A pure sample of unknown gas has a mass of 147g and a volume of 103L at STP. What is its molecular mass?

Answer 1

STP (standard temperature and pressure) means a temperature 273.15 K (0° C) and pressure of 100 kPa. Using the ideal gas law, PV = nRT, the value of vloume given (103L) and a value of R (to match the pressure in kiloPascals and the volume in liters) of 8.314462, we can calculate the number of moles:

PV = nRT

n = PV/RT

n = (100•103)/(8.314462•273.15) = 4.53526 moles

With a mass of 147 g, the molar mass is 147/4.53526 = 32.4127 g/mol.

The molecular mass is the same number, just different units because it is NOT the mass of a mole of the gas, NOR is it in units of grams. It is just a number (no units) and represents a mass "comparison", if you will. It is the mass of a single molecule.

So the molecular mass = 32.4

Sometimes, the "unit" or identifier "amu" is used (which also is called a dalton (Da) or unified atomic mass unit (u). So, you can also say the molecular mass is 32.4 amu or 32.4 amu or 32.2 u but these are really just placeholders because the molecular mass is really just a ratio so it doesn't actually have a real "unit"

Answer 2

Molecular mass is given as g/mol. The question gives us the number of grams, so we can divide this by the number of moles to get our molecular mass.

We aren't given the number of moles but we are given the volume at STP (P=1atm, T=273°K). We could plug this information into the ideal gas law PV=nRT and solve for n, but there is an easier way.

At STP the volume of any gas 22.4L/mol. We are given that the volume of the gas is 103L, so we can use this information to solve for the number of moles.

Once we have moles, we remember to divide g/mol to get the molecular mass.