Chemical Kinetics Question 287

Question: Consider the two hypothetical reactions given below:

I $ aA\to $ Products, $ k=x,mo{l^{-1}}Lmi{n^{-1}} $

II $ bB\to $ Products, $ k=y,mi{n^{-1}} $

The half-lives of both the reactions are the same, equal to 1 hr when molar concentration of the reactant is 1.0 M in each case. If these reactions are started at the same time taking 1M of the reactant in each case, the ratio [A]/[B] after 3 hr will be:

Options:

A) 0.5

B) 4

C) 1

D) 2

Show Answer

Answer:

Correct Answer: D

Solution:

[d] Units of k indicate that reaction I is of second order and reaction II is first order. For I reaction, $ {t_{1/2}}\propto 1/a $ first $ {t_{1/2}}=1,hr, $ second $ {t_{1/2}}=2hr $

$ [A]=1M\xrightarrow{1,hr}0.5M\xrightarrow{2,hr}0.25M $

$ [B]=1M\xrightarrow{1,hr}0.5M\xrightarrow{1,hr}0.25M\xrightarrow{1hr}0.125M $

$ \frac{[ A ]}{[ B ]}=\frac{0.25M}{0.125M}=2 $



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