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FINDING THE MOLAR MASS OF A GAS USING IDEAL GAS LAW
by Ken Costello

We want to use modify the ideal gas law to solve for the molar mass (molecular/atomic weight) of a gas.

PV=nRT

State molar mass in words:

molar mass is grams per mole

Now express it in math terms:

molar mass = grams
             mole

Make the reciprocal:

     1     = moles
molar mass   gram

Multiply both sides by grams. Grams cancels on right side:

     1    x grams = moles x grams
molar mass          gram

This simplifies to moles, which is "n" in PV=nRT:

   grams   = moles(n)
molar mass

Since moles (n) is grams divided by molar mass, we can substitute that for "n" in PV=nRT:

PV =   grams  RT
    molar mass

Multiply both sides by molar mass:

PV x molar mass =   grams  RT x molar mass
                 molar mass

To give:

PV x molar mass =grams x RT
                 

Divide both sides by PV:

PV x molar mass =grams x RT
     PV             PV

To give the final formula of:

molar mass =grams x RT
                PV

Use this formula in the homework problem to find the molar mass of the gas to see if it matches the molar mass of CO2.
Finding the Density of a Gas at Temperatures Different than O°C.

When you calculate the molar mass of a gas using the Periodic Table, this gives you the weight of one mole of that gas, which would have a volume of 22.4 liters. This assumes that the pressure is 1 atmosphere and the temperature is O°C. This is called STP (standard pressure and temperature). You can calculate the density of the gas by dividing grams by liters. For example, nitrogen gas is N2 and has the molar mass of 28 grams per mole. If these 28 grams occupies 22.4 liters, then it has 28 grams per 22.4 liters density. Simplify this to 1.25 grams per liter.

 28 grams   = 1.25 g/L
22.4 Liters

If the temperature is warmer than 0°C, then the nitrogen molecules will move faster and try to spread out more. Assuming that the pressure stays the same (1 atmosphere), then their volume will increase. If the temperature goes to, let's say, 100°C, we can figure the volume by setting up a fraction that will make the volume go up. For gases, we always change Celsius into Kelvin. So 0°C to 100°C is 273K to 373K. To make the volume go up, just put 373K on top. Our new volume is 30.6 liters.

373K  x 22.4 Liters = 30.6 Liters
273K

To get density do the same as before; take the grams and divide by the volume. As predicted, the density is less as the gas warms up and spreads out.

 28 grams   = 0.91 g/L
30.6 Liters