Ideal Gas Law Calculator (PV = nRT)
The Ideal Gas Law Calculator solves for the number of moles (n) of a gas using the equation PV = nRT, where P is absolute pressure in Pascals (Pa), V is volume in cubic meters (m³), T is absolute temperature in Kelvin (K), and R is the universal gas constant (8.314 J·mol⁻¹·K⁻¹). This law combines Boyle's Law (P∝1/V), Charles's Law (V∝T), and Avogadro's Law (V∝n) into one unified equation. It is valid for ideal gas behavior — low pressures and high temperatures where intermolecular forces are negligible. Enter any three known variables to instantly solve for the fourth.
When to use this calculator
- Chemistry lab: calculating how many moles of nitrogen gas are contained in a 10 L tank pressurized to 5 atm (506,625 Pa) at room temperature (298 K).
- Engineering: verifying the amount of CO₂ produced in a combustion reaction by measuring post-reaction gas pressure and volume in a sealed vessel.
- Education: confirming that exactly 1 mole of any ideal gas occupies 22.414 L at STP (0°C, 1 atm) — the classic molar volume demonstration.
- Scuba diving safety: estimating how the volume of a gas bubble changes as a diver ascends from 30 m depth (4 atm) to the surface (1 atm) at constant temperature.
- Industrial process control: determining the number of moles of hydrogen gas produced during electrolysis by measuring tank pressure increase over time at a known temperature.
Calculation Example
- 1 atm, 22.4 L, 273K
- n = 101325×0.0224/(8.314×273) = 1 mol
How it works
3 min readHow It Is Calculated
The Ideal Gas Law relates four state variables of an ideal gas:
PV = nRT
Solving for moles:
n = (P × V) / (R × T)
Where:
P = Absolute pressure [Pascals, Pa]
V = Volume [cubic meters, m³]
n = Amount of substance [moles, mol]
R = Universal gas constant 8.314 J·mol⁻¹·K⁻¹ (NIST CODATA 2018)
T = Absolute temperature [Kelvin, K]
Unit conversions you must apply BEFORE calculating:
1 atm = 101,325 Pa
1 L = 0.001 m³
°C → K = °C + 273.15
1 bar = 100,000 Pa
1 psi = 6,894.76 PaThe value of R = 8.314462618 J·mol⁻¹·K⁻¹ is an exact defined constant since the 2019 SI redefinition of the mole (NIST).
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Reference Table
Common conditions and corresponding molar volumes for an ideal gas:
| Condition | T (K) | P (Pa) | Molar Volume (L/mol) |
|---|---|---|---|
| STP (IUPAC 1982) | 273.15 | 101,325 | 22.414 |
| STP (IUPAC 2014) | 273.15 | 100,000 | 22.711 |
| NTP (20°C, 1 atm) | 293.15 | 101,325 | 24.055 |
| Room Temp (25°C, 1 atm) | 298.15 | 101,325 | 24.466 |
| Body Temp (37°C, 1 atm) | 310.15 | 101,325 | 25.447 |
| Liquid N₂ boiling (77 K, 1 atm) | 77.00 | 101,325 | 6.319 |
> Note: IUPAC changed the standard pressure definition from 101,325 Pa (1 atm) to exactly 100,000 Pa (1 bar) in 1982. Many textbooks still use the older definition. Always verify which STP your course or industry uses.
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Typical Cases
Case 1 — Classic STP Verification
Case 2 — Pressurized Nitrogen Tank
Case 3 — CO₂ from Dry Ice Sublimation
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Common Errors
1. Using Celsius instead of Kelvin for T. The gas law requires absolute temperature. Using T = 25°C instead of 298.15 K inflates the denominator error — at 25°C vs 298.15 K, results differ by a factor of ~12×. Always add 273.15.
2. Mixing pressure units (atm or psi instead of Pa). If you enter P = 1 instead of P = 101,325, your result for n will be off by a factor of 101,325. Convert everything to SI units (Pa, m³, K) before calculating.
3. Using liters instead of cubic meters for V. 22.4 L ≠ 22.4 m³. Divide liters by 1,000 to get m³. Failing to do so overestimates n by a factor of 1,000.
