Determine the molar mass of a gas if a 4.23g sample of the gas occupies 4.00L at 27 degrees Celsius and a pressure of 715 torr.

The Ideal Gas Law relates pressure, volume, temperature and number of moles of a gas:

PV=nRT, or PV/nT = R, a constant. 

You're given the following information:

P=715 torr

V=4.00L

T=27ºC, Kelvin temperature = 27ºC + 273 = 300K

mass = 4.23 grams

R = 62.36 L-torr/mol-K (ideal gas constant)

n = number of moles 

You could solve for n, the number of moles, and then use mass/moles = molar mass. 

Here's a shortcut: Since molar...

The Ideal Gas Law relates pressure, volume, temperature and number of moles of a gas:

PV=nRT, or PV/nT = R, a constant. 

You're given the following information:

P=715 torr

V=4.00L

T=27ºC, Kelvin temperature = 27ºC + 273 = 300K

mass = 4.23 grams

R = 62.36 L-torr/mol-K (ideal gas constant)

n = number of moles 

You could solve for n, the number of moles, and then use mass/moles = molar mass. 

Here's a shortcut: Since molar mass M = mass/moles, moles = mass/M

We can substitute m/M (mass/molar mass) for n in the ideal gas law and solve for M:

PV=nRT

n=PV/RT

m/M=PV/RT

M=mRT/PV

M=(4.23g)(62.36 L-torr/mol-K)(300K)/(715 torr)(4.00L) = 27.7 g/mol

Here are a few things to keep in mind when using the Ideal Gas Law:

1. Temperature must be in Kelvins because the Celsius scale isn't proportional.

2. The value of the ideal gas constant R depends on the unit used for pressure. When looking up R be sure to use the value that includes the given pressure unit, in this case torr.

3. Include all units so that you can verify that the answer has the correct units. In this case liters, torr and Kelvins canceled out to give grams/mole, a molar mass unit.