Q1(a). Van der Waals equation

Answer in brief

(p+an²/V²)(V-nb)=nRT; [a]=Pa m⁶ mol⁻² and [b]=m³ mol⁻¹.

Key points

• p is gas pressure, V total volume, n amount of gas, T absolute temperature and R the molar gas constant.
• The attraction parameter a corrects the measured pressure: intermolecular attraction reduces the force of wall collisions, so the pressure correction is positive.
• The excluded-volume parameter b corrects the available volume: molecules have finite size, leaving V-nb for translational motion in this model.
• Since an²/V² has pressure units, a has units Pa m⁶ mol⁻²=kg m⁵ s⁻² mol⁻². Since nb is a volume, b has units m³ mol⁻¹.
• In base dimensions, [a]=ML⁵T⁻²N⁻² and [b]=L³N⁻¹, where N denotes amount of substance. For one mole, (p+a/Vₘ²)(Vₘ-b)=RT.