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?

1 Answer
Dec 4, 2015

"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".