dividing the mass by the new volume. The following equation, called the Combined Gas Law and
derived from Boyle’s and Charles’s laws, is used to relate changes in the temperature, volume, and
pressure of a gas:
where the subscripts 1 and 2 refer to the two states of the gas (at STP and under the actual
conditions). Rearranging it gives:
V 2 is then used to find the density of the gas under nonstandard conditions by d = m/V 2 . Since we
started by assuming 1 mole of gas (22.4 L at STP), the mass used will be the molar mass.
If you try to anticipate how the changes in pressure and temperature affect the volume of the gas,
this can serve as a check to be sure you have not accidentally confused the pressure or temperature
value that belongs in the numerator with the one that belongs in the denominator.
Example: What is the density of HCl gas at 2 atm and 45°C?
Solution: At STP, a mole of gas occupies 22.4 liters. Since the increase in pressure to 2 atm
decreases volume, 22.4 L must be multiplied by 1/2. And since the increase in
temperature increases volume, the temperature factor will be 318/273.
Calculating Molar Mass
Sometimes the identity of a gas is unknown, and the molar mass must be determined in order to
identify it. The density of the gas at STP is calculated using the gas laws and experimentally
determined values of mass and volume. The molecular weight is then found by multiplying the
density at STP by 22.4 liters, the volume of one mole of gas at STP. Alternatively, the number of