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A reaction of first-order completed 90% in 90 minutes, hence, it is completed 50% in approximately.
- a)50 min
- b)54 min
- c)27 min
- d)62 min
Correct answer is option 'C'. Can you explain this answer?
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Given:
- A first-order reaction is completed 90% in 90 minutes.
- We need to find the time taken for the reaction to complete 50%.
We can use the formula for first-order reactions to solve this problem:
ln(Nt/N0) = -kt
where,
- Nt is the concentration at time t
- N0 is the initial concentration
- k is the rate constant
- t is the time
To find the time taken for the reaction to complete 50%, we need to find the time at which Nt/N0 = 0.5.
ln(0.5) = -k(t)
Solving for t, we get:
t = ln(0.5)/(-k)
We know that the reaction is completed 90% in 90 minutes, which means that Nt/N0 = 0.1 when t = 90.
ln(0.1) = -k(90)
Solving for k, we get:
k = ln(0.1)/(-90)
Substituting the value of k in the equation for t, we get:
t = ln(0.5)/(-ln(0.1)/90)
t = 27.03 minutes
Therefore, the time taken for the reaction to complete 50% is approximately 27 minutes (option C).
- A first-order reaction is completed 90% in 90 minutes.
- We need to find the time taken for the reaction to complete 50%.
We can use the formula for first-order reactions to solve this problem:
ln(Nt/N0) = -kt
where,
- Nt is the concentration at time t
- N0 is the initial concentration
- k is the rate constant
- t is the time
To find the time taken for the reaction to complete 50%, we need to find the time at which Nt/N0 = 0.5.
ln(0.5) = -k(t)
Solving for t, we get:
t = ln(0.5)/(-k)
We know that the reaction is completed 90% in 90 minutes, which means that Nt/N0 = 0.1 when t = 90.
ln(0.1) = -k(90)
Solving for k, we get:
k = ln(0.1)/(-90)
Substituting the value of k in the equation for t, we get:
t = ln(0.5)/(-ln(0.1)/90)
t = 27.03 minutes
Therefore, the time taken for the reaction to complete 50% is approximately 27 minutes (option C).
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A reaction of first-order completed 90% in 90 minutes, hence, it is completed 50% in approximately.a)50 minb)54 minc)27 mind)62 minCorrect answer is option 'C'. Can you explain this answer?
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