The equilibrium constant is given for one of the reactions below. Determine the value of the missing equilibrium constant.

Question

2 SO₂(g) + O₂(g) ⇌ 2 SO₃(g) K_c = 1.7 × 10⁶

 SO₃(g) ⇌ 1/2 O₂(g) + SO₂(g) K_c = ?

A. 7.7 * 10^-4

B. 3.4 * 10^2

C. 1.3 * 10^3

D. 1.2 * 10^-6

D. 8.5

Answer 1

The way equilibrium constants are connected to equations is easy to remember if you note that energies associated with reactions follow linear rules (you multiply the rxn by a constant, energy is multiplied by the same constant, if you add or subtract reaction, you add or subtract energies) and that K's are linked to e to the gibb's free energy, you realize that multiplying a rxn by a constant takes K to that power, reversing a reaction (energy x -1) inverts K (takes it to the -1), and adding an subtracting rxns becomes multiplying and dividing Ks.

So, what's been done to this rxn? It has been reversed and multiplied by 1/2. Therefore, the new K will be

K^-1/2 or 1/K^1/2

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