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A first-order reaction is 50 percent complete in 30 minutes. Calculate the time taken for completion of 87.5 percent of the reaction.
- a)30 minutes
- b)60 minutes
- c)90 minutes
- d)120 minutes
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A first-order reaction is 50 percent complete in 30 minutes. Calculate...
To solve this problem, we can use the first-order reaction equation:
ln(No/N) = kt
Where:
No = initial concentration of the reactant
N = concentration of the reactant at a given time
k = rate constant
t = time
We are given that the reaction is 50 percent complete in 30 minutes. This means that N/No = 0.5. Substituting this into the equation, we get:
ln(0.5) = k * 30
Solving for k, we find:
k = ln(0.5)/30
Now we need to find the time taken for completion of 87.5 percent of the reaction. This means that N/No = 0.125. Substituting this into the equation and solving for t, we get:
ln(0.125) = (ln(0.5)/30) * t
Simplifying this equation, we find:
ln(0.125) = ln(0.5)/30 * t
Taking the exponential of both sides, we get:
0.125 = e^(ln(0.5)/30 * t)
Simplifying further, we find:
0.125 = (0.5)^(1/30 * t)
Taking the logarithm of both sides, we get:
log(0.125) = log((0.5)^(1/30 * t))
Using the logarithmic identity log(a^b) = b * log(a), we can rewrite the equation as:
log(0.125) = (1/30 * t) * log(0.5)
Simplifying further, we find:
log(0.125) = (1/30 * t) * (-0.301)
Solving for t, we find:
t = (log(0.125) / (-0.301)) * 30
Calculating this expression, we find that t is approximately 89.9 minutes. Thus, the time taken for completion of 87.5 percent of the reaction is approximately 90 minutes, which corresponds to option c.
ln(No/N) = kt
Where:
No = initial concentration of the reactant
N = concentration of the reactant at a given time
k = rate constant
t = time
We are given that the reaction is 50 percent complete in 30 minutes. This means that N/No = 0.5. Substituting this into the equation, we get:
ln(0.5) = k * 30
Solving for k, we find:
k = ln(0.5)/30
Now we need to find the time taken for completion of 87.5 percent of the reaction. This means that N/No = 0.125. Substituting this into the equation and solving for t, we get:
ln(0.125) = (ln(0.5)/30) * t
Simplifying this equation, we find:
ln(0.125) = ln(0.5)/30 * t
Taking the exponential of both sides, we get:
0.125 = e^(ln(0.5)/30 * t)
Simplifying further, we find:
0.125 = (0.5)^(1/30 * t)
Taking the logarithm of both sides, we get:
log(0.125) = log((0.5)^(1/30 * t))
Using the logarithmic identity log(a^b) = b * log(a), we can rewrite the equation as:
log(0.125) = (1/30 * t) * log(0.5)
Simplifying further, we find:
log(0.125) = (1/30 * t) * (-0.301)
Solving for t, we find:
t = (log(0.125) / (-0.301)) * 30
Calculating this expression, we find that t is approximately 89.9 minutes. Thus, the time taken for completion of 87.5 percent of the reaction is approximately 90 minutes, which corresponds to option c.
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Community Answer
A first-order reaction is 50 percent complete in 30 minutes. Calculate...
Reaction is 50 percent complete in 30 minutes. Hence, t1/2 = 30 minutes
75 percent of the reaction is completed in two half-lives. Hence, t = 2 × 30 = 60 minutes
87.5 percent of the reaction is completed in three half-lives. Hence, t = 3 × 30 = 90 minutes.
75 percent of the reaction is completed in two half-lives. Hence, t = 2 × 30 = 60 minutes
87.5 percent of the reaction is completed in three half-lives. Hence, t = 3 × 30 = 90 minutes.
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A first-order reaction is 50 percent complete in 30 minutes. Calculate the time taken for completion of 87.5 percent of the reaction.a)30 minutesb)60 minutesc)90 minutesd)120 minutesCorrect answer is option 'C'. Can you explain this answer?
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