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प्रश्न
Show that for a first order reaction half life is independent of initial concentration.
Show that half-life period does not depend upon the initial concentration for the first order reaction.
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उत्तर
For a first order reaction, the half-life is a constant, i.e., it does not depend on the initial concentration.
The rate constant for a first order reaction is given by,
k = `2.303/t log ([A_0])/([A])`
at t = `t_(1//2)`; [A] = `([A_0])/2`
k = `2.303/t_(1//2) log ([A_0])/(([A_0])/2)`
k = `2.303/t_(1//2) log (2)`
k = `(2.303 xx 0.3010)/t_(1//2)`
k = `0.693/t_(1//2)`
`t_(1//2) = 0.693/k`
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संबंधित प्रश्न
The integrated rate equation for first order reaction is A → products
Derive the relation between half life and rate constant for a first order reaction
The rate constant for a first order reaction is 100 s–1. The time required for completion of 50% of reaction is _______.
(A) 0.0693 milliseconds
(B) 0.693 milliseconds
(C) 6.93 milliseconds
(D) 69.3 milliseconds
A first order reaction takes 30 minutes for 50% completion. Calculate the time required for 90% completion of this reaction.
(log 2 = 0.3010)
The experimental data for decomposition of N2O5.
\[\ce{2N2O5 -> 4NO2 + O2}\] in gas phase at 318 K are given below:
| t/s | 0 | 400 | 800 | 1200 | 1600 | 2000 | 2400 | 2800 | 3200 |
| 102 × [N2O5]/mol L−1 | 1.63 | 1.36 | 1.14 | 0.93 | 0.78 | 0.64 | 0.53 | 0.43 | 0.35 |
- Plot [N2O5] against t.
- Find the half-life period for the reaction.
- Draw a graph between log [N2O5] and t.
- What is the rate law?
- Calculate the rate constant.
- Calculate the half-life period from k and compare it with (ii).
Show that the time required for 99% completion is double of the time required for the completion of 90% reaction.
The half life period of a first order reaction is 6. 0 h . Calculate the rate constant
A reaction has a half-life of 1 min. The time required for 99.9% completion of the reaction is ______ min.
(Round off to the nearest integer).
[Use: In 2 = 0.69; In 10 = 2.3]
The unit of rate constant of zero order reaction is ______.
A first order reaction takes 40 min for 30% decomposition. Calculate `"t"_(1/2)`.
