Question

A gaseous compound composed of sulfur and oxygen, which is linked to the formation of acid rain, has a density of 3.58 g/L at STP. What Is the molar mass of this gas?

Answer 1

`"81.3 g/mol "` (or possibly `"80.2 g/mol"`)

Explanation:

Your strategy here will be pick a sample of this gas and use the definition of the molar volume of a gas at STP to help you find the number of moles it contains.

To make the calculations easier, let's say that we're going to pick a `"1.00-L"` sample of this gas.

As you know, one mole of any ideal gas occupies exactly `"22.71 L"` under STP conditions, which are defined as a pressure of `"100 kPa"` and a temperature of `0^@"C"`.

So, if one mole of this gas will occupy `"22.71 L"` at STP, it follows that our `"1.00-L"` sample will contain

`1.00 color(red)(cancel(color(black)("L"))) * "1 mole"/(22.71 color(red)(cancel(color(black)("L")))) = "0.04403 moles"`

According to the given density, this `"1.00-L"` sample will contain `3.58` grams of this unknown gas. As you know, molar mass is defined as

`color(blue)("molar mass" = "mass in grams"/"number of moles")`

This means that the gas' molar mass will be

`M_"M" = "3.58 g"/"0.04403 moles" = color(green)("81.3 g/mol")`

SIDE NOTE It is very likely that this problem meant for you to use the old definition of STP, which is a pressure of `"1 atm"` and a temperature of `0^@"C"`.

In this case, the molar volume of a gas at STP is equal to 22.4 L. This in turn will make the molar mass of the gas equal to `"80.2 g/mol"`.