Key Takeaways
- The Ideal Gas Law is PV = nRT, relating pressure, volume, moles, and temperature
- The gas constant R = 0.0821 L·atm/(mol·K) when using standard units
- Temperature must always be in Kelvin (K = °C + 273.15)
- At STP (0°C, 1 atm), 1 mole of ideal gas occupies 22.4 liters
- Real gases deviate from ideal behavior at high pressures and low temperatures
What Is the Ideal Gas Law?
The Ideal Gas Law is a fundamental equation in chemistry and physics that describes the relationship between pressure (P), volume (V), amount of substance (n), and temperature (T) for an ideal gas. This equation combines Boyle's Law, Charles's Law, and Avogadro's Law into a single comprehensive formula.
An "ideal gas" is a theoretical gas composed of randomly moving, non-interacting point particles. While no real gas is perfectly ideal, many gases behave approximately as ideal gases under normal conditions, making this law extremely useful for calculations in chemistry, physics, and engineering.
PV = nRT
The Universal Gas Constant (R)
The gas constant R can have different values depending on the units used. Here are the most common values:
| Value of R | Units | Common Use |
|---|---|---|
| 0.0821 | L·atm/(mol·K) | This calculator (most common) |
| 8.314 | J/(mol·K) | SI units, thermodynamics |
| 62.36 | L·mmHg/(mol·K) | When pressure is in mmHg |
| 1.987 | cal/(mol·K) | Energy calculations in calories |
How to Use This Calculator
Identify the Unknown Variable
Determine which variable (P, V, n, or T) you need to calculate. Leave that field empty.
Enter Known Values
Fill in the three known values. Make sure temperature is in Kelvin (add 273.15 to Celsius).
Click Calculate
The calculator will solve for the missing variable using PV = nRT with R = 0.0821 L·atm/(mol·K).
Interpret Results
Results are displayed with appropriate units. Verify your answer makes physical sense.
Pro Tip: Temperature Conversion
Always convert Celsius to Kelvin before using the ideal gas law: K = °C + 273.15. For example, room temperature (25°C) = 298.15 K. Using Celsius directly will give incorrect results!
Derived Equations
The ideal gas law can be rearranged to solve for any variable:
P = nRT/V
V = nRT/P
n = PV/RT
T = PV/nR
Standard Temperature and Pressure (STP)
At Standard Temperature and Pressure (STP), defined as 0°C (273.15 K) and 1 atm, one mole of an ideal gas occupies exactly 22.4 liters. This is known as the molar volume of an ideal gas at STP.
You can verify this using the ideal gas law:
V = nRT/P = (1 mol)(0.0821 L·atm/mol·K)(273.15 K)/(1 atm) = 22.4 L
Real Gases vs. Ideal Gases
The ideal gas law works well under these conditions:
- Low pressure - Molecules are far apart
- High temperature - Kinetic energy overcomes intermolecular forces
- Non-polar gases - Weaker intermolecular attractions
Real gases deviate from ideal behavior when:
- Pressure is very high (molecules are compressed)
- Temperature is very low (molecules move slowly)
- The gas is near its condensation point
For real gases under extreme conditions, the Van der Waals equation provides more accurate results by accounting for molecular size and intermolecular forces.
Frequently Asked Questions
The ideal gas law requires an absolute temperature scale because gas volume is directly proportional to absolute temperature. At 0 Kelvin (absolute zero), an ideal gas would have zero volume. The Celsius scale has an arbitrary zero point (freezing point of water), which would give incorrect results.
At Standard Temperature and Pressure (0°C and 1 atm), one mole of any ideal gas occupies 22.4 liters. This is a useful constant for quick calculations in stoichiometry involving gases.
Yes, for most practical purposes at moderate temperatures and pressures. Real gases like nitrogen, oxygen, and helium behave very similarly to ideal gases under normal conditions. For high precision or extreme conditions, use the Van der Waals equation instead.
Common pressure conversions: 1 atm = 760 mmHg = 760 torr = 101.325 kPa = 1.01325 bar = 14.696 psi. This calculator uses atmospheres (atm), so convert your pressure to atm before entering.
No real gas is perfectly ideal, but noble gases (helium, neon, argon) and diatomic gases (H2, N2, O2) at room temperature and atmospheric pressure behave very close to ideally. Gases with strong intermolecular forces (like water vapor or ammonia) deviate more from ideal behavior.