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Question
Benzene diazonium chloride in aqueous solution decomposes according to the equation \[\ce{C6H5N2Cl -> C6H5Cl + N2}\]. Starting with an initial concentration of 10 g L−1, the volume of N2 gas obtained at 50°C at different intervals of time was found to be as under:
| t (min): | 6 | 12 | 18 | 24 | 30 | ∞ |
| Vol. of N2 (ml) |
19.3 | 32.6 | 41.3 | 46.5 | 50.4 | 58.3 |
Show that the above reaction follows the first order kinetics. What is the value of the rate constant?
Solution
For a first order reaction
k = `2.303/"t" log (["A"_0])/(["A"])`
k = `2.303/"t" log "V"_∞/("V"_∞ - "V"_"t")`
In the present case, V∞ = 58.3 ml. The value of k at different time can be calculated as follows:
| t (min) | Vt | V∞ − Vt | `2.303/"t" log "V"_∞/("V"_∞ - "V"_"t")` |
| 6 | 19.3 | 58.3 − 19.3 = 39.0 | k = `2.303/6 log (58.3/39)` = 0.0670 min−1 |
| 12 | 32.6 | 58.3 − 326 = 25.7 | k = `2.303/12 log (58.3/25.7)` = 0.0683 min−1 |
| 18 | 41.3 | 58.3 − 41.3 = 17.0 | k = `2.303/18 log (58.3/17)` = 0.0685 min−1 |
| 24 | 46.5 | 58.3 − 46.5 = 11.8 |
k = `2.303/24 log (58.3/11.8)` = 0.0666 min−1 |
Since the value of k comes out to be nearly constant, the given reaction is of the first order. The mean value of k = 0.0676 min−1
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