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 X_{2}(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 X_{2}

**Step 3**

Find mass of 1 mol of X_{2}

3 mol X_{2} = 502.8 g

1 mol X_{2} = 167.6 g

**Step 4**

Find the mass of X

1 mol X = ½( mol X_{2})

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.

**Answer**

Element X is Krypton.