Question:
Relationship between \( t_{90} \) and \( t_{99} \) for a first order reaction:
Relationship between \( t_{90} \) and \( t_{99} \) for a first order reaction:
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For first-order reactions, the relation \( t_{99} = 20.693t_{90} \) helps determine the time required for 99% of the reactant to be consumed.
Updated On: Apr 18, 2026
- \( t_{99} = 3t_{90} \)
- \( t_{99} = 2t_{90} \)
- \( t_{99} = 2.303t_{90} \)
- \( t_{99} = 20.693t_{90} \)
- \( t_{99} = 6.93t_{90} \)
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The Correct Option is D
Solution and Explanation
For a first-order reaction, the time taken for the concentration of a reactant to reduce to 90% of its initial value is related to the time taken for the concentration to reduce to 99%. The relationship is derived from the integrated rate law for a first-order reaction.
\[
t_{99} = 20.693 \times t_{90}
\]
Thus, the correct relation between \( t_{90} \) and \( t_{99} \) is:
\[
t_{99} = 20.693t_{90}
\]
Final Answer: (D) \( t_{99} = 20.693t_{90} \)
Final Answer: (D) \( t_{99} = 20.693t_{90} \)
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