Question

At a certain temperature, the equilibrium constant for the following chemical equation is 2.60.

SO2 + NO2 = SO3 + NO

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

Lets call the moles NO? needed as X so we get the chart:
[Where it says unknown I mean that we will get that through later processes]
(I put in the following chart all that is given to us and we will work from here)
Reaction: SO?(g)__ + NO?(g) ? _SO?(g) +__ NO(g)
Initial____2.53_______X________0_______...
Change__unknown___unknown__unknown__unk...
Final____unknown___unknown__1.10______u...

So notice that for SO?, we started from 0 and ended up with 1.10 so the change must be +1.10:
Reaction: SO?(g)_ + NO?(g) ? _SO?(g) +_ NO(g)
Initial____2.53______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: SO?(g)_ + NO?(g) ? SO?(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: SO?(g) + NO?(g) ? SO?(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][SO?]/[SO?][NO?]
Plotting the numbers in we get:
2.60 = [1.10][1.10]/[1.43][X-1.10]
Solving for X we get:
X = 1.42 (3 sig figs)
So we get that we need 1.42 moles of NO?(g) to get 1.10 mol of SO?(g) at equilibrium