Question

At a certain temperature, the equilibrium constant for the following chemical equation is 3.40. At this temperature, calculate the number of moles of NO2(g) that must be added to 2.53 mol of SO2(g) in order to form 1.10 mol of SO3(g) at equilibrium.

Answer 1

Let the moles of NO₂ needed as X so we get the chart:
Reaction: SO₂(g)__ + NO₂(g) ⇌ _SO₃(g) +__ NO(g)
Initial____2.53_______X________0_______...
Change__unknown___unknown__unknown__unk...
Final____unknown___unknown__1.10______u...

So notice that for SO₃, we started from 0 and ended up with 1.10 so the change must be +1.10:
Reaction: SO₂(g)_ + NO₂(g) ⇌ _SO₃(g) +_ NO(g)
Initial____2.64______X________0_______0
Change__unknown__unknown__+1.10___unkno...
Final____unknown__unknown___1.10____unk...

Now notice that the coefficient of all the products and reactants is 1 so the change in all of them will be equal (Recall that the change in the reactants, although the same, will have an opposite sign)
So our chart then becomes:
Reaction: SO₂(g)_ + NO₂(g) ⇌ SO₃(g) +NO(g)
Initial____2.53______X_______0______0
Change__-1.10_____-1.10____+1.10__+1.10
Final____unknown__unknown__1.10___unkno...

Since Final = Initial + Change
We get:
Reaction: SO₂(g) + NO₂(g) ⇌ SO₃(g) + NO(g)
Initial____2.53_____X_______0_______0
Change__-1.10____-1.10____+1.10___+1.10
Final____1.43_____X-1.10___1.10____1.10

Recall that:
Kc = [NO][SO₃]/[SO₂][NO₂]
Plotting the numbers in we get:
3.40 = [1.10][1.10]/[1.43][X-1.10]
Solving for X we get:
X = 1.349 (3 sig figs)
So we get that we need 1.349 moles of NO₂(g) to get 1.10 mol of SO₃(g) at equilibrium