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 = <span>dRT/P = (0.216 x 0.082 x 300) / 0.65 = 8.4738 grams </span> 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
