The rate of photodecomposition of the herbicide piclo- ram in aqueous systems was determined by exposure to sunlight for a number of days. One such experiment produced the following results. (Data from R.T. Hedlun and C.R. Youngson, “The Rates of Photodecomposition of Picloram in Aqueous Systems," Fate of Organic Pesticides in tbe Aquatic Environment, Advances in Chemistry Series, #111, American Chemical Society (1972), 159—172.)
Exposure Time, t (days) | [Pidoram] |
(mol L_1)
Determine the order of reaction, the rate constant, and the half-life for the photodecomposition of picloram.
Interpretation:
To interpret the data collected and to determine the order of reaction, rate constant and the half-life for the photochemical decomposition of Picloram
Concept Introduction:
For a first order reaction:
And half-life is given by:
Where,
k = decay constant
t = time taken
Answer to Problem 11.49PAE
Solution:
The order of reaction:
First
The value of rate constant:
Half life of reaction:
Explanation of Solution
Given information:
Data collected for decomposition of Picloram is:
Time, t (days) | [Picloram] (mol L-1) |
0 | 4.14 |
7 | 3.70 |
14 | 3.31 |
21 | 2.94 |
28 | 2.61 |
35 | 2.30 |
42 | 2.05 |
49 | 1.82 |
56 | 1.65 |
From the given data we will first calculate if the reaction is first order,
For the first order reaction, we will use the formula
Case 1)
When time (t) is 7 days
Substituting the values,
Case 2)
When time (t) is 14 days
Substituting the values,
The value of
The half-life of the reaction can be calculated with the help of formula
Substituting the value of k
Hence, the half-life is
The decomposition of Picloram is a first order reaction with rate constant
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