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Question
What is the half life of a first order reaction if time required to decrease concentration of reactant from 0.8 M to 0.2 M is 12 h?
Options
12 h
3 h
1.5 h
6 h
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Solution
6 h
Explanation:
`k = 2.303/t log((A_0)/(A_t))`
Where,
A0 is the initial concentration,
At is the concentration after time t,
t is the time taken.
`k = 2.303/12 log((0.8)/(0.2))`
`k = 2.303/12 log(4)`
`k = 2.303/12 2log(2)`
`k = 2.303/12 xx 0.6020`
`k = (2.303 xx 0.6020)/12`
`k = 1.384306/12`
k ≈ 0.11536 hr−1
`t_(1//2) = 0.693/k`
`t_(1//2) = 0.693/0.11536`
`t_(1//2) ≈ 6.01` h
The half-life of the first-order reaction is approximately 6 hours.
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