Consider the reaction \( aX \rightarrow bY \), for which the rate constant at 30°C is \( 1 \times 10^{-3} \, \text{mol}^{-1} \, \text{L} \, \text{s}^{-1} \). Which of the following statements are true?}
(A) When concentration of \( X \) is increased to four times, the rate of reaction becomes 16 times.
(B) The reaction is a second order reaction.
(C) The half-life period is independent of the concentration of \( X \).
(D) Decomposition of \( \text{N}_2\text{O}_5 \) is an example of the above reaction.
(E) is valid for the reaction
Choose the correct answer from the options given below:
The given reaction is of the form \( aX \rightarrow bY \), and we are provided with the rate constant at 30°C. The relationship between the rate of the reaction and the concentration of \( X \) will depend on the order of the reaction. For a second-order reaction:
\[
\text{Rate} = k [X]^2,
\]
where \( k \) is the rate constant.
- (A) True: For a second-order reaction, if the concentration of \( X \) is increased by a factor of 4, the rate will increase by \( 4^2 = 16 \), as per the rate law.
- (B) True: The reaction is second order, as indicated by the rate law being proportional to \( [X]^2 \).
- (C) False: The half-life period for a second-order reaction is inversely proportional to the concentration of \( X \), so it is dependent on the concentration.
- (D) Not necessarily true: The decomposition of \( \text{N}_2\text{O}_5 \) could be an example of a second-order reaction, but more information is needed.
- (E) True: The equation \( \ln \left( \frac{[R_0]}{[R]} \right) \) is valid for a first-order reaction, not second-order.
Final Answer: A and B Only
