CHM-23

Activity a = γ x

a = γ x. Mole-fraction activity of a nonideal liquid.

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NonidealityLewis activity

Governing equation

a=\gamma x

$x \in \left[0.001, 1\right]$

where

\gamma: Activity coefficient (—)
x: Mole fraction (—)
a: Activity (—)

The figure, part by part

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①

Governing law — red

a=\gamma x

$x \in \left[0.001, 1\right]$

$x = 0.001$ $a = 0.001$

Along the curve

②

Domain of the variable — blue

x_{\min} = 0.001,\quad x_{\max} = 1

$x \in \left[0.001, 1\right]$

$x = 0.001$ $x = 0.001$

Along the curve

③

Response curve — green

a=\gamma x

$x \in \left[0.001, 1\right]$

$x = 0.001$ $a = 0.001$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}a}{\mathrm{d}x}

$x \in \left[0.001, 1\right]$

$x = 0.007$ $a^{\prime} = 1.2$

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-23 — Activity a = γ x) is the form associated with Lewis activity. Working symbols: $\gamma$ , $x$ $\rightarrow$ $a$ . γ → 1 as x → 1 (Raoult convention) or as x → 0 (Henry convention).

Purpose

Purpose: compute

a

from

\gamma

x

in Physical chemistry via

a=\gamma x

a = γ x. Mole-fraction activity of a nonideal liquid. 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

\gamma = 1.200\,\mathrm{—}

x = 0.300\,\mathrm{—}

, the governing relation

a=\gamma x

yields

a = 0.3600\,\mathrm{—}

. Symmetric (Raoult) convention, one component. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Activity coefficient \gamma1.2 —Mole fraction x0.3 —

Outputs

Activity a0.3600 —

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Narration of this film

Symmetric (Raoult) convention, one component.

γ → 1 as x → 1 (Raoult convention) or as x → 0 (Henry convention).

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