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first-order reaction was 70 percent complete in 20 minutes. What is the rate constant of the reaction?
- a)0.07 min-1
- b)0.06 min-1
- c)0.08 min-1
- d)0.09 min-1
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
first-order reaction was 70 percent complete in 20 minutes. What is th...
To determine the rate constant of a first-order reaction, we can use the formula:
ln(C₀/C) = kt
where C₀ is the initial concentration, C is the concentration at a given time t, k is the rate constant, and ln represents the natural logarithm.
In this case, we are given that the reaction is 70% complete in 20 minutes. This means that the concentration at 20 minutes is 30% of the initial concentration (100% - 70% = 30%).
Let's assume the initial concentration is C₀.
Therefore, C = 0.3C₀ at t = 20 minutes.
Substituting these values into the formula, we get:
ln(C₀/0.3C₀) = k(20)
Simplifying, we have:
ln(1/0.3) = 20k
ln(3.33) = 20k
Now, we can solve for the value of k by dividing both sides by 20:
k = ln(3.33)/20
Using a calculator, we find that ln(3.33) is approximately 1.20. Dividing this by 20 gives a value of approximately 0.06 min⁻¹.
Therefore, the rate constant of the reaction is approximately 0.06 min⁻¹, which corresponds to option B.
ln(C₀/C) = kt
where C₀ is the initial concentration, C is the concentration at a given time t, k is the rate constant, and ln represents the natural logarithm.
In this case, we are given that the reaction is 70% complete in 20 minutes. This means that the concentration at 20 minutes is 30% of the initial concentration (100% - 70% = 30%).
Let's assume the initial concentration is C₀.
Therefore, C = 0.3C₀ at t = 20 minutes.
Substituting these values into the formula, we get:
ln(C₀/0.3C₀) = k(20)
Simplifying, we have:
ln(1/0.3) = 20k
ln(3.33) = 20k
Now, we can solve for the value of k by dividing both sides by 20:
k = ln(3.33)/20
Using a calculator, we find that ln(3.33) is approximately 1.20. Dividing this by 20 gives a value of approximately 0.06 min⁻¹.
Therefore, the rate constant of the reaction is approximately 0.06 min⁻¹, which corresponds to option B.
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Community Answer
first-order reaction was 70 percent complete in 20 minutes. What is th...
Given, the reaction is 70 percent complete so, a = 70
Time t = 20 minutes
First order integrated rate equation, k =
Time t = 20 minutes
First order integrated rate equation, k =
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