We know that:
number of moles (n) = mass / molar mass
Now, from the general law of gases:
PV = nRT
where:
P is the pressure = 500 torr = 0.65 atm
V is the volume
n is the number of moles
R is the gas constant = 0.082
T is the temperature = 300 k
We will just rearrange this equation as follows:
P = nRT / V
Then we will substitute n with its equivalent equation mentioned at the beginning:
P = (mass x R x T) / (volume x molar mass) ......> equation I
Now, we know that:
density = mass / volume
We will substitute (mass/volume) in equation I with density as follows:
P = (density x R x T) / molar mass
Rearrange this equation to get the mass as follows:
molar mass = dRT/P = (0.216 x 0.082 x 300) / 0.65 = 8.4738 grams
From the periodic table:
molecular mass of hydrogen = 1 grams
molecular mass of nitrogen = 14 grams
Therefore:
molar mass of hydrogen = 2 x 1 = 2 grams
molar mass of nitrogen = 2 x 14 = 28 grams
We can assume that the number of moles of of each element is y.
We can thus build up the following equation:
2y + 28y = 8.4738
30y = 8.4738
y = 0.28246
Therefore:
mole fraction of hydrogen = 2 x 0.28246 = 0.56492
mole fraction of nitrogen = 28 x 0.28246 = 7.90888
