🧪 Gas Law Calculator
Solve for pressure (P), volume (V), moles (n), or temperature (T) using the Ideal Gas Law: PV = nRT. Enter any three variables and the calculator will find the fourth. Choose the gas constant (R) that matches your units.
What Is the Ideal Gas Law?
The Ideal Gas Law is one of the most fundamental equations in chemistry and physics. It relates the pressure, volume, temperature, and amount of an ideal gas in a single equation:
PV = nRT
P = Pressure | V = Volume | n = Number of moles | R = Gas constant | T = Absolute temperature (Kelvin)
The ideal gas law assumes that gas particles have no volume and exert no intermolecular forces. While no real gas perfectly obeys this law, it provides an excellent approximation for most gases under normal conditions.
The Gas Constant (R)
The gas constant R is a proportionality constant that appears in the ideal gas law. Its value depends on the units used for pressure, volume, and temperature:
- 0.082057 L·atm/(mol·K) — Most common in chemistry (using atm and liters)
- 8.314462618 J/(mol·K) — SI units (using Pa and m³)
- 62.363598 L·Torr/(mol·K) — Using Torr (mmHg) for pressure
- 1.9872043 cal/(mol·K) — Using calories for energy
This calculator lets you choose the gas constant that matches your units. Make sure the units you enter are consistent with your chosen R value!
How to Use This Calculator
- Select what to solve for: Choose pressure (P), volume (V), moles (n), or temperature (T).
- Choose the gas constant (R): Pick the value that matches your units.
- Enter known values: Fill in the three variables you know.
- Click "Calculate": The calculator will solve for the missing variable.
- Adjust precision: Use the precision selector to control decimal places.
Common Gas Law Calculations
- Molar volume at STP: At 0°C (273.15 K) and 1 atm, one mole of an ideal gas occupies 22.414 L.
- Gas density: ρ = (P × M) / (R × T), where M is molar mass.
- Molar mass determination: M = (m × R × T) / (P × V), where m is mass.
- Gas stoichiometry: Use PV = nRT to convert between gas volumes and moles in chemical reactions.
Limitations of the Ideal Gas Law
While the ideal gas law is powerful, it has limitations. Real gases deviate from ideal behavior under certain conditions:
- High pressure: Gas particles are forced closer together, and their volume becomes significant.
- Low temperature: Particles move slowly, and intermolecular forces become more important.
- Polar gases: Gases like H₂O, NH₃, and CO₂ show greater deviations due to dipole interactions.
For more accurate results under non-ideal conditions, use the Van der Waals equation or other real gas equations of state.
❓ Gas Law Calculator FAQ
What is the ideal gas law?
The ideal gas law is PV = nRT. It relates the pressure (P), volume (V), number of moles (n), and absolute temperature (T) of an ideal gas. R is the gas constant.
What are the units for the gas constant R?
R has different values depending on units: 0.082057 L·atm/(mol·K) (most common in chemistry), 8.314462618 J/(mol·K) (SI units), 62.363598 L·Torr/(mol·K), and 1.9872043 cal/(mol·K).
What is STP in gas law calculations?
STP (Standard Temperature and Pressure) is 0°C (273.15 K) and 1 atm. At STP, one mole of an ideal gas occupies exactly 22.414 L.
How do I convert Celsius to Kelvin?
To convert Celsius to Kelvin, add 273.15: K = °C + 273.15. For example, 25°C = 298.15 K. This calculator handles the conversion automatically.
What is the difference between ideal gas and real gas?
An ideal gas assumes particles have no volume and no intermolecular forces. Real gases deviate from ideal behavior at high pressure or low temperature. The ideal gas law is still a good approximation for most gases under normal conditions.
How do I find the molar mass of a gas using PV = nRT?
Use the formula M = (m × R × T) / (P × V), where M is molar mass and m is the mass of the gas sample. This calculator doesn't compute molar mass directly, but you can use it to find moles (n), then divide mass by moles.
What is the volume of 1 mole of gas at STP?
At STP (273.15 K and 1 atm), one mole of an ideal gas occupies 22.414 L. This is a useful reference value for gas stoichiometry problems.
Can I use this calculator for gas mixtures?
For gas mixtures, the ideal gas law applies to the total mixture. Use the total moles (sum of all components) and the total pressure. For partial pressures, use Dalton's Law: P_total = P₁ + P₂ + ...
What is the Van der Waals equation?
The Van der Waals equation is a real gas equation that accounts for molecular volume and intermolecular forces: (P + a(n/V)²)(V - nb) = nRT. It provides more accurate results for real gases under non-ideal conditions.
How do I choose the right gas constant?
Choose R based on the units you're using for pressure, volume, and temperature. If you're using atm and liters, use 0.082057 L·atm/(mol·K). If using Pa and m³, use 8.314462618 J/(mol·K).
What is the relationship between pressure and volume?
According to Boyle's Law (a special case of the ideal gas law at constant temperature and moles), pressure and volume are inversely proportional: P₁V₁ = P₂V₂.
What is the relationship between volume and temperature?
According to Charles's Law (at constant pressure and moles), volume and absolute temperature are directly proportional: V₁/T₁ = V₂/T₂.
What is the relationship between pressure and temperature?
According to Gay-Lussac's Law (at constant volume and moles), pressure and absolute temperature are directly proportional: P₁/T₁ = P₂/T₂.
What is the relationship between volume and moles?
According to Avogadro's Law (at constant pressure and temperature), volume and moles are directly proportional: V₁/n₁ = V₂/n₂.
Is this calculator free?
Yes, this calculator is completely free to use. No registration or personal data storage is required. All calculations are performed in your browser.