Combined Gas Law Calculator (P, V, T)

Combined Gas Law Guide

What do I need to know about The Combined Gas Law?

The combined gas law unifies Boyle's law (P × V = constant), Charles' law (V / T = constant), and Gay-Lussac's law (P / T = constant) into one equation: P₁V₁ / T₁ = P₂V₂ / T₂. Where: P = pressure (any unit, but same on both sides). V = volume (any unit, but same on both sides). T = absolute temperature — MUST be in Kelvin. The amount of gas (moles) stays the same; the law only describes pressure, volume, and temperature changes of a fixed sample. Critical: temperature MUST be in Kelvin (K = °C + 273.15) — using Celsius directly in the gas law equations gives wrong, sometimes negative or nonsensical, results, since the relationship between pressure, volume and temperature only holds on an absolute temperature scale where zero represents the theoretical point of no molecular motion.

What's the key thing to understand about Special Cases?

Boyle's law (constant temperature): T₁ = T₂, so P₁V₁ = P₂V₂. Pressure rises as volume decreases. Examples: squeezing a balloon (more pressure, less volume). Compressing air in a syringe with finger over nozzle. SCUBA tank pressure as breath compressed deeper. Charles' law (constant pressure): P₁ = P₂, so V₁/T₁ = V₂/T₂. Volume rises with temperature. Examples: hot air balloon (warm air rises). Tyres expanding on hot day. Bread rising in oven (CO₂ from yeast expands). Gay-Lussac's law (constant volume): V₁ = V₂, so P₁/T₁ = P₂/T₂. Pressure rises with temperature. Examples: a sealed can heated on a fire (risk of explosion as internal pressure builds), a car tyre's pressure reading being higher after a motorway drive once the tyres have warmed up.

What do I need to know about The Ideal Gas Law?

Full ideal gas law: PV = nRT. Where: n = moles of gas. R = universal gas constant = 8.314 J/(mol·K). For SI units (Pa, m³, K, mol). R = 0.0821 L·atm/(mol·K) for litres and atmospheres. Used when: you need to find moles, mass, or density of gas. Or you want to find a single state (not a change). PV = nRT shows: at standard temperature and pressure (STP: 273.15K, 1atm): 1 mole of any gas occupies 22.4 L. Density of gas: ρ = PM / RT (where M is molar mass). Limits of ideal gas behaviour: works well at typical laboratory conditions (moderate pressure, temperature well above the gas's boiling point) but breaks down at very high pressure or very low temperature, where intermolecular forces and the finite volume of gas molecules themselves become significant — this is where a real-gas correction like the van der Waals equation is needed instead.

What should I know about Worked Examples?

Tyre pressure on cold day: tyre at 32 PSI when 20°C inflated (warm). Same tyre at -10°C: P₂ = P₁ × T₂/T₁ = 32 × 263/293 = 28.7 PSI. Lost ~3 PSI just from temperature drop. Why winter requires re-checking tyre pressure. Hot air balloon: 1m³ of air at 20°C (293K). Heat to 100°C (373K). New volume at same pressure: V₂ = V₁ × T₂/T₁ = 1 × 373/293 = 1.27 m³. 27% expansion creates lift. Compressed gas safety: gas at 200 bar in cylinder (typical SCUBA). Leak to atmosphere (1 bar). Volume increase: V₂ = V₁ × P₁/P₂ = V₁ × 200 (a 200-fold expansion). This is why holding your breath while ascending during a SCUBA dive is dangerous — the air in the lungs expands as ambient pressure drops, and can over-expand the lungs if the diver doesn't exhale continuously on the way up.

What should I know about Avogadro's Law?

Avogadro's law states that at constant temperature and pressure, gas volume is directly proportional to the number of moles present (V ∝ n), meaning equal volumes of any gas contain equal numbers of molecules regardless of what the gas actually is. This is the principle that makes molar volume (22.4 L/mol at STP) a universal constant for ideal gases, and it's the piece that, together with Boyle's and Charles's laws, combines into the full ideal gas law PV = nRT — the combined gas law itself is really just Boyle's and Charles's laws merged, holding the amount of gas (n) fixed.

What do I need to know about Gay-Lussac's Law?

Gay-Lussac's law describes how pressure and temperature relate at constant volume: P ∝ T, or P₁/T₁ = P₂/T₂ (with T always in kelvin). This is exactly why a sealed can or a car tyre shows rising pressure as it warms in the sun, even though its volume barely changes, and why aerosol cans carry warnings against incineration — heating the fixed-volume gas inside raises its pressure directly, potentially to the point of rupture. Gay-Lussac's law is the third of the three simple gas laws (alongside Boyle's and Charles's) that together underpin the combined and ideal gas laws.

How Do the Simple Gas Laws Compare at a Glance?

Each simple gas law holds one variable fixed while relating the other two — the combined and ideal gas laws are what you get when these are merged together.

What Is Dalton's Law of Partial Pressures?

Dalton's law states that in a mixture of gases that don't react with each other, the total pressure exerted equals the sum of the partial pressures each individual gas would exert if it alone occupied the same volume at the same temperature: P_total = P1 + P2 + P3 + ... Each gas's partial pressure is proportional to its mole fraction in the mixture: P_gas = (mole fraction of gas) × P_total. This matters practically in diving physiology (the partial pressure of oxygen and nitrogen in breathing gas changes with depth even though the gas mixture's composition stays the same, because total pressure rises with depth), in atmospheric science (the partial pressure of water vapour in air is what drives evaporation and condensation), and in any lab situation involving gas collected over water, where the measured total pressure includes a contribution from water vapour that has to be subtracted out using Dalton's law before the pressure of the actual gas of interest can be found.

What's the Difference Between STP and SATP?

Both STP and SATP are reference conditions used to compare gas measurements on a standard footing, but they use different values, and mixing them up is a common source of error. The traditional STP (Standard Temperature and Pressure), still widely taught, is 0°C (273.15K) and 1 atm (101.325 kPa), under which one mole of an ideal gas occupies 22.4 litres. IUPAC's more modern STP definition uses 0°C and 100 kPa exactly, giving a very slightly different molar volume of 22.7 litres. SATP (Standard Ambient Temperature and Pressure), sometimes used in chemistry to better reflect typical lab conditions, is defined as 25°C (298.15K) and 100 kPa (or 1 bar), under which one mole occupies roughly 24.8 litres because the higher temperature expands the gas compared with STP. Always check which convention a textbook, exam board, or dataset is using before quoting a molar volume figure, since 22.4 L/mol (old STP) and 24.8 L/mol (SATP) are both 'standard' in different contexts but differ by over 10%.

Worked Example: Finding Moles of Gas with the Ideal Gas Law

A rigid 2.0 litre cylinder holds gas at a pressure of 1.5 atm and a temperature of 300K. Using PV = nRT, rearranged to find moles: n = PV ÷ RT. With R = 0.0821 L·atm/(mol·K) (the gas constant in litre-atmosphere units): n = (1.5 × 2.0) ÷ (0.0821 × 300) = 3.0 ÷ 24.63 ≈ 0.122 mol. This is the calculation used whenever a gas's pressure, volume, and temperature are all known but the amount of gas present is not — common in lab situations where a gas has been generated by a reaction and collected in a container of known volume, and the quantity produced needs to be worked out from the measured pressure and temperature rather than weighed directly.