A 0.211 mol sample of an unknown gas contained in a 5.00 L flask is found to have a density of 2.50 g/L. The molecular weight of the unknown gas is g/mol.?

1 Answer
Feb 23, 2018

Answer:

#"59.2 g mol"^(-1)#

Explanation:

The idea here is that the density of the gas tells you the mass of this gas that occupies exactly #"1 L"# at some unspecified conditions for pressure and temperature.

In this case, you know that the gas had a density of #"2.50 g L"^(-1)#. This tells you that #"2.50 g"# of this gas occupy exactly #"1 L"# at the conditions for pressure and temperature used in the experiment.

You also know that the total volume of the flask is equal to #"5.00 L"#. At this point, you can use the density of the gas to calculate the mass of gas needed in order for the sample to occupy the given volume.

#5.00 color(red)(cancel(color(black)("L"))) * "2.50 g"/(1color(red)(cancel(color(black)("L")))) = "12.5 g"#

Now, in order to find the molar mass of the gas, you need to find the mass of exactly #1# mole. You know that this sample contains #0.211# moles of gas and has a mass of #"12.5 g"#, so you can say that #1# mole will have a mass of

#1 color(red)(cancel(color(black)("mole gas"))) * "12.5 g"/(0.211 color(red)(cancel(color(black)("moles gas")))) = "59.24 g"#

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

#color(darkgreen)(ul(color(black)("molar mass = 59.2 g mol"^(-1)))#

This means that #1# mole of this gas has a mass of #"59.2 g"#.

The answer is rounded to three sig figs.