Pressure (P)
—
Pa
Volume (V)
—
L
Amount (n)
—
mol
Temperature (T)
—
K
Mode
Ideal Gas
Method used
Apply ideal gas law (PV = nRT) and combined gas law (P₁V₁/T₁ = P₂V₂/T₂) calculations. Solve for any variable with step-by-step physics solutions and unit conversion.
Leave the variable you want to solve for empty.
Problem: What is the volume occupied by 1 mole of an ideal gas at standard temperature and pressure (STP: 273.15 K, 101325 Pa)?
Solution: Using PV = nRT, solve for V:
V = nRT / P = (1 mol)(8.314 J/mol·K)(273.15 K) / 101325 Pa
= 22.414 L (0.022414 m³)
This is the well-known molar volume of an ideal gas at STP — a fundamental constant in chemistry.
Problem: A 12 L SCUBA tank contains 3.0 moles of air at 25°C. What is the pressure inside the tank?
Solution: Using PV = nRT with T = 25°C = 298.15 K, V = 12 L = 0.012 m³
P = nRT / V = (3.0)(8.314)(298.15) / 0.012
= 6.20 × 10⁵ Pa (6.12 atm, ~90 psi)
Standard SCUBA tanks are typically filled to about 200-300 bar for diving.
Problem: A balloon contains 2 L of air at 20°C. What will its volume be if heated to 80°C at constant pressure?
Solution: Using Charles's Law (V₁/T₁ = V₂/T₂ at constant P):
V₂ = V₁ × T₂ / T₁ = 2 L × (80 + 273.15) K / (20 + 273.15) K
= 2 × 353.15 / 293.15 = 2.41 L
The volume increases as temperature rises, exactly as Charles's Law predicts for constant pressure.
Problem: A weather balloon has a volume of 5.0 m³ at sea level (1 atm, 15°C). At 10 km altitude, the pressure drops to 0.265 atm and temperature to -50°C. What is the new volume?
Solution: Using P₁V₁/T₁ = P₂V₂/T₂, solve for V₂:
V₂ = P₁V₁T₂ / (P₂T₁) = (1 atm)(5.0 m³)(223.15 K) / (0.265 atm)(288.15 K)
= 14.6 m³
The balloon expands nearly threefold at altitude due to the much lower atmospheric pressure.
Where P is pressure (Pa), V is volume (m³), n is the amount of substance (mol), R = 8.314462618 J/(mol·K) is the universal gas constant, and T is absolute temperature (K).
Combines Boyle's Law, Charles's Law, and Gay-Lussac's Law into one expression for a fixed amount of gas.
P₁V₁ = P₂V₂
At constant temperature, the pressure and volume of a gas are inversely proportional. If the volume doubles, the pressure is halved, and vice versa.
V₁/T₁ = V₂/T₂
At constant pressure, the volume of a gas is directly proportional to its absolute temperature (in Kelvin). Heating a gas causes it to expand.
P₁/T₁ = P₂/T₂
At constant volume, the pressure of a gas is directly proportional to its absolute temperature. Heating a gas in a rigid container raises the pressure.
V₁/n₁ = V₂/n₂
At constant pressure and temperature, the volume of a gas is directly proportional to the number of moles. Equal volumes of gases at the same T and P contain equal numbers of molecules.
An ideal gas is a theoretical model where gas molecules have negligible volume, no intermolecular forces, and perfectly elastic collisions. Real gases approximate ideal behavior at low pressures and high temperatures. The ideal gas law works well for most gases under ordinary conditions.
The universal gas constant R = 8.314462618 J/(mol·K) in SI units. In other common units, R = 0.082057 L·atm/(mol·K) or R = 1.987 cal/(mol·K). Our calculator handles all unit conversions internally so you can work in any convenient units.
All gas law calculations require absolute temperature in Kelvin (K). Convert using: K = °C + 273.15, or K = (°F + 459.67) × 5/9. Never use Celsius or Fahrenheit directly in gas law formulas — the proportionality breaks without absolute zero as the reference point.
Real gases deviate from ideal behavior at high pressure (molecules are close together, their finite volume matters) and low temperature (molecules slow down, intermolecular attractive forces become significant). For better accuracy under these conditions, use the van der Waals equation: (P + a(n/V)²)(V - nb) = nRT.
⚠️ Important Note: This calculator applies the ideal gas law (PV = nRT), which assumes ideal gas behavior. Real gases may deviate from ideal behavior at high pressures (where molecular volume matters) and low temperatures (where intermolecular attractive forces become significant). For precise work under non-ideal conditions, consider using more advanced equations of state such as van der Waals, Redlich-Kwong, or Peng-Robinson.
The combined gas law (P₁V₁/T₁ = P₂V₂/T₂) relates the initial and final states of a fixed amount of gas (n is constant) without needing the gas constant R. It combines Boyle's Law (P₁V₁ = P₂V₂ at constant T), Charles's Law (V₁/T₁ = V₂/T₂ at constant P), and Gay-Lussac's Law (P₁/T₁ = P₂/T₂ at constant V) into a single expression. The ideal gas law (PV = nRT) is more general — it can handle changes in the amount of gas (n) and can solve for any single variable when the other three are known, making it suitable for a wider range of chemistry and physics problems.