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Chemical Kinetics and Nuclear Chemistry question

2019 · 12 Jan · Shift 1 · Q8
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Chemical Kinetics and Nuclear Chemistry question

2019 · 12 Jan · Shift 1 · Q8

JEE MainChemistryChemical Kinetics and Nuclear ChemistryMCQ+4 / −1
Decomposition of X exhibits a rate constant of 0.05 μ\muμ g/year. How many year are required for the decomposition of 5 μ\muμ g of X into 2.5 μ\muμ g?
  1. A
    50
  2. B
    20
  3. C
    25
  4. D
    40
View written solutionFree

Correct answer: A

  1. Identify the order of reaction from units of rate constant

    The given rate constant is k=0.05 μg/yeark = 0.05\ \mu\text{g/year}k=0.05 μg/year

    Since the units of kkk are mass/time, this corresponds to a zero-order reaction.

    For a zero-order decomposition, [X]t=[X]0−kt[X]_t = [X]_0 - kt[X]t​=[X]0​−kt

  2. Substitute the given values

    Initial amount: [X]0=5 μg[X]_0 = 5\ \mu\text{g}[X]0​=5 μg

    Final amount: [X]t=2.5 μg[X]_t = 2.5\ \mu\text{g}[X]t​=2.5 μg

    Rate constant: k=0.05 μg/yeark = 0.05\ \mu\text{g/year}k=0.05 μg/year

    Using [X]t=[X]0−kt[X]_t = [X]_0 - kt[X]t​=[X]0​−kt we get 2.5=5−0.05t2.5 = 5 - 0.05t2.5=5−0.05t

  3. Solve for time

    0.05t=5−2.5=2.50.05t = 5 - 2.5 = 2.50.05t=5−2.5=2.5

    t=2.50.05=50t = \frac{2.5}{0.05} = 50t=0.052.5​=50

  4. Final answer

    t=50 yearst = 50\ \text{years}t=50 years

So, the correct option is A.

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