Ideal Gas Law Calculator
Free solve for pressure, volume, temperature, or number of moles using pv=nrt. calculate any variable.
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What is the Ideal Gas Law?
The ideal gas law (PV = nRT) is a fundamental equation in thermodynamics that describes the relationship between pressure (P), volume (V), number of moles (n), and temperature (T) of an ideal gas.
An ideal gas is a theoretical gas composed of point particles that have no volume and experience no intermolecular forces. While no real gas is perfectly ideal, most gases behave nearly ideally at moderate temperatures and pressures.
The ideal gas law combines Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law into a single equation. It's widely used in chemistry, physics, and engineering for gas calculations.
Ideal Gas Law Formula
Where:
- • P = Pressure (Pa)
- • V = Volume (m³)
- • n = Number of moles (mol)
- • R = Universal gas constant = 8.314 J/(mol·K)
- • T = Absolute temperature (K)
Rearranged formulas:
P = nRT / V
V = nRT / P
T = PV / (nR)
n = PV / (RT)
How to Calculate
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1
Identify what to solve for
Determine which variable (P, V, T, or n) you need to calculate based on your known values.
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2
Convert to SI units
Convert pressure to Pa, volume to m³, temperature to Kelvin, and ensure moles are in mol.
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3
Apply the formula
Use the appropriate rearrangement: P = nRT/V, V = nRT/P, T = PV/(nR), or n = PV/(RT).
Practical Examples
Example 1: Molar Volume at STP
Calculate the volume of 1 mole of ideal gas at standard temperature and pressure (0°C, 1 atm).
Solution:
P = 101,325 Pa, T = 273.15 K, n = 1 mol, R = 8.314 J/(mol·K)
V = nRT / P = (1 mol × 8.314 × 273.15) / 101,325
V = 0.022414 m³ = 22.414 L
Example 2: Pressure in a Container
A 5 L container holds 0.2 moles of gas at 25°C. What is the pressure?
Solution:
V = 0.005 m³, n = 0.2 mol, T = 298.15 K
P = nRT / V = (0.2 × 8.314 × 298.15) / 0.005
P = 99,200 Pa = 99.2 kPa ≈ 0.98 atm
Applications
Chemistry
Essential for stoichiometry, gas reactions, and determining amounts of gases in chemical processes.
Engineering
Used in HVAC design, gas storage systems, and process engineering calculations.
Automotive
Important for engine design, tire pressure calculations, and airbag systems.
Aerospace
Critical for altitude calculations, cabin pressurization, and gas storage in spacecraft.
Frequently Asked Questions
What is the value of R (gas constant)?
R = 8.314 J/(mol·K) = 0.08206 L·atm/(mol·K) = 62.36 L·torr/(mol·K). The value depends on the units used for pressure and volume.
When does the ideal gas law fail?
At high pressures and low temperatures, real gases deviate from ideal behavior due to molecular volume and intermolecular forces. Use van der Waals equation for better accuracy.
What is standard temperature and pressure (STP)?
STP is 0°C (273.15 K) and 1 atm (101,325 Pa). At STP, 1 mole of ideal gas occupies 22.414 L.
Can I use this for gas mixtures?
Yes! For mixtures, n represents the total number of moles. The ideal gas law applies to the total gas, not individual components.
Why must temperature be in Kelvin?
The gas constant R is defined using Kelvin. Using Celsius or Fahrenheit would give incorrect results because the zero point matters in gas law calculations.