Question

The following data were obtained from a batch experiment for the reaction where A is converted to B.

1)Determine the order of the reaction

            Time (min)      0           10        20        40        60        80        100

            A (mg/lit)        100      74        55        30        17        9          5

2) Consider a first order reaction taking place in a batch reactor.

Develop an expression for the detention time in the reactor.

Answer 1

1)   To determine the order of a reaction from a set of data consisting of concentration and time, make three graphs.

1. [A] versus t (linear for a zero order reaction)
2. ln [A] versus t (linear for a 1^st order reaction)
3. 1 / [A] versus t (linear for a 2^nd order reaction)

time ,t	[A]	ln[A]	1/[A]
(in s)	(in mg/L)
0	100	4.60517	0.01
10	74	4.304065	0.013514
20	55	4.007333	0.018182
40	30	3.401197	0.033333
60	17	2.833213	0.058824
80	9	2.197225	0.111111
100	5	1.609438	0.2

since, ln([A]) vs t graph is a straight line. therefore the given reaction is a first order reaction.

2) Rate equation for the first order reaction is: d[A] = - k[A] dt

d[A]/dt = rate of consumption of A

Integrating the above equation : d[A] /[A] = -k t dt

ln [A]_o   = kt [A]_t   t = 1  ln [A]_o k [A]t here,   't' is the detention time