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Question
A first order reaction takes 40 minutes for 30% decomposition. Calculate t1/2 for this reaction. (Given log 1.428 = 0.1548)
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Solution
|
`A->P` |
||
| t=0 | a | 0 |
| t=t | (a-x) | x |
Now, it takes 40 min for 30% decomposition i.e. reactant left after 40 min is 70% of its initial concentration.
`So,(a-x)=70/100xxa=7/10xxa`
`k=2.303/tlog(a/(a-x)) => k=2.303/40 log a/(7/10)a=2.303/40log1.428`
`therefore k=0.00891 min `
`therefore t_(1/2)=0.693/k=0.693/0.008913=77.78 min`
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