Gas Law Calculator
Calculate pressure, volume, temperature, and amount of gas using fundamental gas laws
Gas Properties
How to Use
Ideal Gas Law Calculations
Use the ideal gas law to calculate pressure, volume, temperature, or amount of gas.
How It Works
- Enter 3 values: Fill in any three of the four variables
- Leave 1 empty: The calculator will solve for the missing value
- Choose units: Select appropriate units for each measurement
- Get results: See the calculated value with step-by-step solution
Ideal Gas Law: PV = nRT
- P: Pressure of the gas
- V: Volume of the gas
- n: Amount of gas in moles
- R: Gas constant (0.08206 L·atm/mol·K)
- T: Temperature in Kelvin
Try Sample Calculation
Click “Load Sample” to see how to calculate pressure for 2 moles of gas at 25°C in a 22.4L container.
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Understanding Gas Laws
Fundamental Gas Laws
- Ideal Gas Law (PV = nRT): Relates pressure, volume, temperature, and amount of gas
- Boyle's Law (P₁V₁ = P₂V₂): Pressure inversely proportional to volume at constant temperature
- Charles's Law (V₁/T₁ = V₂/T₂): Volume directly proportional to temperature at constant pressure
- Gay-Lussac's Law (P₁/T₁ = P₂/T₂): Pressure directly proportional to temperature at constant volume
Key Thermodynamic Concepts
- Pressure: Force per unit area exerted by gas molecules on container walls
- Volume: Space occupied by gas molecules in three dimensions
- Temperature: Measure of average kinetic energy of gas molecules (use Kelvin for calculations)
- Moles: Amount of substance containing Avogadro's number (6.022 × 10²³) of particles
- Gas Constant (R): Universal constant relating energy and temperature (0.08206 L·atm/mol·K)
Kinetic Molecular Theory
- Gas Particles: In constant, random motion with negligible volume
- Elastic Collisions: No energy lost during particle collisions
- No Intermolecular Forces: Ideal gases have no attractive or repulsive forces
- Average Kinetic Energy: Directly proportional to absolute temperature
Real vs. Ideal Gases
- Ideal Gas Assumptions: Point particles, no intermolecular forces, elastic collisions
- Real Gas Deviations: Significant at high pressure and low temperature
- Van der Waals Equation: Accounts for molecular size and intermolecular forces
- Compressibility Factor: Measures deviation from ideal behavior (Z = PV/nRT)
Laboratory Applications
- STP Conditions: Standard Temperature and Pressure (0°C, 1 atm)
- Molar Volume: One mole of ideal gas occupies 22.4 L at STP
- Gas Density: Calculate using d = PM/RT where M is molar mass
- Gas Mixtures: Use Dalton's Law for partial pressures
Frequently Asked Questions
Why must temperature be in Kelvin for gas law calculations?
Gas laws are based on absolute temperature. Kelvin starts at absolute zero (-273.15°C), ensuring temperature ratios in gas laws are mathematically valid. Celsius and Fahrenheit have arbitrary zero points that would give incorrect results.
When do real gases deviate most from ideal behavior?
Real gases deviate from ideal behavior at high pressures (molecules closer together) and low temperatures (slower molecular motion). At these conditions, intermolecular forces and molecular volume become significant.
What's the difference between gauge and absolute pressure?
Absolute pressure is measured from perfect vacuum (0 pressure). Gauge pressure is measured relative to atmospheric pressure. For gas law calculations, always use absolute pressure: P_absolute = P_gauge + P_atmospheric.
How do I convert between different pressure units?
Common conversions: 1 atm = 101,325 Pa = 760 mmHg = 760 torr = 14.7 psi = 1.01325 bar. Our calculator handles these conversions automatically.
What happens to gas volume at absolute zero?
According to Charles's Law, gas volume would theoretically reach zero at 0 K (-273.15°C). In reality, gases liquefy or solidify before reaching absolute zero, so the gas laws no longer apply.
How do I calculate the density of a gas?
Use the ideal gas law rearranged: d = PM/RT, where d is density, P is pressure, M is molar mass, R is gas constant, and T is temperature. This relates gas density to pressure and temperature.
What's the significance of STP in chemistry?
Standard Temperature and Pressure (0°C, 1 atm) provides a reference point for comparing gas properties. At STP, one mole of any ideal gas occupies exactly 22.4 liters, making calculations easier.
How do I handle gas mixtures in calculations?
Use Dalton's Law of Partial Pressures: the total pressure equals the sum of individual gas pressures. Each gas behaves independently and follows the ideal gas law for its partial pressure.
Why is the gas constant R different in various units?
R has the same value but different units depending on the pressure and volume units used. Common values: 0.08206 L·atm/mol·K, 8.314 J/mol·K, 1.987 cal/mol·K. Choose R to match your other units.
How accurate are gas law calculations for real gases?
For most laboratory conditions (near room temperature and pressure), ideal gas calculations are accurate within 1-2%. For high accuracy or extreme conditions, use equations of state like Van der Waals or Peng-Robinson.
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Advanced Gas Law Topics
- Combined Gas Law: (P₁V₁/T₁) = (P₂V₂/T₂) for changing conditions
- Graham's Law: Gas effusion rates inversely proportional to square root of molar mass
- Henry's Law: Gas solubility in liquids proportional to partial pressure
- Raoult's Law: Vapor pressure of solutions with volatile components
- Maxwell-Boltzmann Distribution: Statistical distribution of molecular speeds
Industrial Applications
- Chemical Processing: Reactor design, pressure vessel calculations
- Environmental Science: Atmospheric pressure modeling, pollution dispersion
- Energy Systems: Gas turbine efficiency, combustion analysis
- Materials Science: Gas storage, membrane separation processes
- Pharmaceutical: Drug delivery systems, aerosol formulations