At a certain temperature, Kp is 0.00305 for the reaction: N2(g) + 3 H2(g) ⇌ 2 NH3 (g). What is the value of Kp for the following reaction? NH3 (g) ⇌ 1/2 N2(g) + 3/2 H2(g)

Question

This is the answer: 1.81E1

I just don't understand

Answer 1

N₂(g) + 3 H₂(g) <==> 2NH₃(g) Kp = 0.00305

NH₃(g) <==> 1/2 N₂(g) + 3/2 H₂(g) Kp = ?

This 2nd reaction is not only the reverse of the previous reaction but also 1/2 of that reaction. So, to get the new Kp, we need to take the inverse of the original Kp (to account for reversing the reaction), and also take the square root of that (to account for dividing by 2).

Kp = 1 / √0.00305 = 1 / 0.0552 = 18.1 (this is the same as 1.81E1)