CHM-24

Power-law rate r = k c^n

r = k c^n. Empirical order-n rate in one reactant.

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KineticsMass action

Governing equation

r=k c^n

$c \in \left[0.001, 5\right]$

where

k: Rate constant (—)
c: Concentration (mol/L)
n: Order (—)
r: Rate (mol/(L·s))

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

r=k c^n

$c \in \left[0.001, 5\right]$

$c = 0.001$ $r = 2\times 10^{-5}$

Along the curve

②

Domain of the variable — blue

c_{\min} = 0.001,\quad c_{\max} = 5

$c \in \left[0.001, 5\right]$

$c = 0.001$ $c = 0.001$

Along the curve

③

Response curve — green

r=k c^n

$c \in \left[0.001, 5\right]$

$c = 0.001$ $r = 2\times 10^{-5}$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}r}{\mathrm{d}c}

$c \in \left[0.001, 5\right]$

$c = 0.032$ $r^{\prime} = 0.02$

Along the curve

Lecture brief

Historical brief

Ideal-gas law, van ’t Hoff, Nernst, Michaelis–Menten and Clausius–Clapeyron are physical chemistry’s working equations of equilibrium and rate. The lab is pressure, potential and kinetics. This sheet (CHM-24 — Power-law rate r = k c^n) is the form associated with Mass action. Working symbols: $k$ , $c$ , $n$ $\rightarrow$ $r$ . The order n need not be stoichiometric. Integral laws follow: ln c for n=1, 1/c for n=2.

Purpose

Purpose: compute

r

from

k

c

n

in Physical chemistry via

r=k c^n

r = k c^n. Empirical order-n rate in one reactant. Use it when a real physical chemistry question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

k = 0.020\,\mathrm{—}

c = 0.500\,\mathrm{mol/L}

n = 1.000\,\mathrm{—}

, the governing relation

r=k c^n

yields

r = 0.01000\,\mathrm{mol/(L·s)}

. Irreversible, constant volume, one reactant. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Rate constant k0.02 —Concentration c0.5 mol/LOrder n1 —

Outputs

Rate r0.01000 mol/(L·s)

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Narration of this film

Irreversible, constant volume, one reactant.

The order n need not be stoichiometric. Integral laws follow: ln c for n=1, 1/c for n=2.

Reading speed

Watch on YouTube