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Number of natural life times (Tav ) required for a first order reaction to achieve 99.9% level of completion is
- a)2.3
- b)6.9
- c)9.2
- d)0.105
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Number of natural life times (Tav) required for a first order reaction...
Time required for 99.9% reaction is 10 times of half-life period.
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Number of natural life times (Tav) required for a first order reaction...
Solution:
We know that for a first order reaction, the rate constant is given by:
k = 0.693/t1/2
where t1/2 is the half-life of the reaction.
Now, we need to find the time required for the reaction to achieve 99.9% level of completion. This means that only 0.1% of the reactant is left after the reaction is complete. We can use the following equation to find the time required for this level of completion:
ln(Nt/N0) = -kt
where Nt/N0 is the fraction of reactant remaining at time t, k is the rate constant, and t is the time.
Substituting Nt/N0 = 0.001 and k = 0.693/t1/2, we get:
ln(0.001) = -0.693/t1/2 * t
Solving for t, we get:
t = 6.93 * t1/2
Since we need the reaction to be 99.9% complete, we can assume that t1/2 = Tav/ln2, where Tav is the average lifetime of the reaction. Substituting this value in the above equation, we get:
6.93 * Tav/ln2 = Tav
Solving for Tav, we get:
Tav = 6.93 * ln2 = 9.20
Therefore, the number of natural life times required for the reaction to achieve 99.9% level of completion is 9.20, which is option (B).
We know that for a first order reaction, the rate constant is given by:
k = 0.693/t1/2
where t1/2 is the half-life of the reaction.
Now, we need to find the time required for the reaction to achieve 99.9% level of completion. This means that only 0.1% of the reactant is left after the reaction is complete. We can use the following equation to find the time required for this level of completion:
ln(Nt/N0) = -kt
where Nt/N0 is the fraction of reactant remaining at time t, k is the rate constant, and t is the time.
Substituting Nt/N0 = 0.001 and k = 0.693/t1/2, we get:
ln(0.001) = -0.693/t1/2 * t
Solving for t, we get:
t = 6.93 * t1/2
Since we need the reaction to be 99.9% complete, we can assume that t1/2 = Tav/ln2, where Tav is the average lifetime of the reaction. Substituting this value in the above equation, we get:
6.93 * Tav/ln2 = Tav
Solving for Tav, we get:
Tav = 6.93 * ln2 = 9.20
Therefore, the number of natural life times required for the reaction to achieve 99.9% level of completion is 9.20, which is option (B).
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Number of natural life times (Tav) required for a first order reaction to achieve 99.9% level of completion isa)2.3b)6.9c)9.2d)0.105Correct answer is option 'B'. Can you explain this answer?
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