[as0422]

Hi, I'm a first year undergrad student and I'm having trouble wrapping my head around this problem:

An atmospheric chemist, studying the pollutant sulfur trioxide (SO3), places a mixture of sulfur dioxide (SO2) and oxygen (O2) in a rigid 4.25 L container at 788 K and 1.85 atm. When the reaction occurs, gaseous sulfur trioxide is formed according to the balanced equation below and the pressure falls to 1.50 atm.


SO2 + ½O2 → SO3

 
Assuming that the temperature at the end of the reaction returns to its original value, what is the partial pressure of sulfur trioxide (SO3) after the reaction?

I know that the total pressure is the sum of the partial pressures but after the reaction, there's only sulfur trioxide so what "partial" pressure am I finding exactly?

[AWK]

Look at pressure before and after reaction and take into account the stoichiometry of reaction.

[as0422]

I know the total pressure before the reaction is 1.85 atm and after the reaction it is 1.50 atm.
I'm assuming I have to find the limiting reactant in this problem and see how much SO3 I end up with after the reaction and then find the pressure of that? But I'm not sure if that's the right approach or how to do that with the information that I have.

[AWK]

This is not a problem with the limiting reagent.
A certain amount of oxygen reacts with the oxygen-related amount of sulfur dioxide, and the identical amount of sulfur trioxide is formed. In a constant volume at the same temperature, partial pressures are proportional to the number of molecules. Hence the calculation comes down to one subtraction and one multiplication, which you can do without a calculator.

[as0422]

I still don't understand... 

[Borek]

there's only sulfur trioxide

That's where you are wrong.

Actually thinking in terms of limiting reactant is not an entirely bad idea, just try it the other way - can you think what was in the excess?

[AWK]

Borek is right. You may assume the rest of the gas in the vessel is an excess of oxygen. But this is completely unimportant for calculations.
Let's assume that 1/2 mole of oxygen has reacted. How many moles of SO₂ have reacted and how many moles of SO₃ have been formed? This can be seen from the balanced reaction equation, isn't it?
In the ideal gas equation, we have p = nRT/V where T and V are constant, so the partial pressure of each gas in this vessel in a given condition depends proportionally on the number of moles of each gas. Therefore, the SO₂ loss and SO₃ formed expressed by partial pressure can be calculated in memory based on pressure drop in the vessel. And that's all!

Some data is unnecessary for calculations and causes spiritual dilemmas for a student who wants to use them all for calculations.