The following mechanism has been proposed for the decomposition of dinitrogen pe
ID: 1051615 • Letter: T
Question
The following mechanism has been proposed for the decomposition of dinitrogen pentoxide, which has the experimental rate law, Rate = k[N_2O_5]: N_2O_5(g) _k_2^k_1 NO_2(g) + NO_3(g) Fast, reversible NO_2 (g) + NO_3 (g) rightarrow^k_3 NO(g) + NO_2 (g) + O_2(g) Slow, rate determining NO(g) + NO_3(g) rightarrow^k_4 2 NO_2 (g) Fast Note that the first step must be multiplied by 2 to obtain reaction. Show that the proposed mechanism is consistent with the experimental rate law. Match the words in the left column to the appropriate blanks in the sentences on the right. Make certain each sentence is complete before submitting your answer k_3 [NO_2] [NO_3] Rate_forward = k_1 [N_2 O_5] Rate_reverse = k_1 [N_2 O_5]^2 Because of the equilibrium Rate_forward = Rate_reverse and [NO_2] [NO_3] = k_1 [NO_2] [NO_3] The rate law for the rate determining step is Rate In this rate law substitute for Rate = k[N_2 O_5] k_2/k_1 [N_2 O_5] k_2/k_1 [NO_2] [NO_3] k_1/k_2 [N_2 O_5] k_2 [NO_2] [NO_3] k_2 [NO_2]^4 [O_2] [NO_2] [NO_3] k_4 [NO_2]^2 k_4 [NO] {NO_3] [NO] [NO_3] k_1/k_2 [NO_2] [NO_3] k_3 [NO_2] [NO] [O_2]Explanation / Answer
Rate forward = k1 [N2O5]
rate backward = k2 [ NO2] [NO3]
Becaue of equilibrium rate forward = rate backward . Hence k1[N2O5] = k2 [NO2][NO3]
[NO2] [NO3] = ( k1/k2) [N2O5]
The rate law in rate determining step is Rate = k3 [NO2] [NO3]
In this we substitute for [NO2] [NO3] and
Rate = k3 ( k1/k2) [N2O5] = k [N2O5]
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