Question #1cb83

The trick here is to realize that under STP conditions, which are currently defined as a pressure of #"100 kPa"# and a temperature of #0^@"C"#, #1# mole of any ideal gas occupies #"22.723 L"#--this is known as the molar volume of agas at STP.

Now, you know that at STP, this gas has a density of #"1.7824 g L"^(-1)#. This tells you that at a pressure of #"100 kPa"# and a temperature of #0^@"C"#, #"1.7824 g"# of this gas occupies exactly #"1 L"#.

Use the molar volume of a gas at STP to find the number of moles present in the sample

#1 color(red)(cancel(color(black)("L"))) * "1 mole gas"/(22.723color(red)(cancel(color(black)("L")))) = "0.0440083 moles gas"#

To find the molar mass of the gas, you need to find the mass of exaftly #1# mole. Since you know that #0.0440083# moles have a mass of #"1.7824 g"#, you can say that

#1 color(red)(cancel(color(black)("mole"))) * "1.7824 g"/(0.0440083color(red)(cancel(color(black)("moles")))) = "40.501 g"#

Therefore, you can say that the molar mass of the gas is equal to

#color(darkgreen)(ul(color(black)("molar mass = 40.501 g mol"^(-1))))#

The answer is rounded to five sig figs, the number of sig figs you have for the density of the gas at STP.

#color(white)(a)#
SIDE NOTE More often than not, the molar volume of a gas at STP is given as #"22.414 mol L"^(-1)#, the value that corresponds to a pressure of #"1 atm"# and a temperature of #0^@"C"#.

If that's the value given to you, make sure to redo the calculations using #"22.414 L mol"^(-1)# instead of #"22.723 mol L"^(-1)#.