Question

In a study of the decomposition of the compound X via the reaction

X(g)⇌Y(g)+Z(g)

the following concentration-time data were collected:

Time (min)	[X](M)
0	0.467
1	0.267
2	0.187
3	0.144
4	0.117
5	0.099
6	0.085
7	0.075

What is the order of the reaction?

The reaction is second order.

Part B

Given that the rate constant for the decomposition of hypothetical compound X from part A is 1.60 M−1⋅min−1, calculate the concentration of X after 15.0 min .

Express your answer with the appropriate units.

Answer 1

Solution:

Part A) For the determination of order of a reaction:

If a plot between concentration and time is a straight line, then order will be 0.

If a plot of ln of concentration and time is a straight line, then order will be 1.

If a plot of [1/concentration] Vs time (t) is a straight line, then order of reaction will be 2.

From the given table,

1/0.267= 3.745 at time 1 min

1/0.187 =5.347 at time 2 min

1/ 0.144 =6.94 at time 3 min

Hence, it will give a straight line with time.

Therefore order will be 2.

Part B) According to second order kinetics,

K = 1/ t [x / a (a-x)]

Where, a = initial concentration of X,

rate constant, K = 1.60 M-1 min-1 and t = 15 min

Then on putting the values in above equation we get,

1.60 M-1 min-1 = (1/15 min) [x/a(a-x)]

1.60 M-1 min-1 x 15 min = x/ 0.467 M(0.467 M -x)

24 M-1 = x / (0.2181M^2 - 0.467 x)

x = 0.429 M

Hence, left amount after 15 min = a -x

= 0.467 - 0.429 =0.038 M