Ideal Gas Example Problem With Unknown Gas

Worked Chemistry Problems

If you known the properties of a gas, you can use the Ideal Gas Law to determine its identity.
If you known the properties of a gas, you can use the Ideal Gas Law to determine its identity. Paul Taylor, Getty Images

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

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.

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

Answer

Element X is Krypton.