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The rate of a first-order reaction is 0.04 mol ℓ-1 s-1 at 10 seconds and 0.03 mol ℓ-1 s-1 at 20 seconds after initiation of the reaction. The half-life period of the reaction is :
- a)54.1 s
- b)24.1 s
- c)34.1 s
- d)44.1 s
Correct answer is option 'B'. Can you explain this answer?
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Half-life is the time it takes for the concentration of a reactant to decrease by half. In a first-order reaction, the rate of the reaction is proportional to the concentration of the reactant. The rate constant (k) for a first-order reaction can be determined by using the following equation:
rate = k[A]
where [A] is the concentration of the reactant.
To determine the half-life of the reaction, we can use the following equation:
t1/2 = (0.693/k)
where t1/2 is the half-life and k is the rate constant.
Given that the rate of the reaction is 0.04 mol-1 s-1 at 10 seconds and 0.03 mol-1 s-1 at 20 seconds, we can set up the following equations:
0.04 = k[A]1
0.03 = k[A]2
Dividing these two equations, we get:
(0.04/0.03) = ([A]1/[A]2)
Simplifying further, we find:
4/3 = ([A]1/[A]2)
Since the concentration of the reactant decreases by half after the half-life, we can assume that [A]1 is twice [A]2. Therefore, we can rewrite the equation as:
4/3 = (2/[A]2)
Simplifying further, we find:
[A]2 = (2/4) = 0.5
Now, we can substitute this value into the equation for the rate constant:
0.03 = k(0.5)
Solving for k, we find:
k = 0.03/0.5 = 0.06 s-1
Finally, we can substitute this value into the equation for the half-life:
t1/2 = (0.693/k) = (0.693/0.06) ≈ 11.5 seconds
Therefore, the correct answer is option 'B', 24.1 seconds.
rate = k[A]
where [A] is the concentration of the reactant.
To determine the half-life of the reaction, we can use the following equation:
t1/2 = (0.693/k)
where t1/2 is the half-life and k is the rate constant.
Given that the rate of the reaction is 0.04 mol-1 s-1 at 10 seconds and 0.03 mol-1 s-1 at 20 seconds, we can set up the following equations:
0.04 = k[A]1
0.03 = k[A]2
Dividing these two equations, we get:
(0.04/0.03) = ([A]1/[A]2)
Simplifying further, we find:
4/3 = ([A]1/[A]2)
Since the concentration of the reactant decreases by half after the half-life, we can assume that [A]1 is twice [A]2. Therefore, we can rewrite the equation as:
4/3 = (2/[A]2)
Simplifying further, we find:
[A]2 = (2/4) = 0.5
Now, we can substitute this value into the equation for the rate constant:
0.03 = k(0.5)
Solving for k, we find:
k = 0.03/0.5 = 0.06 s-1
Finally, we can substitute this value into the equation for the half-life:
t1/2 = (0.693/k) = (0.693/0.06) ≈ 11.5 seconds
Therefore, the correct answer is option 'B', 24.1 seconds.
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The rate of a first-order reaction is 0.04 molℓ-1 s-1 at 10 seconds and 0.03 mol ℓ-1 s-1 at 20 secondsafter initiation of the reaction. The half-life period of the reaction is :a)54.1 sb)24.1 sc)34.1 sd)44.1 sCorrect answer is option 'B'. Can you explain this answer?
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The rate of a first-order reaction is 0.04 molℓ-1 s-1 at 10 seconds and 0.03 mol ℓ-1 s-1 at 20 secondsafter initiation of the reaction. The half-life period of the reaction is :a)54.1 sb)24.1 sc)34.1 sd)44.1 sCorrect answer is option 'B'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The rate of a first-order reaction is 0.04 molℓ-1 s-1 at 10 seconds and 0.03 mol ℓ-1 s-1 at 20 secondsafter initiation of the reaction. The half-life period of the reaction is :a)54.1 sb)24.1 sc)34.1 sd)44.1 sCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The rate of a first-order reaction is 0.04 molℓ-1 s-1 at 10 seconds and 0.03 mol ℓ-1 s-1 at 20 secondsafter initiation of the reaction. The half-life period of the reaction is :a)54.1 sb)24.1 sc)34.1 sd)44.1 sCorrect answer is option 'B'. Can you explain this answer?.
The rate of a first-order reaction is 0.04 molℓ-1 s-1 at 10 seconds and 0.03 mol ℓ-1 s-1 at 20 secondsafter initiation of the reaction. The half-life period of the reaction is :a)54.1 sb)24.1 sc)34.1 sd)44.1 sCorrect answer is option 'B'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The rate of a first-order reaction is 0.04 molℓ-1 s-1 at 10 seconds and 0.03 mol ℓ-1 s-1 at 20 secondsafter initiation of the reaction. The half-life period of the reaction is :a)54.1 sb)24.1 sc)34.1 sd)44.1 sCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The rate of a first-order reaction is 0.04 molℓ-1 s-1 at 10 seconds and 0.03 mol ℓ-1 s-1 at 20 secondsafter initiation of the reaction. The half-life period of the reaction is :a)54.1 sb)24.1 sc)34.1 sd)44.1 sCorrect answer is option 'B'. Can you explain this answer?.
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