At a certain temperature, the equilibrium constant for the following chemical eq

Question

At a certain temperature, the equilibrium constant for the following chemical equation is 4.00. At this temperature, calculate the number of moles of NO2(g) that must be added to 2.20 mol of SO2(g) in order to form 1.00 mol of SO3(g) at equilibrium.
At a certain temperature, the equilibrium constant for the following chemical equation is 4.00. At this temperature, calculate the number of moles of NO2(g) that must be added to 2.20 mol of SO2(g) in order to form 1.00 mol of SO3(g) at equilibrium.
At a certain temperature, the equilibrium constant for the following chemical equation is 4.00. At this temperature, calculate the number of moles of NO2(g) that must be added to 2.20 mol of SO2(g) in order to form 1.00 mol of SO3(g) at equilibrium.

Explanation / Answer

Hello there!
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____2.20_______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____2.20______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____2.20______X_______0______0
Change__-1.00_____-1.00____+1.00__+1.00
Final____unknown__unknown__1.00___unkno...

Since Final = Initial + Change
We get:
Reaction: SO?(g) + NO?(g) ? SO?(g) + NO(g)
Initial____2.20_____X_______0_______0
Change__-1.00____-1.00____+1.00___+1.00
Final____1.54_____X-1.00___1.00____1.00

Recall that:
Kc = [NO][SO?]/[SO?][NO?]
Plotting the numbers in we get:
3.50 = [1.00][1.00]/[1.54][X-1.00]
Solving for X we get:
X = 1.32 (3 sig figs)
So we get that we need 1.32 moles of NO?(g) to get 1.00 mol of SO?(g) at equilibrium

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