Calculating the Molar Mass of a Gas

What makes it float?

Helium has long been used in balloons and blimps. Since it is much less dense than air, it will float above the ground. We can buy small balloons filled with helium at stores, but large ones (such as the balloon seen above) are much more expensive and take up a lot more helium. \

Calculating Molar Mass and Density of a Gas

A chemical reaction, which produces a gas, is performed. The produced gas is then collected and its mass and volume are determined. The molar mass of the unknown gas can be found using the ideal gas law, provided the temperature and pressure of the gas are also known.

Sample Problem: Molar Mass and the Ideal Gas Law

A certain reaction occurs, producing an oxide of nitrogen as a gas. The gas has a mass of 1.211 g and occupies a volume of 677 mL. The temperature in the laboratory is 23°C and the air pressure is 0.987 atm. Calculate the molar mass of the gas and deduce its formula. Assume the gas is ideal.

Step 1: List the known quantities and plan the problem.

First, the ideal gas law will be used to solve for the moles of unknown gas $\begin{array}{r}(n)\end{array}$. Then the mass of the gas divided by the moles will give the molar mass.

Step 2: Solve.

 

Now divide g by mol to get the molar mass.

Since N has a molar mass of 14 g/mol and O has a molar mass of 16 g/mol, the formula N₂O would produce the correct molar mass.

Step 3: Think about your result.

The $\begin{array}{r}R\end{array}$ value that corresponds to a pressure in atm was chosen for this problem. The calculated molar mass gives a reasonable formula for dinitrogen monoxide.

 

 

 Summary

• Calculations of molar mass of an ideal gas are described.

Review

1. Why do you need the volume, temperature, and pressure of the gas to calculate molar mass?
2. What assumption about the gas is made in all these calculations?
3. Why do you need the mass of the gas to calculate the molar mass?