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[O2NN H2][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)(f ast 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?

Explanation:

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

the earth would become to overheated and everything alive on it will eventually die from overheating. plants will eventually die as well, water will evaporate, and it will be nothing but a hot planet without anything living on it.