4. Assuming real gases behave ideally at high pressures. Above ~10 atm or near the gas's boiling point, intermolecular forces cause significant deviation. Use the van der Waals equation [P + a(n/V)²][V − nb] = nRT for real gas corrections. For air at 300 atm, the ideal law overestimates n by >5%.
5. Using the wrong value of R. R has different numerical values depending on units: 8.314 J·mol⁻¹·K⁻¹ (SI), 0.08206 L·atm·mol⁻¹·K⁻¹, or 62.364 L·mmHg·mol⁻¹·K⁻¹. Mixing R with incompatible units gives completely wrong results.
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Frequently asked questions
What is the universal gas constant R and where does its value come from?
R = 8.314462618 J·mol⁻¹·K⁻¹, defined exactly since the 2019 SI redefinition of base units (NIST CODATA 2018). It equals the product of Boltzmann's constant (k_B = 1.380649×10⁻²³ J/K) and Avogadro's number (Nₐ = 6.02214076×10²³ mol⁻¹). In non-SI units it becomes 0.082057 L·atm·mol⁻¹·K⁻¹ or 1.987 cal·mol⁻¹·K⁻¹.
What is the difference between STP and NTP, and which should I use?
STP (Standard Temperature and Pressure) is 0°C (273.15 K) and 100,000 Pa (1 bar) per the 1982 IUPAC definition — giving a molar volume of 22.711 L/mol. The older pre-1982 STP used 101,325 Pa (1 atm), yielding 22.414 L/mol, still common in many textbooks. NTP (Normal Temperature and Pressure) is 20°C (293.15 K) and 1 atm — molar volume 24.055 L/mol. When in doubt, check which standard your course or datasheet specifies.
When does the Ideal Gas Law break down and become inaccurate?
The ideal gas approximation fails at high pressures (>10–20 atm) and low temperatures near the gas's condensation point, where intermolecular attractions and molecular volume become significant. For example, CO₂ at 40 atm and 0°C shows a ~7% deviation from ideal behavior. In these cases, the van der Waals equation or other equations of state (Redlich-Kwong, Peng-Robinson) should be used instead.
Can I solve for pressure, volume, or temperature instead of moles?
Yes — PV = nRT can be rearranged for any single unknown: P = nRT/V, V = nRT/P, T = PV/(nR). Simply ensure all known values are in SI units (Pa, m³, K, mol) before rearranging. This calculator specifically solves for n (moles), but the same formula applies by substitution for any of the four variables.
How do I convert common pressure units to Pascals for this calculator?
Key conversions: 1 atm = 101,325 Pa; 1 bar = 100,000 Pa; 1 psi = 6,894.76 Pa; 1 mmHg (torr) = 133.322 Pa; 1 kPa = 1,000 Pa. For example, a 5 atm tank is 5 × 101,325 = 506,625 Pa. Always use absolute pressure (not gauge pressure) — add atmospheric pressure (~101,325 Pa) to gauge readings.
How many molecules are in 1 mole of an ideal gas?
Exactly 6.02214076×10²³ molecules (Avogadro's number, Nₐ), a defined constant since the 2019 SI revision. So at STP (273.15 K, 1 atm), 22.414 liters of any ideal gas contains 6.022×10²³ molecules, whether it's H₂, O₂, or CH₄ — a direct consequence of Avogadro's Law and the ideal gas model.
Is the Ideal Gas Law applicable to gas mixtures like air?
Yes — for ideal gas mixtures, Dalton's Law of Partial Pressures applies: P_total = P₁ + P₂ + P₃ + …, and n_total = n₁ + n₂ + n₃ + …. Dry air at 1 atm behaves very close to an ideal gas at normal temperatures. You can use PV = nRT with P_total to find total moles, then use mole fractions (e.g., O₂ ≈ 20.95%, N₂ ≈ 78.09%) to find individual component amounts.
Why does a balloon shrink in the cold? How does the Ideal Gas Law explain it?
At constant pressure (P) and constant moles (n), the ideal gas law gives V = nRT/P — volume is directly proportional to absolute temperature (Charles's Law). Dropping from 298 K (25°C) to 258 K (−15°C) reduces volume by a factor of 258/298 ≈ 0.866, so a 1 L balloon shrinks to about 0.87 L — roughly a 13% reduction. This is why car tires lose pressure in winter (temperature drop lowers both pressure and effective volume).