AkCalculators

Gas laws explained: from Boyle to PV = nRT

Introduction. Gas laws describe the relationships between pressure (P), volume (V), temperature (T), and amount (n) for gases. Historically, separate empirical laws (Boyle, Charles, Gay-Lussac, Avogadro) were discovered; the Ideal Gas Law unifies them into PV = nRT. This article reviews each law, gives derivations and limits of applicability, presents worked examples, and discusses real-gas deviations and practical tips for using the converter above.

Boyle's Law (P ∝ 1/V at constant T and n)

Robert Boyle found that for a fixed mass of gas at constant temperature, pressure is inversely proportional to volume: P₁V₁ = P₂V₂. It's a direct consequence of the kinetic theory if temperature (i.e., average molecular kinetic energy) is held constant.

Charles's Law (V ∝ T at constant P and n)

Jacques Charles observed that volume is proportional to absolute temperature at constant pressure: V₁/T₁ = V₂/T₂. Note: temperatures must be in absolute units (Kelvin) — using Celsius will give incorrect results unless converted.

Gay-Lussac's Law (P ∝ T at constant V and n)

Gay-Lussac described how pressure changes with temperature at constant volume: P₁/T₁ = P₂/T₂. Again, absolute temperature is required.

Avogadro's Law (V ∝ n at constant P and T)

Avogadro's law states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules; hence V₁/n₁ = V₂/n₂. This is the basis for molar volume at STP and stoichiometric gas calculations.

Combined Gas Law

Combining Boyle, Charles and Gay-Lussac yields the Combined Gas Law: P₁V₁/T₁ = P₂V₂/T₂ (for fixed n). This is useful when a process changes P, V and T simultaneously and the amount of gas is constant.

Ideal Gas Law (PV = nRT)

The Ideal Gas Law unifies the previous laws and introduces the gas constant R: PV = nRT. For one mole (n=1) at standard conditions, the relation gives the molar volume. Common values of R depend on chosen units: 0.082057 L·atm·mol⁻¹·K⁻¹ or 8.314462 J·mol⁻¹·K⁻¹.

Units, conversions and practical advice

Absolute temperature (Kelvin) is mandatory in gas-law calculations. Pressure units are convertible: 1 atm = 101.325 kPa = 101325 Pa. Volume units: 1 L = 1e-3 m³. Amount n is in moles. The converter above performs these conversions automatically — ensure you select matching units for R in ideal-gas mode.

Worked examples

1) Boyle's law: A gas at 1.2 atm occupies 3.0 L. If compressed to 1.8 atm at constant T, new volume V₂ = P₁V₁/P₂ = (1.2×3.0)/1.8 = 2.0 L.

2) Ideal gas: How many moles are in 5.00 L of gas at 2.00 atm and 300 K? Use n = PV/(RT) with R = 0.082057 L·atm·mol⁻¹·K⁻¹: n = (2.00×5.00)/(0.082057×300) ≈ 0.406 mol.

Limitations and real gases

Ideal-gas behavior assumes negligible intermolecular forces and molecular volumes. At high pressures and low temperatures, real gases deviate — use compressibility factors (Z) or equations of state (van der Waals, Redlich-Kwong) for accuracy. For most laboratory conditions near STP, the ideal approximation is adequate.

Tips for using the converter

• Always convert temperatures to Kelvin when using gas laws involving T.
• Use matching units for R when solving PV = nRT; the tool helps by offering common R values.
• When solving for unknowns, leave that input blank and select the variable in the "Solve for" dropdown.

Summary

This converter simplifies routine gas calculations across the classic empirical laws and the ideal-gas model. For non-ideal regimes consider using real-gas corrections. Use the CSV export for reporting or classroom worksheets.