Q8 / 155 · WBJEE 2019 · Chemistry

Consider the following two first order reactions occurring at 298 K with same initial concentration of $A$ :(1) $A \rightarrow B ;$ rate constant, $k=0.693 \mathrm{min}^{-1}$ (2) $A \rightarrow C$; half-life, $l_{1 / 2}=0.693$ min Choose the correct option.

  • A
    Reaction (1) is faster than reaction (2).
  • Correct answer
    B
    Reaction (1) is slower than reaction (2).
  • C
    Both reactions proceed at the same rate.
  • D
    Since two different products are formed, rates cannot be compared.

Solution

Given, for two first order reactions. $$ A \rightarrow B k=0.693 \mathrm{min}^{-1}...(1) $$ and $$ A \rightarrow C, t_{1 / 2}=0.693 \mathrm{min}...(2) $$ For first order reaction $$ t_{1 / 2}=\frac{0.693}{k} $$ Thus, for the reaction $A \rightarrow B$ $$ t_{1 / 2}=\frac{0.693}{k}=\frac{0.693}{0.693}=1.0 \mathrm{min} $$ Also, for first order reaction, lower the $t_{1 / 2}$ value, faster is the reaction. $$ t_{1 / 2} \propto \frac{1}{k} $$ and $k$ for $A \rightarrow C$ is $\frac{0.693}{0.693}=1 \mathrm{min}^{-1}$ Thus, reaction (2) is faster than reaction (1) or reaction (1) is slower than reaction (2) Hence, option (b) is the correct answer.

Hence, the correct answer is option: 'B'.

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