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This page explains the ideal gas law and shows how to compute pressure, volume, moles, or temperature. It gives clear formulas, unit notes, and worked examples you can copy.

Core formula

The ideal gas law is:

P × V = n × R × T

Where:

  • P = pressure
  • V = volume
  • n = amount of substance (moles)
  • R = gas constant
  • T = absolute temperature (kelvin)

Common gas constant values

  • R = 8.314462618 J·mol⁻¹·K⁻¹ (SI: Pa·m³ per mol·K)
  • R = 0.082057366 L·atm·mol⁻¹·K⁻¹ (when P in atm and V in litres)
  • Pick the R that matches your pressure and volume units.

How to use

  1. Decide which variable you need: P, V, n, or T.
  2. Rearrange the formula. Example: P = nRT ÷ V.
  3. Convert units so R fits. Common conversions: 1 atm = 101325 Pa, 1 L = 0.001 m³.
  4. Compute and report units with the answer.

Worked examples

Example 1 — standard conditions (find volume)

Given: P = 1 atm, n = 1.00 mol, T = 273.15 K. Use R = 0.082057366 L·atm·mol⁻¹·K⁻¹.

V = nRT ÷ P = 1 × 0.082057366 × 273.15 ÷ 1 ≈ 22.414 L.

Example 2 — find pressure (SI units)

Given: V = 0.010 m³, n = 0.5 mol, T = 300 K. Use R = 8.314462618 J·mol⁻¹·K⁻¹.

P = nRT ÷ V = 0.5 × 8.314462618 × 300 ÷ 0.010 ≈ 124,716.94 Pa ≈ 1.231 atm.

Example 3 — solve for moles

Given: P = 2 atm, V = 10 L, T = 350 K. Use R = 0.082057366.

n = PV ÷ (RT) = 2 × 10 ÷ (0.082057366 × 350) ≈ 0.699 mol.

Unit tips & conversions

  • For Pa and m³, use R = 8.314462618. Then P in pascals and V in cubic metres.
  • For atm and litres, use R = 0.082057366. Then P in atm and V in L.
  • Common conversions: 1 atm = 101325 Pa. 1 L = 0.001 m³.
  • Temperature must be in kelvin: T(K) = T(°C) + 273.15.

When the ideal gas law breaks down

The law assumes point particles with no interactions. It works well at low pressure and moderate temperature. It fails near condensation, at very high pressure, or for gases with strong intermolecular forces. Use real gas models (van der Waals, virial) then.

Quick rearrangements

  • P = nRT ÷ V
  • V = nRT ÷ P
  • n = PV ÷ (RT)
  • T = PV ÷ (nR)

Common mistakes

  • Using Celsius instead of kelvin.
  • Mismatched units for R, P, and V.
  • Applying the law at very high pressure or near liquefaction.
  • Forgetting to convert L ↔ m³ or atm ↔ Pa when switching R values.

FAQ

What if I have pressure in mmHg?

Convert mmHg to atm: 760 mmHg = 1 atm. Or convert mmHg to Pa: 1 mmHg ≈ 133.322 Pa.

Can I use kPa units?

Yes. If you use kPa, make sure R matches kPa·L·mol⁻¹·K⁻¹ or convert to Pa and m³. 1 kPa = 1000 Pa.

How do I handle gas mixtures?

Use partial pressures (Dalton's law). For each component: P_iV = n_iRT. Sum partial pressures for total P.

What is molar volume at STP?

At 1 atm and 273.15 K, one mole of an ideal gas occupies about 22.414 L.

Are vapors ideal gases?

Often they behave roughly ideal at low pressure and well above boiling point. Check conditions before assuming ideal behavior.

How precise is R?

R is known to many digits. Use enough digits to match your input precision. For most work 8.314 or 0.08206 is fine.

Can I use mass instead of moles?

Yes. Convert mass to moles: n = mass ÷ M, where M is molar mass (g/mol). Then use PV = nRT.

How to find density from ideal gas law?

Density ฯ = mass/volume = (nM)/V. Using PV = nRT, ฯ = PM ÷ (RT), where M is molar mass in kg/mol.

What if gas is compressible at high pressure?

Use real gas corrections (e.g., compressibility factor Z or van der Waals equation). Ideal law will over- or under-estimate.

Why must T be in kelvin?

Kelvin is an absolute scale. The law relies on absolute temperature. Celsius or Fahrenheit will give wrong results.

How to check units quickly?

Use R that matches P and V units. Do a unit check: (Pa·m³) = J and J/(mol·K) × mol × K → Pa·m³, consistent.

How to convert atm to Pa in one step?

Multiply atm by 101325 to get pascals.

Can I use partial pressures to find composition?

Yes. From measured total P and known n, you can solve for unknown partial pressures or mole fractions if enough data is given.

Is PV = nRT valid for solids or liquids?

No. The ideal gas law describes gases. Solids and liquids need different thermodynamic models.

What is compressibility factor Z?

Z = PV ÷ (nRT). For ideal gas Z = 1. For real gases Z deviates from 1; use tables or equations of state.