Given the values of K shown below, determine the value of K for the reaction

Question

Given the values of K shown below, determine the value of K for the reaction

N₂(g) + 2 O₂(g) <=> 2 NO₂(g).

N₂(g) + O₂(g) <=> 2 NO(g)       K = 2

NO₂(g) <=> NO + 1/2 O₂(g)    K = 15

the correct answer is: 0.0089

please explain how you got your answer

Answer 1

This is an example of using Hess' Law (look it up and read about it).

The target equation is N₂(g) + 2 O₂(g) <=> 2 NO₂(g)

We are given

(1) N₂(g) + O₂(g) <=> 2 NO(g)       K = 2

(2) NO₂(g) <=> NO + 1/2 O₂(g)    K = 15

If we take (1) and copy it down and then take (2) and reverse it and multiply it by 2, we have...

(1) N₂(g) + O₂(g) <=> 2 NO(g)       K = 2

(2) 2NO(g) + O₂(g) <=> 2NO₂(g) K = 15² = 225 since multiplied by 2 we must raise K to the 2nd power). BUT, we must also take the inverse since we reversed the reaction. This gives us K = 1/225 = 0.00444

Summing these reactions, we obtain the desired target equation: N₂(g) + 2O₂(g) <=> 2NO₂(g)

And if we sum the equations, we multiply the values of K, so we have 2 x 0.00444 = 0.0089