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In a chemical reaction a substance changes into another such that the rate of decomposition of a chemical substance x present at instant t is proportional to x itself i.e. amount of unchanged substance still present . If half of the substance present initially has been converted at the end of 1 minute then the time at the end of which 99 % of the substance will have changed is
- a)log2 10 minute
- b)log2 99 minute
- c)log2 50 minute
- d)log2 100 minute
Correct answer is option 'D'. Can you explain this answer?
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Given information:
A chemical reaction follows first-order kinetics, where the rate of decomposition of a chemical substance x at any instant t is proportional to the amount of unchanged substance still present.
At the end of 1 minute, half of the substance present initially has been converted.
Understanding the problem:
We need to find the time at which 99% of the substance will have changed.
Let's assume the initial amount of substance x is X.
Given that at the end of 1 minute, half of the substance has been converted, we can express this as:
X/2 = X * e^(-k*1)
Where k is the rate constant.
Solving the problem:
We can rewrite the equation as:
e^(-k) = 1/2
Taking the natural logarithm on both sides, we get:
-k = ln(1/2)
k = -ln(1/2)
Now, we need to find the time at which 99% of the substance will have changed.
Let's assume the time required for 99% change is t.
At time t, the amount of substance x remaining will be X * e^(-k*t).
We can express this as:
X * e^(-k*t) = 0.01X
Dividing both sides by X, we get:
e^(-k*t) = 0.01
Taking the natural logarithm on both sides, we get:
-k*t = ln(0.01)
Substituting the value of k, we have:
-(-ln(1/2))*t = ln(0.01)
t = ln(0.01)/ln(1/2)
t = -ln(0.01)/ln(2)
t ≈ 6.64
Answer:
The time at which 99% of the substance will have changed is approximately log2 100 minutes (option D).
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In a chemical reaction a substance changes into another such that the rate of decomposition of a chemical substance x present at instant t is proportional to x itself i.e. amount of unchanged substance still present . If half of the substance present initially has been converted at the end of 1 minute then the time at the end of which 99 % of the substance will have changed isa)log2 10 minuteb)log299 minutec)log2 50 minuted)log2 100 minuteCorrect answer is option 'D'. Can you explain this answer?
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In a chemical reaction a substance changes into another such that the rate of decomposition of a chemical substance x present at instant t is proportional to x itself i.e. amount of unchanged substance still present . If half of the substance present initially has been converted at the end of 1 minute then the time at the end of which 99 % of the substance will have changed isa)log2 10 minuteb)log299 minutec)log2 50 minuted)log2 100 minuteCorrect answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a chemical reaction a substance changes into another such that the rate of decomposition of a chemical substance x present at instant t is proportional to x itself i.e. amount of unchanged substance still present . If half of the substance present initially has been converted at the end of 1 minute then the time at the end of which 99 % of the substance will have changed isa)log2 10 minuteb)log299 minutec)log2 50 minuted)log2 100 minuteCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a chemical reaction a substance changes into another such that the rate of decomposition of a chemical substance x present at instant t is proportional to x itself i.e. amount of unchanged substance still present . If half of the substance present initially has been converted at the end of 1 minute then the time at the end of which 99 % of the substance will have changed isa)log2 10 minuteb)log299 minutec)log2 50 minuted)log2 100 minuteCorrect answer is option 'D'. Can you explain this answer?.
In a chemical reaction a substance changes into another such that the rate of decomposition of a chemical substance x present at instant t is proportional to x itself i.e. amount of unchanged substance still present . If half of the substance present initially has been converted at the end of 1 minute then the time at the end of which 99 % of the substance will have changed isa)log2 10 minuteb)log299 minutec)log2 50 minuted)log2 100 minuteCorrect answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a chemical reaction a substance changes into another such that the rate of decomposition of a chemical substance x present at instant t is proportional to x itself i.e. amount of unchanged substance still present . If half of the substance present initially has been converted at the end of 1 minute then the time at the end of which 99 % of the substance will have changed isa)log2 10 minuteb)log299 minutec)log2 50 minuted)log2 100 minuteCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a chemical reaction a substance changes into another such that the rate of decomposition of a chemical substance x present at instant t is proportional to x itself i.e. amount of unchanged substance still present . If half of the substance present initially has been converted at the end of 1 minute then the time at the end of which 99 % of the substance will have changed isa)log2 10 minuteb)log299 minutec)log2 50 minuted)log2 100 minuteCorrect answer is option 'D'. Can you explain this answer?.
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ample number of questions to practice In a chemical reaction a substance changes into another such that the rate of decomposition of a chemical substance x present at instant t is proportional to x itself i.e. amount of unchanged substance still present . If half of the substance present initially has been converted at the end of 1 minute then the time at the end of which 99 % of the substance will have changed isa)log2 10 minuteb)log299 minutec)log2 50 minuted)log2 100 minuteCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
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