# 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.?

Feb 23, 2018

${\text{59.2 g mol}}^{- 1}$

#### Explanation:

The idea here is that the density of the gas tells you the mass of this gas that occupies exactly $\text{1 L}$ at some unspecified conditions for pressure and temperature.

In this case, you know that the gas had a density of ${\text{2.50 g L}}^{- 1}$. This tells you that $\text{2.50 g}$ of this gas occupy exactly $\text{1 L}$ at the conditions for pressure and temperature used in the experiment.

You also know that the total volume of the flask is equal to $\text{5.00 L}$. 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 $\text{12.5 g}$, 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 $\text{59.2 g}$.

The answer is rounded to three sig figs.