The Ideal Gas Law: Units, Rearrangements, and Where the Model Breaks

Use PV = nRT consistently, understand its molecular assumptions, and recognize non-ideal conditions.

01

Four state variables in one model

The ideal gas law relates absolute pressure P, volume V, amount n, and absolute temperature T. The constant R packages the unit relationship between them.

The equation combines empirical gas laws: pressure-volume, volume-temperature, and amount-volume behavior become parts of one expression.

FormulaPV = nRT
02

Choose R to match the units

For a strict SI calculation, use pressure in pascals, volume in cubic meters, amount in moles, and temperature in kelvin. Then R has units J·mol⁻¹·K⁻¹ because one pascal-cubic-meter equals one joule.

Alternative R values are valid only with their matching pressure and volume units. Mixing 8.314 with liters and atmospheres creates a large error.

FormulaR = 8.314462618 J·mol⁻¹·K⁻¹
03

Rearrange before substituting

Isolating the unknown symbolically reduces calculator-entry mistakes and makes dimensional checks easier.

FormulaP = nRT/V · V = nRT/P · n = PV/RT · T = PV/nR
Worked check

At 100,000 Pa and 298.15 K, one mole occupies V ≈ 0.02479 m³ = 24.79 L in the ideal model.

04

Ideal is an approximation

The model treats particles as having negligible volume and no intermolecular attraction except during elastic collisions. Real gases approach this behavior most closely at relatively low pressure and high temperature.

At high pressure, low temperature, or near a phase transition, molecular size and attraction become important. Equations such as van der Waals or measured property data may then be more appropriate.

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References

Sources were selected for their authority and direct relevance to the equations discussed. Links open the original publisher.

  1. The Ideal Gas LawOpenStax Chemistry 2e
  2. Ideal Gas LawOpenStax College Physics 2e

Educational article, not professional advice. Editorial policy · Calculation methodology