# 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?

Dec 4, 2015

$\text{81.3 g/mol }$ (or possibly $\text{80.2 g/mol}$)

#### 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 $\text{1.00-L}$ sample of this gas.

As you know, one mole of any ideal gas occupies exactly $\text{22.71 L}$ under STP conditions, which are defined as a pressure of $\text{100 kPa}$ and a temperature of ${0}^{\circ} \text{C}$.

So, if one mole of this gas will occupy $\text{22.71 L}$ at STP, it follows that our $\text{1.00-L}$ 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 $\text{1.00-L}$ sample will contain $3.58$ grams of this unknown gas. As you know, molar mass is defined as

$\textcolor{b l u e}{\text{molar mass" = "mass in grams"/"number of moles}}$

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 $\text{1 atm}$ and a temperature of ${0}^{\circ} \text{C}$.

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 $\text{80.2 g/mol}$.