Ideal Gas Law Calculator

What do I need to know about PV = nRT?

The ideal gas law combines Boyle's (PV = constant at fixed T, n), Charles's (V/T = constant at fixed P, n), and Avogadro's (V ∝ n at fixed P, T) laws. P = pressure (Pa), V = volume (m³), n = moles, R = 8.314 J/mol·K, T = temperature (K). At STP (0°C, 1 atm = 101,325 Pa): molar volume = RT/P = 8.314 × 273.15 / 101,325 = 0.02241 m³/mol = 22.41 L/mol. At RTP (25°C, 1 atm): molar volume = 8.314 × 298.15 / 101,325 = 24.47 L/mol. The ideal gas law assumes: no intermolecular forces, negligible molecular volume compared to the container, and perfectly elastic collisions between particles with no energy lost. Real gases approximate this behaviour reasonably well at low pressure and high temperature, which is why STP and RTP molar volumes (22.4 L/mol and 24.5 L/mol) are useful reference figures for most calculations.

What should I know about Boyle's and Charles's Laws?

Boyle's law (fixed T and n): P₁V₁ = P₂V₂. Doubling pressure halves volume. Syringe compression: push plunger halfway = pressure doubles. Diving: at 30m depth (4 atm), lung volume compressed to ¼ of surface volume. Charles's law (fixed P and n): V₁/T₁ = V₂/T₂ (T in Kelvin). Balloon shrinks in the cold (V decreases as T decreases). Hot air balloon rises: heating air at constant pressure increases volume, reducing density below ambient. Gay-Lussac's law (fixed V and n): P₁/T₁ = P₂/T₂. Aerosol warning labels ('do not store above 50°C' or similar) exist because of this law: heating a sealed aerosol can at constant volume raises the internal pressure sharply, and if it exceeds the can's structural limit, it can rupture or explode.

What do I need to know about Gas Mixtures and Partial Pressure?

Dalton's Law of Partial Pressures: total pressure = sum of partial pressures of each gas. P_total = P_A + P_B + P_C + ... Partial pressure of gas A: P_A = x_A × P_total, where x_A = mole fraction of A. Air composition at 1 atm: N₂ (78%): P = 0.78 atm = 79 kPa. O₂ (21%): P = 0.21 atm = 21 kPa. CO₂ (0.04%): P = 0.0004 atm = 0.04 kPa. At altitude (Mt Everest, 0.33 atm): P(O₂) = 0.21 × 0.33 = 0.07 atm — approximately ⅓ of sea-level oxygen partial pressure. This is why supplemental oxygen is used above about 3,500-4,000m altitude — the partial pressure of oxygen has fallen so far that the lungs can no longer load enough oxygen into the blood by passive diffusion alone, even though the percentage of oxygen in the air (21%) hasn't changed.

What's the difference between Real and Ideal Gases?

The ideal gas law fails under high pressure and low temperature where: intermolecular attractions are significant (gas molecules attract each other at close range — reduces pressure below ideal). Molecular volume is non-negligible (at high pressure, molecules themselves occupy significant fraction of total volume — increases pressure above ideal). van der Waals equation: (P + a/V²)(V − b) = nRT. a = attraction parameter (stronger intermolecular forces = larger a). b = molecular volume correction. At very high pressure, the (V − b) term becomes significant because the gas molecules themselves take up a meaningful fraction of the container's volume, leaving less free space than the ideal gas law assumes — this pushes the real pressure higher than the ideal prediction, the opposite effect to the intermolecular attraction correction.