Ideal Gas Law Calculator

The ideal gas law calculator solves the equation PV = nRT for any one of its four variables — pressure (P), volume (V), amount in moles (n), or temperature (T) — given the other three. The ideal gas law is one of the most important equations in chemistry and physics, describing the behavior of a hypothetical 'ideal' gas whose particles have negligible volume and exert no intermolecular forces on each other.

The law consolidates three earlier empirical gas laws. Boyle's Law (1662) established that pressure and volume are inversely proportional at constant temperature: P ∝ 1/V. Charles's Law (1787) showed that volume and absolute temperature are directly proportional at constant pressure: V ∝ T. Avogadro's Law (1811) stated that equal volumes of gas at the same temperature and pressure contain the same number of molecules, so V ∝ n. Combining these three relationships gives PV = nRT.

The universal gas constant R = 8.31446 J/(mol·K) in SI units. For calculations involving pressure in atmospheres and volume in litres, the common form R = 0.082057 L·atm/(mol·K) is used. The calculator uses this latter form. Temperature must always be in Kelvin (K = °C + 273.15) because the law requires absolute temperature — inserting Celsius values produces physically meaningless results.

Real gases deviate from ideal behavior at high pressures (where intermolecular distances shrink and particle volumes matter) and low temperatures (where intermolecular attractions become significant relative to kinetic energy). The van der Waals equation corrects for these deviations using empirical constants a and b unique to each gas. For most introductory chemistry problems and for gases at room temperature and moderate pressures, the ideal gas law is accurate to within a few percent.

STP (Standard Temperature and Pressure) is defined by IUPAC as 0 °C (273.15 K) and 100 kPa (≈ 0.9869 atm). At STP, one mole of ideal gas occupies 22.414 L — the molar volume of an ideal gas, a useful reference figure. Note that older texts use 1 atm rather than 100 kPa as the standard pressure, giving a slightly different molar volume of 22.711 L.

To solve the ideal gas law, isolate the unknown variable algebraically before substituting numbers. For pressure: P = nRT/V. For volume: V = nRT/P. For moles: n = PV/(RT). For temperature: T = PV/(nR). Ensure consistent units before substituting: pressure in atm, volume in litres, temperature in Kelvin, and n in moles when using R = 0.082057 L·atm/(mol·K).

Unit conversions are the most common source of error. Pressure may be given in kPa (÷ 101.325 to convert to atm), mmHg or torr (÷ 760 for atm), or psi (÷ 14.696 for atm). Volume may be given in mL (÷ 1000 for litres) or cm³ (also ÷ 1000). Temperature must be converted from Celsius to Kelvin by adding 273.15. Never add 273 without the decimal if more than three significant figures are required.

For combined gas law problems where initial and final states are compared for a fixed amount of gas (n constant), the relationship P₁V₁/T₁ = P₂V₂/T₂ is more efficient than applying the full ideal gas law twice. This form eliminates R and n entirely, requiring only the ratio of states. The calculator handles the single-state form (PV = nRT) and you can use it twice — once for each state — to solve combined gas law scenarios.

Gas density can be derived from the ideal gas law: since n = mass/M (where M is molar mass in g/mol) and density ρ = mass/V, substitution gives ρ = PM/(RT). This form lets you calculate the density of any gas at any temperature and pressure without needing a sample to weigh, or conversely, determine the molar mass of an unknown gas from its measured density.

Ideal Gas Law Calculator Primary Governing Equation

Ideal Gas Law

Pressure

Volume

Moles

Temperature

Gas Density

A 2.50 L rigid container holds 0.120 mol of nitrogen gas (N₂). What pressure does it exert at 25 °C?

Convert temperature to Kelvin: T = 25 + 273.15 = 298.15 K. Identify the known values: n = 0.120 mol, R = 0.082057 L·atm/(mol·K), T = 298.15 K, V = 2.50 L.

Apply the pressure formula: P = nRT / V = (0.120 × 0.082057 × 298.15) / 2.50 = (2.9358) / 2.50 = 1.174 atm.

To verify with a second approach: at STP (273.15 K, 1 atm), 0.120 mol would occupy 0.120 × 22.414 = 2.690 L. At 25 °C the volume expands proportionally: 2.690 × (298.15/273.15) = 2.937 L. In a 2.50 L container, the pressure must be higher than 1 atm by the ratio 2.937/2.50 = 1.175 atm — confirming our direct calculation within rounding.

Converting to other pressure units: 1.174 atm × 101.325 kPa/atm = 118.9 kPa; 1.174 × 760 mmHg/atm = 892 mmHg.

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Kinetic molecular theory (KMT) provides the microscopic foundation for the ideal gas law. KMT assumes that gas particles are point masses in constant random motion, that all collisions between particles and with container walls are perfectly elastic (no kinetic energy loss), and that there are no intermolecular forces. From these assumptions, the pressure exerted by a gas can be derived as P = (1/3)(N/V)m⟨v²⟩, which leads directly to the ideal gas law and relates temperature to average kinetic energy: (3/2)kT = (1/2)m⟨v²⟩.

The van der Waals equation (P + a/V²)(V − b) = nRT corrects the ideal gas law for real gas behavior. The constant a accounts for intermolecular attractive forces (which reduce the observed pressure), and b accounts for the finite volume of gas molecules (which reduces the available volume). Real gases approach ideal behavior at low pressures and high temperatures, where molecular spacing is large and kinetic energy dominates over intermolecular attractions.

Partial pressure is the pressure a gas would exert if it alone occupied the entire container volume at the same temperature. Dalton's Law of Partial Pressures states that the total pressure of a gas mixture equals the sum of the partial pressures of each component. Each component obeys the ideal gas law independently: P_i = n_i RT / V. This is essential for problems involving gas mixtures and for calculating vapor pressure corrections in gas collection experiments.

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