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A first order reaction is half completed in 45 minutes. How long does it need for 99.9% of the reaction to be completed?
- a)5 hours
- b)7.5 hours
- c)10 hours
- d)20 hours
Correct answer is option 'B'. Can you explain this answer?
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A first order reaction is half completed in 45 minutes. How long does...
Solution:
Given: A first order reaction is half completed in 45 minutes.
We know that the time taken for a first order reaction to complete 99.9% of the reaction is given by:
t = (2.303/k) log(Co/C)
where t is the time taken for the reaction to complete 99.9% of the reaction, k is the rate constant, Co is the initial concentration of the reactant, and C is the concentration of the reactant at the end of the reaction.
Let us assume that the initial concentration of the reactant is 1.
Then, we know that the half-life of a first order reaction is given by:
t1/2 = (0.693/k)
Given that the reaction is half completed in 45 minutes, we can write:
t1/2 = 45 minutes
Therefore, we can calculate the rate constant as:
k = 0.693/t1/2
k = 0.693/45
k = 0.0154 min^-1
Substituting the values in the equation for t, we get:
t = (2.303/k) log(Co/C)
t = (2.303/0.0154) log(1/0.001)
t = 7.5 hours (approx)
Therefore, the time taken for 99.9% of the reaction to be completed is 7.5 hours.
Hence, option (B) is the correct answer.
Given: A first order reaction is half completed in 45 minutes.
We know that the time taken for a first order reaction to complete 99.9% of the reaction is given by:
t = (2.303/k) log(Co/C)
where t is the time taken for the reaction to complete 99.9% of the reaction, k is the rate constant, Co is the initial concentration of the reactant, and C is the concentration of the reactant at the end of the reaction.
Let us assume that the initial concentration of the reactant is 1.
Then, we know that the half-life of a first order reaction is given by:
t1/2 = (0.693/k)
Given that the reaction is half completed in 45 minutes, we can write:
t1/2 = 45 minutes
Therefore, we can calculate the rate constant as:
k = 0.693/t1/2
k = 0.693/45
k = 0.0154 min^-1
Substituting the values in the equation for t, we get:
t = (2.303/k) log(Co/C)
t = (2.303/0.0154) log(1/0.001)
t = 7.5 hours (approx)
Therefore, the time taken for 99.9% of the reaction to be completed is 7.5 hours.
Hence, option (B) is the correct answer.
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A first order reaction is half completed in 45 minutes. How long does it need for 99.9% of the reaction to be completed?a)5 hoursb)7.5 hoursc)10 hoursd)20 hoursCorrect answer is option 'B'. Can you explain this answer?
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