Calculate nitrogen gas volume from mass or moles at STP or your own pressure and temperature, or convert liquid nitrogen to gas volume and back.
Related Calculators
- Liters To Moles Calculator
- Volume To Moles Calculator
- Moles To mL Calculator
- Z Factor Calculator
- All Chemistry Calculators
Nitrogen Volume Formula
The ideal-gas estimate is V = nRT/P, with absolute pressure and temperature above 0 K. The general prescribed-compressibility relation is V = ZnRT/P. In these gas-law modes, supply a Z that matches the actual nitrogen state. The cylinder and pipe mode uses tabulated real-gas density instead. The liquid/gas conversion modes instead use the stated expansion ratio, approximately 696:1 near 70ยฐF and 1 atm by default.
| Variable | Symbol | SI Unit | Common Alt. |
|---|---|---|---|
| Volume | V | mยณ | L, ftยณ |
| Amount (moles) | n | mol | |
| Gas constant | R | 8.31446 J/(molยทK) | 0.082057 Lยทatm/(molยทK) |
| Temperature | T | K | ยฐC + 273.15 |
| Absolute pressure (not gauge) | P | Pa | atm, psi, bar |
Nitrogen in a Cylinder or Pipe
Select Gas in a cylinder or pipe. Enter the cylinderโs water capacity or another known internal volume. For a straight pipe of uniform size, you can instead enter the inside diameter and length. Pipe volume is ฯ ร inside diameterยฒ ร length รท 4, using consistent length units.
Enter the stabilized gas temperature and the nitrogen pressure. The calculator adds 1.01325 bar to a gauge reading. If atmospheric pressure at the gauge differs from 1.01325 bar, add the actual local atmospheric pressure yourself and choose an absolute unit.
The calculator interpolates nitrogen density from NIST Chemistry WebBook data between โ20 and 60 ยฐC and 1.01325 and 351.01325 bar absolute. Nitrogen mass equals the internal volume multiplied by the density at the entered conditions. Free gas volume equals that mass divided by 1.16483 kg/mยณ, the nitrogen density at 20 ยฐC and 1 atm absolute. Check the reference conditions when comparing volumes from different suppliers.
For example, a 50 L cylinder containing pure nitrogen at 200 bar gauge and 20 ยฐC has an estimated 11.0 kg of nitrogen, equivalent to about 9.42 mยณ at 20 ยฐC and 1 atm absolute. Choose mยณ as the answer unit to see that reference volume directly.
The result describes total inventory in a vessel or straight pipe filled with pure nitrogen. Usable cylinder supply depends on residual pressure and delivery limits. A nitrogen generatorโs rating is a flow at a specified purity and pressure. Compare its output with demand on the same reference basis, including peak flow and duty cycle. The inventory estimate does not size a generator, estimate a purge or calculate pressure loss while gas flows.
Nitrogen Physical Properties
Nitrogen (N2) is a diatomic gas. An ideal-gas approximation can be useful near ambient conditions, but accuracy depends on the actual state. The table gives approximate physical reference values; real-gas densities need not equal the ideal-gas density computed with Z = 1. The calculator uses a conventional molar mass of 28.0134 g/mol and the chosen gas model.
| Property | Value |
|---|---|
| Molar mass | 28.014 g/mol |
| Density at STP (0ยฐC, 1 atm) | 1.2506 g/L |
| Density at NTP (20ยฐC, 1 atm) | 1.165 g/L |
| Molar volume at STP | 22.414 L/mol |
| Critical temperature (Tc) | 126.2 K (-147ยฐC) |
| Critical pressure (Pc) | 3.3958 MPa (33.958 bar; approximately 33.5 atm or 493 psia) |
| Van der Waals constant a | 1.390 Lยฒยทatm/molยฒ |
| Van der Waals constant b | 0.0391 L/mol |
Ideal Gas Accuracy for Nitrogen
The compressibility factor Z = PV/(nRT) describes departure from ideal-gas behavior. Ideal-gas accuracy depends on temperature and absolute pressure; no universal 1% accuracy range is assumed here. For compressed nitrogen, use a state-appropriate Z or a validated nitrogen equation of state, such as the models documented by NIST REFPROP. A prescribed Z is not a phase-stability or equipment-rating check.
At fixed nitrogen amount, temperature and absolute pressure, Vreal = Z ร Videal. If Z > 1, the ideal law underpredicts volume; if 0 < Z < 1, it overpredicts volume. Obtain actual-state values from a validated property source.
High-density, cryogenic and near-critical nitrogen can depart materially from the ideal model. An assumed Z = 1 does not establish an acceptable error for a pressurized cylinder. Nitrogen can displace oxygen; liquid nitrogen and cold vapor can cause burns, and trapped liquid can produce dangerous overpressure. Follow gas-supplier guidance, equipment ratings and approved procedures; these volume estimates do not establish safe containment, ventilation or filling.
Example Calculations
Example 1: Basic volume calculation
Given: absolute P = 100 psia (approximately 6.80460 atm), T = 300 K, n = 1 mol, and the ideal-gas assumption Z = 1.
V = nRT/P = (1 ร 8.31446261815324 ร 300) / 689,475.7293 โ 0.003617733 mยณ โ 3.617733 L โ 0.127759 ftยณ.
Example 2: Industrial nitrogen cylinder
For an illustrative calculation only, assume a vessel volume of 49.9 L, an absolute pressure of 2,200 psia (approximately 149.701 atm), and a temperature of 20ยฐC (293.15 K). This example uses Z = 1 to demonstrate ideal-gas arithmetic; actual cylinder capacity requires a real-gas model and the manufacturerโs rated conditions. A 2,200 psig reading would require adding local atmospheric pressure first.
For this ideal model, n = PV/RT = (15,168,466.04497 Pa ร 0.0499 mยณ) / (8.31446261815324 ร 293.15 K) โ 310.540413 mol.
Keeping the same ideal-gas assumption and amount at 1 atm absolute and 20ยฐC gives V = nRT/P โ 7,470.085918 L โ 263.803595 ftยณ. This idealized result does not validate a cylinderโs advertised capacity, allowable pressure or safe fill level; use state-appropriate real-gas data and the manufacturerโs documentation.
