Chain45154/Getty Images
An atm (atmosphere) is a unit of gas pressure. One atm equals the standard atmospheric pressure at sea level: 14.7 psi, 101 325 Pa, 1.01325 bar, or 1 013.25 mbar. The Ideal Gas Law lets you link a gas’s pressure inside a container to the number of moles it contains, as long as temperature and volume remain constant.
At the standard temperature and pressure (STP) of 273 K (0 °C / 32 °F) and 1 atm, one mole of an ideal gas occupies 22.4 L. This relationship is the basis for converting pressures measured in atmospheres to moles of gas.
The Ideal Gas Law is expressed as:
PV = nRT
where P is pressure, V is volume, n is the number of moles, T is absolute temperature in Kelvin, and R is the ideal gas constant. When pressure is measured in atmospheres, R = 0.082057 L atm mol⁻¹ K⁻¹. If you prefer SI units, R = 8.3145 J mol⁻¹ K⁻¹ (≈ 8.3145 m³ Pa mol⁻¹ K⁻¹).
This equation holds for an ideal gas—one whose molecules are perfectly elastic and occupy no volume. While no real gas meets these criteria exactly, the law is a good approximation for most gases under STP conditions.
Rearranging the Ideal Gas Law gives two useful forms:
P = (n R T)/V or n = (P V)/(R T)
If you keep temperature and volume constant, pressure and the number of moles are directly proportional: P = C n and n = P/C, where C = R T/V.
To calculate C, measure volume in liters or cubic meters, and use the corresponding value of R. Temperature must always be expressed in Kelvin; convert from Celsius by adding 273.15, or from Fahrenheit by subtracting 32, multiplying by 5/9, then adding 273.15.
Consider a 0.5‑L bulb filled with argon at a pressure of 3.2 atm when the bulb is off and the room temperature is 25 °C. How many moles of argon does the bulb contain?
First, determine C using R = 0.082 L atm mol⁻¹ K⁻¹:
C = (R T)/V = (0.082 × 298.15)/0.5 = 48.9 atm mol⁻¹
Then compute the moles:
n = P/C = 3.2 / 48.9 ≈ 0.065 moles
