#
Ideal Gas Example Problem With Unknown Gas

##
Worked Chemistry Problems

by Todd Helmenstine

Updated March 06, 2017

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

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.

Click Here to open a printable periodic table (.pdf).

**Answer**

Element X is Krypton.