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The time taken for 90% of a first order reaction to complete is approximately
  • a)
    1•1 times that of half-life
  • b)
    2•2 times that of half-life
  • c)
    3•3 times that of half-life
  • d)
    4•4 times that of half-life
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The time taken for 90% of a first order reaction to complete is approx...
Explanation:

First Order Reaction:
- A first order reaction is a reaction in which the rate of reaction is directly proportional to the concentration of a single reactant.
- The integrated rate law for a first order reaction is: ln([A]t/[A]0) = -kt, where [A]t is the concentration of the reactant at time t, [A]0 is the initial concentration, k is the rate constant, and t is time.

Time taken for 90% completion:
- For a first order reaction, the time taken for a certain percentage of the reaction to complete can be calculated using the equation: t90% = (2.303/k) * log([A]0/[A]0 - 0.9[A]0).
- For 90% completion, [A]t = 0.1[A]0.

Relation to Half-life:
- The half-life of a first order reaction is defined as the time taken for the concentration of the reactant to reduce to half of its initial value.
- The half-life of a first order reaction is given by: t1/2 = 0.693/k.

Comparison:
- The time taken for 90% of a first order reaction to complete is approximately 3.3 times the half-life of the reaction. This can be understood by comparing the equations for t90% and t1/2.
- Therefore, the correct answer is option 'c) 3.3 times that of half-life'.
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There are many reactions which obey a first order rate equation although it reality they are bi- or ter-molecular. As an example of these may be taken the decomposition of Carbonyl sulfide in water, namely, COS + H20 002 + H2SAccording to the law of mass action this reaction should be second order with the rate dependent on the concentration of both the carbonyl sulfide and the water. Actually however, the rate is found to be first order with respect to the carbonyl sulfide and independent of the water Reactions exhibiting such behaviour are said to be pseudo-molecular.The pseudo-unimoecuar nature of this reaction is explainable by the fact that water is present in such excess that its concentration remains practically constant during the course of the reaction. Under these condition b x = b, and the rate equation becomesOn integration this leads towhich is the equation for a first order reaction. It is evident, however, that the now constant k is not independent of the concentration, as is the case with true first order constants, but may vary with b if the latter is changed appreciably, When such is the case, the true constant k2 can be obtained from k by dividing the latter by b. pseudo-molecular reactions are encountered whenever one or more of the reactants remain constants during the course of an experiment. This is the case with reactions conducted in solvents which are themselves one of the reactants, as in the decomposition of carbonyl sulfide in water, or in the esterification of acetic anhydride in alcohol(CH3C0)20 + 2C2H5OH 2CH3C00C2H5 + H20Again, this is also true of reactions subject to catalysis, in which case the concentration of the catalyst does not change. The decomposition of diacetone alcohol to acetone in aqueous solution is catalysed by hydroxyl ions, with the rate proportional to the concentration of the alcohol and that of the base. Since the concentration of the base does not change within any one experiment, however, the rate equation reduces to one of first order with respect to the alcohol. But the rateconstant k obtained for various concentrations of base are not identical, as may be seen from table. To obtain from these the true second order velocity constant, the ks must be divided by the hydroxyl ion concentration. When this is done excellent k2 values result, as column 3 indicatesTable : Decomposition of diacetone alcohol in water at 25C (Catalyst : NaOH)Q.By what factor does the rate of reaction of diacetone alcohol in water solution change if p0H is increased by 2 units other things remaining same ?

The time taken for 90% of a first order reaction to complete is approximatelya)1•1 times that of half-lifeb)2•2 times that of half-lifec)3•3 times that of half-lifed)4•4 times that of half-lifeCorrect answer is option 'C'. Can you explain this answer?
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The time taken for 90% of a first order reaction to complete is approximatelya)1•1 times that of half-lifeb)2•2 times that of half-lifec)3•3 times that of half-lifed)4•4 times that of half-lifeCorrect answer is option 'C'. 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 The time taken for 90% of a first order reaction to complete is approximatelya)1•1 times that of half-lifeb)2•2 times that of half-lifec)3•3 times that of half-lifed)4•4 times that of half-lifeCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The time taken for 90% of a first order reaction to complete is approximatelya)1•1 times that of half-lifeb)2•2 times that of half-lifec)3•3 times that of half-lifed)4•4 times that of half-lifeCorrect answer is option 'C'. Can you explain this answer?.
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