A mixture of h2 and n2 has a density of 0.216 at 300k and 500 torr. what is the mole fraction composition of the mixture

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