Question 6.8: Using the Ideal Gas Equation to Calculate a Gas Density What...
Using the Ideal Gas Equation to Calculate a Gas Density
What is the density of oxygen gas (O_2) at 298 K and 0.987 atm?
Analyze
The gas is identified, and therefore the molar mass can be calculated. We are given a temperature in Kelvin and a pressure in atmospheres, so we can use equation (6.14) directly with R = 0.08206 atm L K^{-1} mol^{-1}.
d = \frac{m}{V} = \frac{MP}{RT} (6.14)
The molar mass of O_2 is 32.0 g mol^{-1}. Now, use equation (6.14).
d = \frac{m}{V} = \frac{MP}{RT} = \frac{32.00 g mol^{-1} \times 0.987 atm}{0.08206 atm L mol^{-1} K^{-1} \times 298 K} = 1.29 g/L
Assess
We can solve this problem in another way. To calculate the density of a gas at a certain temperature and pressure, use a 1.00 L sample of the gas. The mass of a 1.00 L sample is equal to the density in grams per liter. To calculate the mass of a 1.00 L sample, first use the ideal gas equation to calculate the number of moles in the sample, and then convert the amount in moles to an amount in grams by using the molar mass as a conversion factor. In the present case, the amount of O_2 (g) in a 1.00 L sample at 0.987 atm and 298 K is 0.0404 mol O_2, or 1.29 g O_2. Because a 1.00 L sample of O_2 at this temperature and pressure has a mass of 1.29 g, the density is 1.29 g/L.