CHM-02

van der Waals equation

(p + a/Vm²)(Vm − b) = R T. Attraction and covolume.

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Equation of statevan der Waals 1873

Governing equation

\left(p+\dfrac{a}{V_m^2}\right)(V_m-b)=RT

where

V_m: Molar volume (L/mol)
T: Temperature (K)
a: Attraction a (L²·bar/mol²)
b: Covolume b (L/mol)
p: Pressure (bar)

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-02 — van der Waals equation) is the form associated with van der Waals 1873. Working symbols: $V_m$ , $T$ , $a$ , $b$ $\rightarrow$ $p$ . The first cubic EOS. a corrects for attractions, b for finite molecular volume.

Purpose

Purpose: compute

p

from

V_m

T

a

b

in Physical chemistry via

\left(p+\dfrac{a}{V_m^2}\right)(V_m-b)=RT

(p + a/Vm²)(Vm − b) = R T. Attraction and covolume. 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

V_m = 2.000\,\mathrm{L/mol}

T = 300.000\,\mathrm{K}

a = 1.370\,\mathrm{L^{2}·bar/mol^{2}}

b = 0.039\,\mathrm{L/mol}

, the governing relation

\left(p+\dfrac{a}{V_m^2}\right)(V_m-b)=RT

yields

p = 12.377\,\mathrm{bar}

. One mole. a in L²·bar/mol², b in L/mol, p in bar. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Molar volume V_m2 L/molTemperature T300 KAttraction a a1.37 L²·bar/mol²Covolume b b0.039 L/mol

Outputs

Pressure p12.377 bar

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Narration of this film

One mole. a in L²·bar/mol², b in L/mol, p in bar.

The first cubic EOS. a corrects for attractions, b for finite molecular volume.

Reading speed

Watch on YouTube