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A first-order reaction is 50 percent complete in 30 minutes. Calculate the time taken for completion of 87.5 percent of the reaction.
- a)30 minutes
- b)60 minutes
- c)90 minutes
- d)120 minutes
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A first-order reaction is 50 percent complete in 30 minutes. Calculate...
Solution:
Given, the reaction is a first-order reaction.
We know that the rate of a first-order reaction is proportional to the concentration of the reactant. Hence, it follows the following integrated rate law:
ln([A]t/[A]0) = -kt
where [A]0 is the initial concentration of the reactant, [A]t is the concentration of the reactant at time t, k is the rate constant of the reaction, and t is the time.
Let us assume that the initial concentration of the reactant is 1 unit. Then, at 50% completion, [A]t/[A]0 = 0.5. Substituting these values in the integrated rate law, we get:
ln(0.5) = -k(30)
or, k = ln(0.5)/(-30)
Now, we need to find the time taken for 87.5% completion. At this point, [A]t/[A]0 = 0.125. Substituting these values in the integrated rate law, we get:
ln(0.125) = -k(t)
or, t = -ln(0.125)/k
Substituting the value of k, we get:
t = -ln(0.125)/[ln(0.5)/(-30)]
or, t = 90 minutes.
Hence, the correct answer is option (c) 90 minutes.
Given, the reaction is a first-order reaction.
We know that the rate of a first-order reaction is proportional to the concentration of the reactant. Hence, it follows the following integrated rate law:
ln([A]t/[A]0) = -kt
where [A]0 is the initial concentration of the reactant, [A]t is the concentration of the reactant at time t, k is the rate constant of the reaction, and t is the time.
Let us assume that the initial concentration of the reactant is 1 unit. Then, at 50% completion, [A]t/[A]0 = 0.5. Substituting these values in the integrated rate law, we get:
ln(0.5) = -k(30)
or, k = ln(0.5)/(-30)
Now, we need to find the time taken for 87.5% completion. At this point, [A]t/[A]0 = 0.125. Substituting these values in the integrated rate law, we get:
ln(0.125) = -k(t)
or, t = -ln(0.125)/k
Substituting the value of k, we get:
t = -ln(0.125)/[ln(0.5)/(-30)]
or, t = 90 minutes.
Hence, the correct answer is option (c) 90 minutes.
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Community Answer
A first-order reaction is 50 percent complete in 30 minutes. Calculate...
Reaction is 50 percent complete in 30 minutes. Hence, t1/2 = 30 minutes
75 percent of the reaction is completed in two half-lives. Hence, t = 2 × 30 = 60 minutes
87.5 percent of the reaction is completed in three half-lives. Hence, t = 3 × 30 = 90 minutes.
75 percent of the reaction is completed in two half-lives. Hence, t = 2 × 30 = 60 minutes
87.5 percent of the reaction is completed in three half-lives. Hence, t = 3 × 30 = 90 minutes.
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