Question

The experimental data for decomposition of N₂O₅

in gas phase at 318K are given below:

t(s)	0	400	800	1200	1600	2000	2400	2800	3200
	1.63	1.36	1.14	0.93	0.78	0.64	0.53	0.43	0.35

(i) Plot [N₂O₅] against t.

(ii) Find the half-life period for the reaction.

(iii) Draw a graph between log [N₂O₅] and t.

(iv) What is the rate law?

(v) Calculate the rate constant.

(vi) Calculate the half-life period from k and compare it with (ii).

Answer 1

(ii) Time corresponding to the concentration, is the half life. From the graph, the half life is obtained as 1450 s.

(iii)

t(s)
0	1.63	− 1.79
400	1.36	− 1.87
800	1.14	− 1.94
1200	0.93	− 2.03
1600	0.78	− 2.11
2000	0.64	− 2.19
2400	0.53	− 2.28
2800	0.43	− 2.37
3200	0.35	− 2.46

(iv) The given reaction is of the first order as the plot, v/s t, is a straight line. Therefore, the rate law of the reaction is

(v) From the plot, v/s t, we obtain

Again, slope of the line of the plot v/s t is given by

.

Therefore, we obtain,

(vi) Half-life is given by,

This value, 1438 s, is very close to the value that was obtained from the graph.