Consider the reaction aX bY, for which the rate constant at 30°C is 1 10^ -3 mol^ -1 L 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 peri

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Consider the reaction aX bY, for which the rate constant at 30°C is 1 10^ -3 mol^ -1 L 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 N_2 O_5 is an example of the above reaction. E. [R_o] [R] vs time is valid for the above reaction. Choose the correct answer from the options given below:

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Correct answer: A. A and B Only

The unit of the rate constant k is mol^ -1 L s^ -1 . The general unit of the rate constant for an n-th order reaction is (mol L^ -1 )^ 1-n s^ -1 . Equating the powers of the concentration units, we get 1-n = -1 n = 2. Thus, the reaction is a second-order reaction. Statement B is correct. For a second-order reaction, Rate = k[X]^2. When the concentration of X is increased to 4 times, the new rate is k(4[X])^2 = 16k[X]^2, which is 16 times the original rate. Statement A is correct. The half-life of a second-order reaction is t_ 1/2 = 1 k[X]_0 , which depends inversely on the initial concentration. Statement C is incorrect. The decomposition of N_2O_5 is a well-known first-order reaction. Statement D is incorrect. The equation [R_o] [R] = kt represents the integrated rate law for a first-order reaction, not a second-order reaction. Statement E is incorrect. Therefore, only statements A and B are correct. Answer: A and B Only

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