mathrm{—}. Four concentration bars, a K ratio. Move a slider: the numbers are this situation, not a canned story.

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Inputs

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.

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