CHM-31

Second-order 1/c

Bimolecular.

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Physical chemistrysecond order

Governing equation

1/c=1/c_0+kt

$t \in \left[0, 500\right]$

where

c_0: c0 (M)
k: k (1/M/s)
t: t (s)
c: c (M)

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

1/c=1/c_0+kt

$t \in \left[0, 500\right]$

$t = 0$ $c = 0.1$

Along the curve

②

Domain of the variable — blue

t_{\min} = 0,\quad t_{\max} = 500

$t \in \left[0, 500\right]$

$t = 0$ $t = 0$

Along the curve

③

Response curve — green

1/c=1/c_0+kt

$t \in \left[0, 500\right]$

$t = 0$ $c = 0.1$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}c}{\mathrm{d}t}

$t \in \left[0, 500\right]$

$t = 3.145$ $c^{\prime} = -4.85\times 10^{-4}$

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-31 — Second-order 1/c) is the form associated with second order. Working symbols: $c_0$ , $k$ , $t$ $\rightarrow$ $c$ . Bimolecular.

Purpose

Purpose: compute

c

from

c_0

k

t

in Physical chemistry via

1/c=1/c_0+kt

Bimolecular. 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

c_0 = 0.100\,\mathrm{M}

k = 0.050\,\mathrm{1/M/s}

t = 20.000\,\mathrm{s}

, the governing relation

1/c=1/c_0+kt

yields

c = 0.0909\,\mathrm{M}

. Bimolecular. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

c0 c_00.1 Mk k0.05 1/M/st t20 s

Outputs

c c0.0909 M

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Narration of this film

Bimolecular.

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