Question

The decomposition of nitramide, ( mathrm{O}_{2} mathrm{NNH}_{2} ), in water has the chemical equation and rate law [ mathrm{O}_{2} mathrm{NNH}_{2}(mathrm{aq}) longrightarrow mathrm{N}_{2} mathrm{O}(mathrm{g})+mathrm{H}_{2} mathrm{O}(mathrm{l}) quad ext { rate }=k frac{left[mathrm{O}_{2} mathrm{NNH}_{2} ight]}{left[mathrm{H}^{+} ight]} ] A proposed mechanism for this reaction is 1. ( mathrm{O}_{2} mathrm{NNH}_{2}(mathrm{aq}) underset{k_{-1}}{stackrel{k_{1}}{ ightleftharpoons}} mathrm{O}_{2} mathrm{NNH}^{-}(mathrm{aq})+mathrm{H}^{+}(mathrm{aq}) quad ) (fast equilibrium) 2. ( mathrm{O}_{2} mathrm{NNH}^{-}(mathrm{aq}) xrightarrow{k_{2}} mathrm{~N}_{2} mathrm{O}(mathrm{g})+mathrm{OH}^{-}(mathrm{aq}) quad ) (slow) 3. ( mathrm{H}^{+}(mathrm{aq})+mathrm{OH}^{-}(mathrm{aq}) xrightarrow{k_{3}} mathrm{H}_{2} mathrm{O}(mathrm{l}) quad ) (fast) What is the relationship between the observed value of ( k ) and the rate constants for the individual steps of the mechanism?

          The decomposition of nitramide, ( mathrm{O}_{2} mathrm{NNH}_{2} ), in water has the chemical equation and rate law
[
mathrm{O}_{2} mathrm{NNH}_{2}(mathrm{aq}) longrightarrow mathrm{N}_{2} mathrm{O}(mathrm{g})+mathrm{H}_{2} mathrm{O}(mathrm{l}) quad 	ext { rate }=k frac{left[mathrm{O}_{2} mathrm{NNH}_{2}
ight]}{left[mathrm{H}^{+}
ight]}
]

A proposed mechanism for this reaction is
1. ( mathrm{O}_{2} mathrm{NNH}_{2}(mathrm{aq}) underset{k_{-1}}{stackrel{k_{1}}{
ightleftharpoons}} mathrm{O}_{2} mathrm{NNH}^{-}(mathrm{aq})+mathrm{H}^{+}(mathrm{aq}) quad ) (fast equilibrium)
2. ( mathrm{O}_{2} mathrm{NNH}^{-}(mathrm{aq}) xrightarrow{k_{2}} mathrm{~N}_{2} mathrm{O}(mathrm{g})+mathrm{OH}^{-}(mathrm{aq}) quad ) (slow)
3. ( mathrm{H}^{+}(mathrm{aq})+mathrm{OH}^{-}(mathrm{aq}) xrightarrow{k_{3}} mathrm{H}_{2} mathrm{O}(mathrm{l}) quad ) (fast)

What is the relationship between the observed value of ( k ) and the rate constants for the individual steps of the mechanism?

$The decomposition of nitramide, ( mathrmO2 mathrmNNH2 ), in water has the chemical equation and rate law [ mathrmO2 mathrmNNH2(mathrmaq) longrightarrow mathrmN2 mathrmO(mathrmg)+mathrmH2 mathrmO(mathrml) quad ext rate =k fracleft[mathrmO2 mathrmNNH2 ight]left[mathrmH^+ ight] ] A proposed mechanism for this reaction is 1. ( mathrmO2 mathrmNNH2(mathrmaq) undersetk-1stackrelk1 ightleftharpoons mathrmO2 mathrmNNH^-(mathrmaq)+mathrmH^+(mathrmaq) quad ) (fast equilibrium) 2. ( mathrmO2 mathrmNNH^-(mathrmaq) xrightarrowk2 mathrm N2 mathrmO(mathrmg)+mathrmOH^-(mathrmaq) quad ) (slow) 3. ( mathrmH^+(mathrmaq)+mathrmOH^-(mathrmaq) xrightarrowk3 mathrmH2 mathrmO(mathrml) quad ) (fast) What is the relationship between the observed value of ( k ) and the rate constants for the individual steps of the mechanism?$

Added by Lisa B.

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