Question

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.?

Answer 1

`"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.