Understanding the Ideal Gas Law
The ideal gas law, expressed as PV = nRT, is one of the most fundamental equations in chemistry and physics. It describes the relationship between pressure, volume, temperature, and the number of moles of an ideal gas, allowing us to predict gas behavior under various conditions.
What is the Ideal Gas Law?
The ideal gas law combines several simpler gas laws (Boyle's, Charles's, and Avogadro's laws) into a single equation:
PV = nRT
Where:
- P: Pressure (typically in atmospheres, atm)
- V: Volume (typically in liters, L)
- n: Number of moles of gas
- R: Universal gas constant (0.0821 LĀ·atm/molĀ·K)
- T: Temperature (must be in Kelvin)
Why the Ideal Gas Law Matters
- Predicting behavior: Calculate how gases respond to changing conditions
- Engineering applications: Design pressure vessels, engines, and HVAC systems
- Laboratory work: Determine gas quantities and concentrations
- Safety: Predict pressure changes to prevent explosions
- Environmental science: Model atmospheric processes
- Industrial processes: Optimize reactions involving gases
The Gas Constant R
The universal gas constant R has different values depending on units:
- 0.0821 LĀ·atm/(molĀ·K) - most common in chemistry
- 8.314 J/(molĀ·K) - SI units
- 62.36 LĀ·torr/(molĀ·K) - when using torr
- 8.314 Ć 10Ā³ LĀ·Pa/(molĀ·K) - when using pascals
Our calculator uses R = 0.0821 LĀ·atm/(molĀ·K) by default.
Example Calculations
Example 1: Finding Pressure
Calculate the pressure of 2.0 mol of gas in a 10.0 L container at 298 K:
- P = nRT / V
- P = (2.0 mol)(0.0821)(298 K) / 10.0 L
- P = 4.89 atm
Example 2: Finding Volume
What volume does 1.0 mol of gas occupy at STP (1 atm, 273.15 K)?
- V = nRT / P
- V = (1.0)(0.0821)(273.15) / 1.0
- V = 22.4 L (the molar volume at STP)
Assumptions of the Ideal Gas Law
The ideal gas law assumes:
- Gas molecules have negligible volume
- No intermolecular forces between molecules
- Collisions are perfectly elastic
- Molecules move randomly
Real gases deviate from ideal behavior at high pressures and low temperatures. For real gases, use the van der Waals equation instead.
Standard Temperature and Pressure (STP)
STP is defined as:
- Temperature: 273.15 K (0Ā°C)
- Pressure: 1 atm (101.325 kPa)
- Molar volume: 22.4 L/mol
Note: IUPAC now defines STP as 273.15 K and 1 bar (100 kPa), giving 22.7 L/mol.
Applications
- Scuba diving: Calculating air consumption at depth
- Hot air balloons: Determining lift from heated air
- Tire pressure: Predicting pressure changes with temperature
- Chemical reactions: Calculating gas yields
- Atmospheric science: Modeling air pressure and density
- Respiration: Understanding lung volumes and gas exchange
Related Gas Laws
- Boyle's Law: PāVā = PāVā (at constant T and n)
- Charles's Law: Vā/Tā = Vā/Tā (at constant P and n)
- Gay-Lussac's Law: Pā/Tā = Pā/Tā (at constant V and n)
- Avogadro's Law: Vā/nā = Vā/nā (at constant P and T)
- Combined Gas Law: PāVā/Tā = PāVā/Tā (at constant n)
Tips for Using the Ideal Gas Law
- Always convert temperature to Kelvin (K = Ā°C + 273.15)
- Ensure all units are consistent with your choice of R
- Remember pressure can be in many units (atm, Pa, torr, psi)
- For real gases, corrections may be needed at extreme conditions
- Check reasonableness of answers (e.g., negative values indicate errors)
Whether you're a student learning gas laws, a chemist working with gases, or an engineer designing systems, our ideal gas law calculator provides quick, accurate results for all your PV=nRT calculations.