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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`
संबंधित प्रश्न
For a first order reaction, show that time required for 99% completion is twice the time required for the completion of 90% of reaction.
A first order reaction takes 23.1 minutes for 50% completion. Calculate the time required for 75% completion of this reaction.
(log 2 = 0.301, log 3 = 0.4771, log 4 = 0.6021)
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).
The rate constant for the first order decomposition of H2O2 is given by the following equation:
log k = 14.34 − 1.25 × 104 K/T.
Calculate Ea for this reaction and at what temperature will its half-period be 256 minutes?
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
Define half life of a reaction.
Obtain a relation, `k_2/k_1 = ((t_(1/2))_2)/((t_(1/2))_1)`, where k1 and k2 are rate constants while (t1/2)1 and (t1/2)2 are half-life periods of the first order reaction at temperatures T1 and T2 respectively. Write the relation for activation energy.
Calculate the half-life of a first order reaction from the rate constant given below:
2 min−1
