1. What is the Ideal Gas Volume Calculator?

Definition: This calculator computes the volume (\( V \)) of an ideal gas using the ideal gas law, as shown in the formula image above. Volume is calculated via:

\( V = \frac{nRT}{P} \)

Users input pressure (\( P \)), amount of substance (\( n \)), and temperature (\( T \)), with support for multiple units. Results are displayed with 5 decimal places for precision, in units such as m³, cm³, L, cu ft, or cu in.[](https://www.omnicalculator.com/physics/ideal-gas-volume)

Purpose: Essential for thermodynamics, chemical engineering, and physics to determine gas volume in systems like reactors, balloons, or atmospheric studies.

2. How Does the Calculator Work?

The calculator uses the ideal gas law (\( PV = nRT \)), rearranged to solve for volume:

\( V = \frac{nRT}{P} \)

Where:

• \( V \): Volume (m³, cm³, L, cu ft, cu in);
• \( P \): Pressure (Pa, kPa, atm, bar, psi, mmHg);
• \( n \): Amount of substance (mol);
• \( T \): Temperature (K, °C, °F);
• \( R \): Universal gas constant, default 8.31446261815324 J/(mol·K).

Common Gases and Molecular Masses (for Reference):

Gas	Molecular Mass (g/mol)
Air	28.96
Nitrogen	28.02
Oxygen	32.00
Carbon Dioxide	44.01
Methane	16.04

Steps:

• Enter pressure with units (Pa, kPa, atm, bar, psi, mmHg).
• Enter amount of substance in moles.
• Enter temperature with units (K, °C, °F).
• Enter the universal gas constant (\( R \)), defaulting to 8.31446261815324 J/(mol·K).
• Submit to calculate volume.
• Change the output unit (m³, cm³, L, cu ft, cu in) to convert the result instantly.
• Results are formatted to 5 decimal places, with scientific notation for values less than 0.001.

3. Importance of Ideal Gas Volume Calculation

Gas volume calculations are critical for:

• Chemical Engineering: Designing reactors and gas storage systems.
• Aerodynamics: Analyzing gas behavior in balloons or propulsion systems.
• Environmental Science: Studying gas volumes in atmospheric conditions.

4. Using the Calculator

Example 1: Calculate the volume of 1 mol of gas at 1 atm and 25°C, with \( R = 8.31446261815324 \, \text{J/(mol·K)} \), output in m³ and L:

• Pressure: \( P = 1 \, \text{atm} = 101325 \, \text{Pa} \)
• Amount of Substance: \( n = 1 \, \text{mol} \)
• Temperature: \( T = 25 \, \text{°C} = 298.15 \, \text{K} \)
• Calculation: \( V = \frac{1 \times 8.31446261815324 \times 298.15}{101325} \approx 0.02447 \, \text{m³} \)
• Unit conversion: \( 0.02447 \times 1000 \approx 24.46533 \, \text{L} \)

Results:

• Volume: 0.02447 m³
• Volume (converted): 24.46533 L

Example 2: Calculate the volume of 0.5 mol of gas at 100 kPa and 77°F, output in cm³ and cu ft:

• Pressure: \( P = 100 \, \text{kPa} = 100000 \, \text{Pa} \)
• Amount of Substance: \( n = 0.5 \, \text{mol} \)
• Temperature: \( T = 77 \, \text{°F} = (77 - 32) \times \frac{5}{9} + 273.15 = 298.15 \, \text{K} \)
• Calculation: \( V = \frac{0.5 \times 8.31446261815324 \times 298.15}{100000} \approx 0.01239 \, \text{m³} \)
• Unit conversion:
  • cm³: \( 0.01239 \times 1000000 \approx 12390.45656 \, \text{cm³} \)
  • cu ft: \( 0.01239 \div 0.0283168466 \approx 0.43734 \, \text{cu ft} \)

Results:

• Volume: 12390.45656 cm³
• Volume (converted): 0.43734 cu ft

5. Frequently Asked Questions (FAQ)

Q: What is the ideal gas law?
A: The ideal gas law (\( PV = nRT \)) relates pressure, volume, amount of substance, and temperature for an ideal gas, assuming no intermolecular forces and elastic collisions.

Q: Why use Kelvin for temperature?
A: Kelvin is an absolute scale, ensuring positive temperatures for accurate calculations.

Q: Can this calculator be used for real gases?
A: Yes, for low pressures and high temperatures where real gases approximate ideal behavior. For high pressures, consider the van der Waals equation.

Q: What is the universal gas constant?
A: The universal gas constant (\( R \)) is 8.31446261815324 J/(mol·K), relating energy to temperature and moles in the ideal gas law.

Q: How do I convert between volume units?
A: Use the output unit dropdown to instantly convert volume to m³, cm³, L, cu ft, or cu in.

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