Given below are two statements: R=8.314 J K^ -1 mol^ -1 and 1 cal =4.2 J Statement I: When E_a=12.6 kcal/mol, the room temperature rate constant is doubled by a 10\,^ increase in temperature (298 K to 308 K) Statement II: For a first order reactions A B, Here [A]_o is the initial concentration of A and t_ 1/2 is half life of reaction. In the light of the above statements, choose the correct answer from the options given below:
C. Statement I is true but Statement II is false
For Statement I: According to the Arrhenius equation: ( k_2 k_1 ) = E_a 2.303 R ( T_2 - T_1 T_1 T_2 ) Given that the rate constant doubles, k_2 = 2k_1. The temperatures are T_1 = 298 K and T_2 = 308 K. The gas constant R = 8.314 J K^ -1 mol^ -1 = 8.314 4.2 cal K^ -1 mol^ -1 1.98 cal K^ -1 mol^ -1 . Substituting the values: (2) = E_a 2.303 1.98 ( 308 - 298 298 308 ) 0.301 = E_a 4.56 ( 10 91784 ) E_a = 0.301 4.56 91784 10 12598 cal/mol 12.6 kcal/mol. Thus, Statement I is true. For Statement II: For a first order reaction, the half-life is given by: t_ 1/2 = 0.693 k This indicates that the half-life of a first order reaction is independent of the initial concentration [A]_o. The graph of t_ 1/2 versus [A]_o should be a horizontal line parallel to the concentration axis. The given graph shows t_ 1/2 directly proportional to [A]_o, which corresponds to a zero order reaction (t_ 1/2 = [A]_o 2k ). Thus, Statement II is false. Therefore, Statement I is true but Statement II is false. Answer: Statement I is true but Statement II is false
Related: Chemistry — Chemical Kinetics · All PYQ Banks