Ideal gas law calculator

Solve the ideal gas law PV = nRT for pressure, volume, moles or temperature in any units, or find a new state with the combined gas law.

Обновлено 28 сентября 2026 г.Проверенные примеры: 6

Объём

Значащих цифр: 6; До ближайшего, при равенстве — от нуля

Давление: 101.325kPa / 1atm
Amount of gas: 1mol
Температура: 273.15K / 0°C
Molar volume V/n: 22.414L/mol
Number of molecules: 6.02214 × 10²³

1 mol of ideal gas at 273.15 K (0 °C) and 101.325 kPa occupies 22.414 L — 22.414 L per mole.

Isotherm through this state (P–V)

Как выполняется расчёт S

Convert to SI units
$P = 101{,}325\ \mathrm{Pa},\ V = 0.022414\ \mathrm{m^3},\ n = 1\ \mathrm{mol},\ T = 273.15\ \mathrm{K}$
Temperature is always absolute in gas laws: K = °C + 273.15.
Solve PV = nRT for V
$V = \frac{nRT}{P} = \frac{(1)(8.314462618)(273.15)}{101{,}325} = 0.022414\ \mathrm{m^3} = 22.414\ \mathrm{L}$

О калькуляторе: Ideal gas law calculator

The ideal gas law, PV = nRT, links the pressure, volume, amount and absolute temperature of a gas through the molar gas constant R = 8.314 462 618… J/(mol·K). Choose the unknown and enter the other three in any units; the calculator converts to pascals, cubic metres, moles and kelvin before solving. The combined gas law mode holds the amount fixed and uses P₁V₁/T₁ = P₂V₂/T₂ to find a new pressure, volume or temperature.

Students use it to find the volume of gas a reaction gives off, and engineers use it to estimate how much gas a tank holds. With the defaults, 1 mol at 0 °C and 1 atm occupies 22.414 L, the CODATA molar volume of an ideal gas at those conditions.

The law ignores molecular size and attraction. Carbon dioxide at 25 °C and 1 atm deviates from it by about 0.5 %; the calculator warns above 100 bar or below 150 K, where a van der Waals or virial equation fits better.

Примеры с решением

1 mol at 0 °C and 1 atm

Law: PV = nRT
Solve for: Объём
Pressure P: 1 atm
Amount of gas n: 1
Amount unit: mol
Temperature T: 0 °C

Объём: 22.414 L

Источник проверки: CODATA 2022 molar volume of an ideal gas at 273.15 K, 101.325 kPa: 22.413 969 54 L/mol

Pressure of 2 mol in 10 L at 300 K

Law: PV = nRT
Solve for: Давление
Volume V: 10 L
Amount of gas n: 2
Amount unit: mol
Temperature T: 300 K

Давление: 498.868 kPa

Источник проверки: Python 3.8 decimal: 2 × 8.31446261815324 × 300 / 0.01 = 498867.757 Pa

Moles in 1 m³ at 100 kPa and 25 °C

Law: PV = nRT
Solve for: Amount
Pressure P: 100 kPa
Volume V: 1 m³
Temperature T: 25 °C

Amount of gas: 40.3395 mol

Источник проверки: Python 3.8 decimal: 100000 / (8.31446261815324 × 298.15) = 40.3395455

Temperature of 1 mol in 24.465 L at 1 atm

Law: PV = nRT
Solve for: Температура
Pressure P: 1 atm
Volume V: 24.465 L
Amount of gas n: 1
Amount unit: mol

Температура: 298.145 K

Источник проверки: Python 3.8 decimal: 101325 × 0.024465 / 8.31446261815324 = 298.14508 K

Вопросы

What is the value of R in PV = nRT?

R = 8.314 462 618 153 24 J/(mol·K), exact since the 2019 SI revision because it is the product of two fixed constants, the Avogadro constant and the Boltzmann constant. In other units it is 0.082 057 L·atm/(mol·K), 8.314 L·kPa/(mol·K) and 62.364 L·mmHg/(mol·K). Use the version that matches your pressure and volume units, or convert everything to SI as this calculator does.

What volume does one mole of gas occupy at STP?

It depends on which STP is meant. At 0 °C and 1 atm (101.325 kPa), one mole of ideal gas occupies 22.414 L; at 0 °C and 100 kPa, the standard pressure IUPAC has recommended since 1982, it occupies 22.711 L; at 25 °C and 1 atm it occupies 24.465 L. Check which definition your textbook or exam uses, since the first two differ by 1.3 %.

Why does temperature have to be in kelvin?

Gas pressure and volume are proportional to absolute temperature, which starts at absolute zero, −273.15 °C. Going from 10 °C to 20 °C looks like doubling, but the absolute temperature only rises from 283.15 K to 293.15 K, a 3.5 % increase, so at constant pressure the gas expands by 3.5 %, not 100 %. The calculator converts °C and °F to kelvin before solving.

What is the combined gas law?

P₁V₁/T₁ = P₂V₂/T₂ for a fixed amount of gas. It merges Boyle's law (PV constant at fixed temperature), Charles's law (V/T constant at fixed pressure) and Gay-Lussac's law (P/T constant at fixed volume). Heating a sealed rigid container from 20 °C to 40 °C raises 100 kPa to 106.8 kPa, because the pressure scales with 313.15 K ÷ 293.15 K.

Насколько точен «Ideal gas law calculator»?

Точность зависит от введённых данных и допущений метода. Десятичная арифметика использует 50 значащих цифр, но оценки, численные методы и исходные данные могут быть менее точными; округление на экране не устраняет эти ограничения. Решённые примеры, проверенные по независимым источникам: 6. Например, «1 mol at 0 °C and 1 atm» проверяется по источнику CODATA 2022 molar volume of an ideal gas at 273.15 K, 101.325 kPa: 22.413 969 54 L/mol.

Откуда взята методика?

CODATA 2022 — molar gas constant R and molar volume of an ideal gas (22.413 969 54 L/mol at 273.15 K, 101.325 kPa); OpenStax Chemistry 2e, §9.2 Relating pressure, volume, amount, and temperature: the ideal gas law.

Об этом калькуляторе

PV = nRT,\ R = 8.314\,462\,618\ldots\ \mathrm{J\,mol^{-1}\,K^{-1}}\ (\text{exact});\qquad \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}

Источники

Проверено по источникам

В калькулятор включены решённые примеры с ответами из независимых источников. Их количество: 6. Они входят в набор тестов, и вы также можете запустить их здесь.