How to use gas laws to calculate the partial pressure of a gas that has partly condensed from a mixture?

Question

A mixture of three gases N₂, CO₂ and O₂ has a total pressure of 106000 Pa. The mixture is cooled to -100°C and the resulting pressure is found to have decreased to 82500 Pa. What gas is condensed and what is its partial pressure?
(BP N₂ = -196°C, BP O₂ = -183°C and BP CO₂ = -78°C)

I've had a look at all the formulas and laws that have been covered in my Chemistry textbook like Dalton's law of partial pressure and the combined gas equation but it appears that there is not enough information to solve it. I mean, if it asked to find the initial temperature, I could do it, but I'm not sure how to find the partial pressure of the gas(es) from the information provided.

Answer 1

You would need the initial temperature to be able to solve this.

You could use the combined gas law (or Gay-Lussac's Law) to determine the total pressure of the gas at -100°C, assuming none had condensed. This ideal gas pressure would differ from the 82.5kPa by the partial pressure of the condensed gas at -100°C.

The question doesn't specify at which conditions it wants to know the partial pressure of the missing gas. If it's -100°C, you'd be done at that point. If it's at the original temperature, you would have to apply the same gas law in reverse to get back to your original conditions.

The boiling point information you added should allow you to determine which of the three gases condensed. Only one would be a liquid or solid at -100°C.