CK-12-Chemistry Intermediate

14.3. Ideal Gases http://www.ck12.org

• T = 23°C = 296 K

• P = 0.987 atm


• R = 0.08206 L•atm/K•mol

Unknown

• n =? mol


• molar mass =? g/mol

First, the ideal gas law will be used to solve for the moles of unknown gas (n). Then, the mass of the gas divided by
the moles will give the molar mass.

Step 2: Solve.

n=

PV

RT

=

0 .987 atm× 0 .677 L

0 .08206 L·atm/K·mol×296 K

= 0 .0275 mol

Now divide the mass of the sample (in g) by the amount (in mol) to get the molar mass.

molar mass=

1 .211 g

0 .0275 mol

= 44 .0 g/mol

Since nitrogen has a molar mass of 14 g/mol, and oxygen has a molar mass of 16 g/mol, the formula N 2 O would
produce the correct molar mass.

Step 3: Think about your result.

The R value that includes units of atm was chosen for this problem. The calculated molar mass corresponds to a
reasonable molecular formula for a compound composed of nitrogen and oxygen.

Practice Problem

3. Determine the molar mass of a gas if 4.91 g of the gas occupies a volume of 2.85 L at a pressure of 812 mmHg
   and a temperature of 29°C. Which of the noble gases would be consistent with this data?

The ideal gas law can be used to find the density of a gas at conditions that are not standard. For example, we
will determine the density of ammonia (NH 3 ) at 0.913 atm and 20°C, assuming the ammonia acts as an ideal gas.
First, the molar mass of ammonia is calculated from its formula to be 17.04 g/mol. Next, assume exactly 1 mol of
ammonia (n = 1) and calculate the volume that such an amount would occupy at the given temperature and pressure.

V=

nRT

P

=

1 .00 mol× 0 .08206 L·atm/K·mol×293 K

0 .913 atm

= 26 .3 L

Now, the density can be calculated by dividing the mass of one mole of ammonia by the volume above.

density=

17 .04 g

26 .3 L

= 0 .647 g/L

As a point of comparison, this density is slightly less than the density of ammonia at STP, which is equal to (17.04
g/mol)/(22.4 L/mol) = 0.761 g/L. It makes sense that the density should be lower than at STP, since both the increase
in temperature (from 0°C to 20°C) and the decrease in pressure (from 1 atm to 0.913 atm) would cause the NH 3
molecules to spread out a bit farther from one another.

Video lectures are extremely helpful in learning about ideal gases. You can find five successive lectures at: