Question

What is the molar mass of a gas that has a density of 1.18g/L at 25°C and 1 atm?

Answer 1

You can get this from the Ideal Gas Law.

Explanation:

We are going to solve this by first figuring out what the volume of one mole of a gas is at `25^o`C and 1 atm. Once we know how many liters of gas we need for one mole, we will be able to figure out how many grams of gas are in one mole, given the gas density.

Let us start with the Ideal Gas Law: PV=nRT.

For 1 mole of a gas, n=1. You are at (`25^o`C) and 1 atm.
R = 0.082057 liter-atm/mol-K.

So, solving PV=nRT for V, V=nRT/P = 24.453 liters.

So now we know that we need 24.453 liters of gas to get one mole. That much gas will weigh:

24.453 liters *1.18 g/liter = 28.854 grams per mole.

Adjusting to 3 significant figures: 28.9 grams per mole.

The key was figuring out how many liters of gas we needed to make one mole, and we got that from the Ideal gas Law.