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

Answer:

#"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"#.