Ideal Gas Law and Density of a Gas

Ideal Gas Law and Density of a Gas

The Ideal Gas Law can also be used to determine the density of a gas. To derive that equation, we begin with the ideal gas law:

(1) ideal-gas-law-small

 

Density is defined as mass per unit volume.

(2)
density

 

Recall that we also derived the equation for the molar mass of a gas in the post Ideal Gas Law and Molar Mass of a Gas as:

(3) ideal-gas-law-mm

 

To solve for g, we multiply each side by PV/RT:

(4) PV4

 

The resulting equation is:

(5) ideal-gas-law-g

 

Plugging equation (5) into our equation for density (2):

(6)ideal-gas-law-density1

 

Notice that volume V cancels out:

(7) ideal-gas-law-density2

 

We now can use equation (7) to solve gas law problems for density.

 

Sample Problem

What is the density of SO2 gas at 1.18 atm and 26 °C?

The gas law equation (7) for density is:

(7)ideal-gas-law-density2

 

Wanted: ? Density

Given:

Molar mass of SO2 gas = 64.06 g/mol

P = 1.18 atm

T = 26 °C

We need to convert degrees Celsius to Kelvin:

299K

 

Plugging these values into equation (7):

308gl

 

The density of of SO2 gas is 3.08 g/L.