In a study of the gas phase decomposition of nitrogen dioxide at 383 degree C NO

Question

In a study of the gas phase decomposition of nitrogen dioxide at 383 degree C NO_2(g) rightarrow NO(g) + 1/2 O_2(g) the following data were obtained: The observed half life for this reaction when the starting concentration is 0.483 M is s and when the starting concentration is 0.242 M is The average delta (1/[NO_2])/delta t from t = 0 s to t = 4.84 s is M^-1 s^-1. The average delta (1/[NO_2])/delta t from t = 4.84 s to t = 14.5 s is M^-1 s^-1. Based on these data, the rate constant for this order reaction is M^-1 s^-1.

Explanation / Answer

Ans. 1. The starting concentration 0.483M is halved (= reduces to 0.242M) in 4.84 seconds. So, half-life of this step is 4.84 seconds.

            0.483 M ---------(4.84 s)------> 0.242 M

Similarly,

Time taken for 0.242 M to reduced to 0.121 M is = T3-T2

= 14.5 s – 4.84 s = 9.66 s

Thus, half-life of this step (C2 to C3) is 9.66 s.

Ans. 2a. Change in concentration from t= 0s to t= 4.84s is-

            d[NO2] = 0.483 M – 0.242 M = 0.241 M                                 ; [d = delta]

            dT = 4.84s – 0s = 4.84s

Now,   

            d(1/[NO2]) / dT = (1/ 0.241M) / 4.84s = 0.857 M-1s-1

Ans. 2a. Change in concentration from t= 4.84s to t= 14.5s is-

            d[NO2] = 0.242 M – 0.121 M = 0.121 M                                 ; [d = delta]

            dT = 14.5s- 4.84s = 9.66s

Now,   

            d(1/[NO2]) / dT = (1/ 0.121M) / 9.66s = 0.856 M-1s-1

Ans. 3. Based on these data, the rate constant for this second order reaction is 0.8565 M-1s-1

Take average of two rates. (0.857 M-1s-1 + 0.857 M-1s-1) / 2 = 0.8565 M-1s-1

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