Question

From the given data, use a graphical method to determine the order and rate constant of the following reaction: 2X ⟶ Y + Z

Time (s) [5.0] [10.0] [15.0] [20.0] [25.0] [ 30.0] [ 35.0] [40.0]

[X] (M) [0.0990] [0.0497] [0.0332] [ 0.0249] [0.0200] [0.0166] [ 0.0143] [ 0.0125]

Answer 1

Integrated rate law:

1. For zero order reaction: [X] = [X]_o - kt
2. For 1st order reaction: ln[X] = ln[X]_o - kt
3. For 2nd order reaction: 1/[X] = 1/[X]₂ + kt

In order to determine the order and rate constant of a reaction from a set of data consisting of concentration and time, we have to make three graphs:

1. [X] versus t (linear for a zero order reaction) , slope = -k
2. ln [X] versus t (linear for a 1st order reaction) , slope = -k
3. 1 / [X] versus t (linear for a 2nd order reaction) , slope = k

The graph which is linear indicates the order of the reaction with respect to X and slope gives the rate constant.

Time	[X]	ln[X]	1/[X]
(in s)	(in M)
5	0.099	-2.313	10.101
10	0.0497	-3.002	20.1207
15	0.0332	-3.405	30.1205
20	0.0249	-3.693	40.1606
25	0.02	-3.912	50
30	0.0166	-4.098	60.241
35	0.0143	-4.247	69.9301
40	0.0125	-4.382	80

Since, graph for 2nd order reaction ( 1/[X] vs t) is a straight line, therefore, the given reaction is a second order reaction w.r.t X and the rate constant, k = 1.9965M^-1s^-1

order = 2 rate constant = 1.9965M^-1s^-1