Ideal Gas Law Calculator (PV = nRT)

About the Ideal Gas Law Calculator (PV = nRT)

Solve the ideal gas law PV = nRT for whichever quantity you need — pressure, volume, amount or temperature — with pressures in kPa, bar, atm, torr, mmHg or psi, volumes in L, mL, m³ or ft³, temperatures in K, °C or °F, and the amount as moles or as a mass (type the gas formula, such as CO2, and its molar mass is worked out). Celsius and Fahrenheit are converted to kelvins for you, and every answer shows the working.

Three more tabs cover the rest of a gases chapter: gas density and molar mass from measurements (the Dumas method, with a list of gases that match), molar volumes under the different “STP” definitions side by side, and a van der Waals comparison that shows how far a real gas departs from ideal behaviour, using textbook constants or values derived from a gas’s critical point.

Common uses

• Chemistry and physics homework on the gas laws, with every step shown.
• Lab work: the moles of gas collected, or the molar mass of a vapour from a Dumas-bulb measurement.
• Converting gas volumes between “standard” conditions used in different textbooks, data sheets and industries.
• Checking when a gas at high pressure or low temperature can no longer be treated as ideal.

The ideal gas law and R

PV = nRT relates the pressure P, volume V, amount n (moles) and absolute temperature T of an ideal gas. The molar gas constant is exact in the SI: R = N_A·k = 8.314 462 618… J/(mol·K), because the Avogadro and Boltzmann constants are fixed exactly (BIPM SI Brochure). In other units:

• 8.314 462 618 L·kPa/(mol·K) = 8.314 462 618 J/(mol·K)
• 0.083 144 626 L·bar/(mol·K)
• 0.082 057 366 L·atm/(mol·K)
• 62.363 598 L·Torr/(mol·K)

Temperatures must be absolute: 25 °C is 298.15 K, and using 25 in place of 298.15 gives an answer that is wrong by a factor of 12.

Density and molar mass of a gas

With n = m/M, the ideal gas law gives the density ρ = PM ÷ RT and the molar mass M = mRT ÷ PV = ρRT ÷ P (OpenStax Chemistry 2e §9.3). This is the Dumas method: vaporise a liquid in a flask of known volume at a known temperature and pressure, weigh the vapour, and calculate M. The tool lists common gases and vapours whose molar mass is within 2 % of the result — a hint, not an identification, since different substances can share a molar mass.

Which “STP”?

IUPAC defines standard temperature and pressure for gases as 0 °C and 100 kPa (1 bar), giving a molar volume of 22.711 L/mol. Many textbooks, including OpenStax Chemistry 2e, still use 0 °C and 1 atm (101.325 kPa), giving the familiar 22.414 L/mol (“22.4 L”). Other reference conditions are common too: 25 °C and 100 kPa (SATP, 24.790 L/mol), 20 °C and 1 atm (often called NTP, 24.055 L/mol) and 15 °C or 60 °F at 1 atm for gas volumes in industry. The Molar volume tab shows them side by side; always state which one you use.

Real gases and the van der Waals equation

Real molecules take up space and attract each other, so gases depart from PV = nRT at high pressure and low temperature. The van der Waals equation corrects for both: (P + a·n²/V²)(V − n·b) = nRT, where b is the excluded volume per mole and a measures the attraction (OpenStax §9.6). The compressibility factor Z = PV ÷ nRT is 1 for an ideal gas; Z < 1 means attractions dominate, Z > 1 that the molecules’ own volume does.

The constants for N₂, O₂, CO₂, H₂O, He and CCl₄ are those of OpenStax Table 9.3. For H₂, Ar, CH₄, NH₃ and Cl₂ they are calculated from the critical point, a = 27R²T_c²/(64p_c) and b = RT_c/(8p_c), with T_c and p_c from the NIST Chemistry WebBook — or enter your own a and b, or a critical point. Different books give slightly different constants, so use the ones your course gives when they differ.

Sources

• BIPM, The International System of Units (SI Brochure, 9th ed.): exact N_A = 6.022 140 76 × 10²³ mol⁻¹ and k = 1.380 649 × 10⁻²³ J/K.
• OpenStax, Chemistry 2e: §9.2 (ideal gas law, Examples 9.9–9.10), §9.3 (density and molar mass, Examples 9.11–9.13) and §9.6 (van der Waals equation, Table 9.3, Example 9.24).
• IUPAC Gold Book, “standard conditions for gases”: 273.15 K and 10⁵ Pa.
• NIST Chemistry WebBook (SRD 69), phase-change data: critical temperatures and pressures of H₂, Ar, CH₄, NH₃ and Cl₂.
• NIST SP 811, Appendix B.8: pressure and volume conversion factors. Molar mass of dry air, 28.9644 g/mol: U.S. Standard Atmosphere, 1976.

Limitations

• The ideal gas law works to within a percent or so for most gases at room temperature and about one atmosphere; it becomes poor at high pressure, at low temperature and close to condensation.
• The van der Waals equation is a two-parameter model: it shows the direction and rough size of real-gas effects, not accurate properties. Near and below the critical temperature it does not say which phase is stable.
• Gas mixtures are treated as one gas: give their mean molar mass (such as 28.9644 g/mol for dry air) for density and mass.
• Molar masses from a formula use IUPAC (CIAAW 2024) atomic weights; the “close to” list is a short built-in list of common gases and vapours.

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