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.
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
In a study of the decomposition of the compound X via the reaction X(g)⇌Y(g)+Z(g) the following...
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