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A 1st order reaction 20% complete in 10 minutes . calculate the time for the completion of 75% of the reaction.
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A 1st order reaction 20% complete in 10 minutes . calculate the time f...
Calculation of Time for Completion of 75% of a 1st Order Reaction
Given:
Step 1: Calculate the Rate Constant (k)
To calculate the rate constant (k), we can use the formula:
k = 0.693/t1/2
where t1/2 is the half-life of the reaction. Since we don't know the half-life, we can use the fact that the reaction is 20% complete after 10 minutes to solve for k.
20% = (1 - e-kt) x 100
0.2 = (1 - e-k(10)) x 100
0.2/100 = 1 - e-10k
0.998 = e-10k
ln 0.998 = -10k
k = 0.0698 min-1
Step 2: Calculate the Time for 75% Completion
To calculate the time for 75% completion, we can use the formula:
ln (At/A0) = -kt
where At is the amount of reactant remaining at time t, and A0 is the initial amount of reactant. We can rearrange this formula to solve for t:
t = -ln ((At/A0)) / k
Since we want to know the time for 75% completion, we can substitute At = 0.25A0 and A0 = 1 into the formula:
t = -ln (0.25) / 0.0698
t = 22.2 minutes
Conclusion:
The time for completion of 75% of the reaction is 22.2 minutes.
Given:
- 1st order reaction
- 20% complete in 10 minutes
Step 1: Calculate the Rate Constant (k)
To calculate the rate constant (k), we can use the formula:
k = 0.693/t1/2
where t1/2 is the half-life of the reaction. Since we don't know the half-life, we can use the fact that the reaction is 20% complete after 10 minutes to solve for k.
20% = (1 - e-kt) x 100
0.2 = (1 - e-k(10)) x 100
0.2/100 = 1 - e-10k
0.998 = e-10k
ln 0.998 = -10k
k = 0.0698 min-1
Step 2: Calculate the Time for 75% Completion
To calculate the time for 75% completion, we can use the formula:
ln (At/A0) = -kt
where At is the amount of reactant remaining at time t, and A0 is the initial amount of reactant. We can rearrange this formula to solve for t:
t = -ln ((At/A0)) / k
Since we want to know the time for 75% completion, we can substitute At = 0.25A0 and A0 = 1 into the formula:
t = -ln (0.25) / 0.0698
t = 22.2 minutes
Conclusion:
The time for completion of 75% of the reaction is 22.2 minutes.
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A 1st order reaction 20% complete in 10 minutes . calculate the time for the completion of 75% of the reaction.
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A 1st order reaction 20% complete in 10 minutes . calculate the time for the completion of 75% of the reaction. for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A 1st order reaction 20% complete in 10 minutes . calculate the time for the completion of 75% of the reaction. covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 1st order reaction 20% complete in 10 minutes . calculate the time for the completion of 75% of the reaction..
A 1st order reaction 20% complete in 10 minutes . calculate the time for the completion of 75% of the reaction. for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A 1st order reaction 20% complete in 10 minutes . calculate the time for the completion of 75% of the reaction. covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 1st order reaction 20% complete in 10 minutes . calculate the time for the completion of 75% of the reaction..
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