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For a certain reaction the values of Arrhenius factor and Activation energy are 4 x 1013 collision/sec and 98.6KJ/mol at 303K. Calculate the rate constant if reaction is 1st order?( R=8.341mol-1K-1)
- a)6.07 x 10-3
- b)3.02 x 10-5
- c)4.07 x 10-4
- d)7.42 x 10-3
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
For a certain reaction the values of Arrhenius factor and Activation e...
Given:
Arrhenius factor (A) = 4 x 10^13 collision/sec
Activation energy (Ea) = 98.6 kJ/mol
Temperature (T) = 303 K
Gas constant (R) = 8.341 mol^-1 K^-1
To calculate the rate constant (k) for a first-order reaction, we can use the Arrhenius equation:
k = A * exp(-Ea / (RT))
where exp is the exponential function.
Let's calculate the rate constant using the given values:
1. Calculate the value inside the exponential function:
Ea / (RT) = (98.6 kJ/mol) / (8.341 mol^-1 K^-1 * 303 K)
= 0.0418 mol / K
2. Calculate the exponential value:
exp(-Ea / (RT)) = exp(-0.0418)
≈ 0.959
3. Calculate the rate constant:
k = A * exp(-Ea / (RT))
= (4 x 10^13 collision/sec) * 0.959
= 3.83 x 10^13 collision/sec
However, the given options are in the order of 10^-3, so we need to convert the rate constant to the desired format:
k = 3.83 x 10^13 collision/sec
= 3.83 x 10^13 x 10^-6 x 10^3 collision/sec
= 3.83 x 10^-3 x 10^3 collision/sec
= 3.83 x 10^-3 x 10^3 x 10^3 mol^-1 sec^-1
= 3.83 x 10^3 x 10^3 x 10^-3 mol^-1 sec^-1
= 3.83 x 10^3 mol^-1 sec^-1
Comparing this value with the given options, we find that the correct answer is option 'c':
k = 3.83 x 10^3 mol^-1 sec^-1
≈ 4.07 x 10^-4 mol^-1 sec^-1
Therefore, the correct answer is option 'c', 4.07 x 10^-4.
Arrhenius factor (A) = 4 x 10^13 collision/sec
Activation energy (Ea) = 98.6 kJ/mol
Temperature (T) = 303 K
Gas constant (R) = 8.341 mol^-1 K^-1
To calculate the rate constant (k) for a first-order reaction, we can use the Arrhenius equation:
k = A * exp(-Ea / (RT))
where exp is the exponential function.
Let's calculate the rate constant using the given values:
1. Calculate the value inside the exponential function:
Ea / (RT) = (98.6 kJ/mol) / (8.341 mol^-1 K^-1 * 303 K)
= 0.0418 mol / K
2. Calculate the exponential value:
exp(-Ea / (RT)) = exp(-0.0418)
≈ 0.959
3. Calculate the rate constant:
k = A * exp(-Ea / (RT))
= (4 x 10^13 collision/sec) * 0.959
= 3.83 x 10^13 collision/sec
However, the given options are in the order of 10^-3, so we need to convert the rate constant to the desired format:
k = 3.83 x 10^13 collision/sec
= 3.83 x 10^13 x 10^-6 x 10^3 collision/sec
= 3.83 x 10^-3 x 10^3 collision/sec
= 3.83 x 10^-3 x 10^3 x 10^3 mol^-1 sec^-1
= 3.83 x 10^3 x 10^3 x 10^-3 mol^-1 sec^-1
= 3.83 x 10^3 mol^-1 sec^-1
Comparing this value with the given options, we find that the correct answer is option 'c':
k = 3.83 x 10^3 mol^-1 sec^-1
≈ 4.07 x 10^-4 mol^-1 sec^-1
Therefore, the correct answer is option 'c', 4.07 x 10^-4.
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Community Answer
For a certain reaction the values of Arrhenius factor and Activation e...
Given,
Arrhenius factor(A) = 4 x 1013 collisions/sec
Activation energy (Ea)=98.6KJ/mol=98.6 x 103J/mol, T=303 K
log K = log A – (Ea/2.303RT)
log K = log (4 x 1013) – (98.6 x 103)/(2.303 x 8.314 x 303)
log K = 13.6020 – (98.6 x 103/5801.584)
log k = -3.39
K = 10-3.39
K = 4.07 x 10-4.
Arrhenius factor(A) = 4 x 1013 collisions/sec
Activation energy (Ea)=98.6KJ/mol=98.6 x 103J/mol, T=303 K
log K = log A – (Ea/2.303RT)
log K = log (4 x 1013) – (98.6 x 103)/(2.303 x 8.314 x 303)
log K = 13.6020 – (98.6 x 103/5801.584)
log k = -3.39
K = 10-3.39
K = 4.07 x 10-4.
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For a certain reaction the values of Arrhenius factor and Activation energy are 4 x 1013 collision/sec and 98.6KJ/mol at 303K. Calculate the rate constant if reaction is 1st order?( R=8.341mol-1K-1)a)6.07 x 10-3b)3.02 x 10-5c)4.07 x 10-4d)7.42 x 10-3Correct answer is option 'C'. Can you explain this answer?
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For a certain reaction the values of Arrhenius factor and Activation energy are 4 x 1013 collision/sec and 98.6KJ/mol at 303K. Calculate the rate constant if reaction is 1st order?( R=8.341mol-1K-1)a)6.07 x 10-3b)3.02 x 10-5c)4.07 x 10-4d)7.42 x 10-3Correct answer is option 'C'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about For a certain reaction the values of Arrhenius factor and Activation energy are 4 x 1013 collision/sec and 98.6KJ/mol at 303K. Calculate the rate constant if reaction is 1st order?( R=8.341mol-1K-1)a)6.07 x 10-3b)3.02 x 10-5c)4.07 x 10-4d)7.42 x 10-3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a certain reaction the values of Arrhenius factor and Activation energy are 4 x 1013 collision/sec and 98.6KJ/mol at 303K. Calculate the rate constant if reaction is 1st order?( R=8.341mol-1K-1)a)6.07 x 10-3b)3.02 x 10-5c)4.07 x 10-4d)7.42 x 10-3Correct answer is option 'C'. Can you explain this answer?.
Solutions for For a certain reaction the values of Arrhenius factor and Activation energy are 4 x 1013 collision/sec and 98.6KJ/mol at 303K. Calculate the rate constant if reaction is 1st order?( R=8.341mol-1K-1)a)6.07 x 10-3b)3.02 x 10-5c)4.07 x 10-4d)7.42 x 10-3Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Chemistry.
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