Determine the value of the equilibrium constant, Kgoal, for the reaction:

Question

N2(g)+O2(g)+H2(g)⇌1/2 N2H4(g)+NO2(g)

1. N2(g)+O2(g)⇌2NO(g), K1 = 4.10×10^−31
2. N2(g)+2H2(g)⇌N2H4(g), K2 = 7.40×10^−26
3. 2NO(g)+O2(g)⇌2NO2(g) , K3 = 6.00×10−13

i know its (K1 * K2 *K3)^1/2 .. but i keep getting the wrong value?

Answer 1

This is a problem where we need to invoke Hess' Law.

N₂(g) + O₂(g) + H₂(g)⇌ 1/2 N₂H₄(g) + NO₂(g) TARGET EQUATION

1. N₂(g) + O₂(g)⇌ 2NO(g), K1 = 4.10×10^⁻³¹
2. N₂(g) + 2H₂(g)⇌ N₂H₄(g), K2 = 7.40×10^⁻²⁶
3. 2NO(g )+ O₂(g)⇌ 2NO₂(g) , K3 = 6.00×10⁻¹³

1/2 of (1): 1/2 N₂(g) + 1/2 O₂(g)⇌ NO(g), K = √4.10x10^-31 = 6.40x10^-16

1/2 of (2): 1/2 N₂ + H₂ <=> 1/2 N₂H₄ K = √7.40x10^-26 = 2.72x10^-13

1/2 of (3): NO + 1/2O₂ <=> NO₂ K = √6.00x10^-13 = 7.75x10^-7

Add up (1), (2) and (3) and combine and/or cancel like items to obtain....

N₂ + H₂ + O₂ <==> 1/2N₂H₄ + NO₂ TARGET EQUATION

To find K for the overall reaction, we multiply the K for each as follows:

(6.40x10^-16)(2.72x10^-13)(7.75x10^-7) = 1.35x10^-34 = K