The decomposition of nitramide, O 2 NNH 2, O2NNH2, in water has the chemical equation and rate law O 2 NNH 2 (aq) ⟶ N 2 O (g) + H 2 O (l) rate = k [ O 2 NNH 2 ] [ H + ] O2NNH2 (aq) ⟶N2O (g) + H2O (l) rate=k[O2NNH2][H+] A proposed mechanism for this reaction is O 2 NNH 2 (aq) k 1 ⇌ k - 1 O 2 NNH - (aq) + H + (aq) (fast equilibrium) O2NNH2 (aq) ⇌k-1k1O2NNH - (aq) + H + (aq) (fast equilibrium) O 2 NNH - (aq) k 2 - → N 2 O (g) + OH - (aq) (slow) O2NNH - (aq) →k2N2O (g) + OH - (aq) (slow) H + (aq) + OH - (aq) k 3 - → H 2 O (l) (fast) H + (aq) + OH - (aq) →k3H2O (l) (fast) What is the relationship between the observed value of k k and the rate constants for the individual steps of the mechaanism?

The given overall reaction is as follows:

O 2 N N H ₂ (a q) k → N ₂O (g) + H ₂ O (l)

The reaction mechanism for this reaction is as follows:

O ₂ N N H ₂ ⇌ k 1 k - 1 O ₂N N H ⁻ + H ⁺ (f a s t e q u i l i b r i u m)

O ₂ N N H - k ₂→ N ₂ O + O H ⁻ (s l ow)

H ⁺ + O H - k ₃→ H ₂ O (f a s t)

The rate law of the reaction is given as follows:

k = [ O ₂ N N H ₂ ] / [ H ⁺ ]

The rate law can be determined by the slow step of the mechanism.

r a t e = k ₂ [ O ₂ N N H ⁻ ] ... (1)

Since, from the equilibrium reaction

k e q = [ O ₂ N N H ⁻ ] [ H ⁺ ] / [ O ₂ N N H ₂ ] = k ₁ / k - 1

[ O ₂ N N H ⁻] = k ₁ / k - 1 * [ O ₂ N N H ₂ ] / [ H ⁺ ] ... (2)

Substitituting the value of equation (2) in equation (1) we get.

r a t e = k ₂ k ₁ / k - 1 * [ O ₂ N N H ₂ ] / [ H ⁺ ]

Therefore, the overall rate constant is

k = k₂k₁/k-1