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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 experimental data for decomposition of N2O5
\[\ce{2N2O5 -> 4NO2 + O2}\]
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| 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 |
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