The gases in a mixture have the following partial pressures at the same volume and temperature: 1,013,000 Pa nitrogen, 700 mm argon, 1.20 atm of helium, 790 torr oxygen, and 0.50 atm of carbon dioxide.

Question

The gases in a mixture have the following partial pressures at the same volume and temperature: 1,013,000 Pa nitrogen, 700 mm argon, 1.20 atm of helium, 790 torr oxygen, and 0.50 atm of carbon dioxide.

Rank these gases in order of increasing mole fraction, putting the gas with the smallest mole fraction first.

Smallest mole fraction

Nitrogen
Argon
Helium
Oxygen
Carbon Dioxide

Largest mole fraction

Answer 1

Anyone can guess in the ranking. How did you arrive at this ranking?

Change the units to the same overall unit--it doesn't matter what you pick but I think atm would be the easiest.
Then X = (partial pressure/total pressure)

Answer 2

nitrogen

argon
helium
oxygen
carbon diocis

Answer 3

To determine the mole fraction of each gas in the mixture, we need to first convert the partial pressures of the gases to the same unit. In this case, let's use atm as the common unit.

Given:

Partial pressure of nitrogen = 1,013,000 Pa = 1,013,000/101,325 = 10 atm
Partial pressure of argon = 700 mm = 700/760 = 0.921 atm
Partial pressure of helium = 1.20 atm
Partial pressure of oxygen = 790 torr = 790/760 = 1.04 atm
Partial pressure of carbon dioxide = 0.50 atm

Now, let's calculate the mole fractions:

Mole fraction of nitrogen = (partial pressure of nitrogen) / (total pressure)
Mole fraction of nitrogen = 10 atm / (10 atm + 0.921 atm + 1.20 atm + 1.04 atm + 0.50 atm) = 0.536

Mole fraction of argon = (partial pressure of argon) / (total pressure)
Mole fraction of argon = 0.921 atm / (10 atm + 0.921 atm + 1.20 atm + 1.04 atm + 0.50 atm) = 0.050

Mole fraction of helium = (partial pressure of helium) / (total pressure)
Mole fraction of helium = 1.20 atm / (10 atm + 0.921 atm + 1.20 atm + 1.04 atm + 0.50 atm) = 0.066

Mole fraction of oxygen = (partial pressure of oxygen) / (total pressure)
Mole fraction of oxygen = 1.04 atm / (10 atm + 0.921 atm + 1.20 atm + 1.04 atm + 0.50 atm) = 0.116

Mole fraction of carbon dioxide = (partial pressure of carbon dioxide) / (total pressure)
Mole fraction of carbon dioxide = 0.50 atm / (10 atm + 0.921 atm + 1.20 atm + 1.04 atm + 0.50 atm) = 0.232

Therefore, the rank from smallest to largest mole fraction is:

1. Argon
2. Helium
3. Oxygen
4. Carbon Dioxide
5. Nitrogen