Equilibrium

A chemist investigated methods to improve the synthesis of sulfur trioxide from sulfur dioxide and oxygen.
2SO2(g) + O2(g) ⇌ 2SO3(g)
The chemist:
• mixed together 1.00 mol SO2 and 0.500 mol O2 with a catalyst at room temperature
• compressed the gas mixture to a volume of 250 cm3
• allowed the mixture to reach equilibrium at constant temperature and without changing the total
gas volume.

Explain what would happen to the pressure as the system was allowed to reach equilibrium.

Why does pressure decrease in this question?

Start by comparing the numbers of moles of gas on each side of the equation.

Because you are starting only with the reactants and no product, is the equilibrium going forward or backwards?

Next, is this therefore leading to an increase or decrease in the number of moles of gas in the container?

Now consider the equation pV = nRT, which rearranges to p = (RT/V)n. Because it tells you the total volume of gas and the temperature are unchanged, RT/V is just a constant that you can simply assign whatever value you like to (e.g you can just say it has a value of 1). Playing about with the value of n in p = (RT/V)n, what happens to the pressure as the number of moles changes in the way you have predicted using the above logic?

The equilibrium is going forward so the number of moles of gas on the left decreases right? But don't those moles just go to the product so the overall pressure remains the same? The volume remains the same and the number of particles does too right or am I mistaken?

“The equilibrium is going forward so the number of moles of gas on the left decreases right?”

That would be correct.

“But don't those moles just go to the product so the overall pressure remains the same?”

Not quite. Look at the equation again and count how many moles of gas there are on each side. Are there more or less moles of gas on the right hand side of the equation? This should give away whether the total moles of gas in the container are increasing or decreasing.

You can even show this - assume that only 0.2 moles of the SO2 (so incidentally 0.1 moles of O2, as well) are consumed in the reaction. This will produce 0.2 moles of SO3 according to the equation and you can now try calculating the total number of moles of gas (use the fact there are originally 1 mol of SO2 and 0.5 mol of O2) or comparing the number of moles of gas consumed with the number of moles of gas produced.

“The volume remains the same and the number of particles does too right or am I mistaken?”

Whilst the volume does remain the same, that doesn’t mean the number of particles remains the same. The number of moles of gas is changing as the reaction proceeds in this case, so the pressure will change.

Ohhh okay I see so because (in your example) 0.3 moles of reactant is used to produce 0.2 moles of product, the pressure decreases?