Ideal Gas Example Problem With Unknown Gas

Worked Ideal Gas Law Chemistry Problems

The ideal gas law is a relation used to describe the behavior of ideal gases. It also works to approximate the behavior of real gases at low pressures and ordinary to high temperatures. You can apply the ideal gas law to identify an unknown gas.

Question

A 502.8-g sample of X2(g) has a volume 9.0 L at 10 atm and 102 °C. What is element X?

Solution

Step 1

Convert temperature to absolute temperature. This is the temperature in Kelvin:

T = 102 °C + 273
T = 375 K

Step 2

Using the Ideal Gas Law:

PV = nRT

where
P = pressure
V = volume
n = number of moles of gas
R = Gas constant = 0.08 atm L/mol K
T = absolute temperature

Solve for n:

n = PV / RT

n = (10.0 atm)(9.0 L) / (0.08 atm L/mol K)(375 K)
n = 3 mol of X2

Step 3

Find mass of 1 mol of X2

3 mol X2 = 502.8 g
1 mol X2 = 167.6 g

Step 4

Find the mass of X

1 mol X = ½( mol X2)
1 mol X = ½(167.6 g)
1 mol X = 83.8 g

A quick search of the periodic table will find that the gas krypton has a molecular mass of 83.8 g/mol.

Here is a printable periodic table (PDF file) you can view and print, if you need to check atomic weights.