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Xenon and fluorine were mixed in a 1:1 ratio by volume and sealed in a vessel attached to a barometer. After some time, crystals were found to have formed on the walls of the vessel and the barometer showed that the pressure had dropped to 70% of the original pressure. Analysis of the gases remaining indicated 4 parts xenon to 3 parts fluorine. Construct a balanced equation for the reaction. Assume constant temperature throughout.

Equal volumes of gas at same temperature and pressure have the same number of molecules, thus I deduce that the mole ratio of the 2 gases initially is 1:1. Since $pV = nRT$ then the number of moles of the two gases combined would be 70% of the total number of moles of the 2 gases at the start of the experiment.

I am unsure of how to proceed from here.

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Xenon and fluorine were mixed in (1) a 1:1 ratio by volume and sealed in a vessel attached to a barometer. After some time, crystals were found to have formed on the walls of the vessel and the barometer showed that (2) the pressure had dropped to 70% of the original pressure. Analysis of the gases remaining indicated (3) 4 parts xenon to 3 parts fluorine. Construct a balanced equation for the reaction. Assume constant temperature throughout.

You have properly analyzed (1) and (2). It remains to analyze (3). We started with ten parts of gas, 5 parts xenon and 5 parts fluorine. From (2) and (3), we see that 4 parts xenon and 3 parts fluorine are left in the gas phase. Hence 1 part xenon ($\ce {Xe}$) and 2 parts fluorine ($\ce {F2}$) must have reacted to form crystalline $\ce{XeF4}$.

The balanced reaction is left as a simple exercise.


The choice of starting with ten parts of gas (as opposed to fifty parts, or a hundred parts) is arbitrary. Since we're given only ratios, we can choose an arbitrary number of parts of gas and work with that throughout. Choosing ten makes the math simple.

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