The equilibrium constant for the reaction 2SO2 + O2 2SO3(all are gases) at a certain const temperature is 846.4mol/dm^3. At equilibrium in a 1dm^3 vessel, 0.5 moles of SO2, 0.1 moles of O2, and 4.6 moles of SO3 were found. How many moles of oxygen must be added to the mixture in the vessel at the same temp to increase the amount of SO3 present at equi to 5 moles?

Question

The equilibrium constant for the reaction 2SO2 + O2 <=> 2SO3(all are gases) at a certain const temperature is 846.4mol/dm^3. At equilibrium in a 1dm^3 vessel, 0.5 moles of SO2, 0.1 moles of O2, and 4.6 moles of SO3 were found. How many moles of oxygen must be added to the mixture in the vessel at the same temp to increase the amount of SO3 present at equi to 5 moles?

I tried an ICE table and everything, but I always get a really complicated cubic equation at the denominator when I try to find the rate constant. the formula I gow was (5)^2/(0.1+x)(0.5-2x)= to the rate constant. Is there something I'm doing wrong? The answer is supposed to be 3.05moles.

DrBob222 · Answer

I didn't do the math but I don't think your set up is quite right but almost right.
K = 846.4 = (4.6-2x)^2/(0.5-2x)^2*(0.1+x)

For cubic equations you can find a calculator on the web that will solve them.
Let me point out a couple of things that I'm picky about.
1. K has no units. Your problem may show units but the thermodynamic constant has no units.
2. This is NOT a rate constant; this is an equilibrium constant. The two are not the same.