A sample of gas has a mass of 20.00 g and occupies 44.8 L at STP. What is the molar mass of the gas?
We know that 1 mol of an ideal gas at STP occupies 22.4 L. So we will use that relationship to find the number of moles of the gas that occupies 44.8 L.
number of moles = 44.8 L * 1 mol/(22.4 L) = 2.00 moles
number of moles = 2.00 moles
Another way of getting the same result is:
STP means that the pressure is 1 atm and the temperature is 273.15 K. And the volume of our sample is 44.8 L
P * V = n * R * T
n = P * V/(R * T)
n = 1 atm * 44.8 L / (0.082 atm*L/mol*K * 273.15 K)
n = 2.00 moles
So two moles of an ideal gas occupies 44.8 L at STP.
The mass of the sample is 20.00 g and we have 2 moles. So the molar mass is:
molar mass = (mass of sample)/(number of moles of the sample)
molar mass = 20.00 g/(2.00 moles)
molar mass = 10.0 g/mol
Another way of solving it:
Since the mass of two moles of our gas is 20.00 g, we can find the mass of 1 mol by solving this:
2.00 moles of gas ______ 20.00 g
1.00 mol of gas _____ x = ?
x = 1.00 mol * 20.00 g/2.00 moles = 10.0 g
So the mass of 1 mol is 10.0 g. Then the molar mass is 10.0 g/mol.
Answer: the molar mass of the gas is 10.0 g/mol