Question

For a reaction $X\to Y$, the rate law is $Rate=k[A{]}^{\frac{1}{2}}$. Which of the following statements are correct?

• A. Half life of the reaction is inversely proportional to the initial concentration
• B. Half life of the reaction is directly proportional to the square root of the initial concentration
• C. The rate constant of the reaction is constant at a particular temperature for this reaction
• D. $\underset{k_t}{\overset{k_{t+10}}{\to }}=2\sim 3$ and this is defined as the temperature coefficient of the reaction

Answer 1

Answer: (B), (C), (D)

The correct options are
B The rate constant of the reaction is constant at a particular temperature for this reaction
C $\underset{k_t}{\overset{k_{t+10}}{\to }}=2\sim 3$ and this is defined as the temperature coefficient of the reaction
D Half life of the reaction is directly proportional to the square root of the initial concentration

(A) For $n^{th}$ order reaction, $t_{\frac{1}{2}}\alpha a^{1-n}$
Half life of the reaction is inversely proportional to the initial concentration raised to the power $0.5$.
Hence, option A is incorrect.
(B) Half life of the reaction is directly proportional to the square root of the initial concentration.
Hence, the option B is correct.
(C) The rate constant of the reaction is constant at a particular temperature for this reaction. As the temperature increases, the rate constant increases.
Hence, the option C is correct.
(D) $\underset{k_t}{\overset{k_{t+10}}{\to }}=2\sim 3$ and this is defined as the temperature coefficient of the reaction. It is the ratio of the rate constants at two different temperatures which differ by $10K$.
Hence, the option D is correct.