Consider A k _ 1 ~B and C k _ 2 D are two reactions. If the rate constant ( k _ 1 ) of the A B reaction can be expressed by the following equation _ 10 k =14.34- 1.5 10^ 4 ~T / K and activation energy of C D reaction (E a_ 2 ) is 1 5 th of the A B reaction (E a_ 1 ), then the value of (E a_ 2 ) is \

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Consider A k _ 1 ~B and C k _ 2 D are two reactions. If the rate constant ( k _ 1 ) of the A B reaction can be expressed by the following equation _ 10 k =14.34- 1.5 10^ 4 ~T / K and activation energy of C D reaction (E a_ 2 ) is 1 5 th of the A B reaction (E a_ 1 ), then the value of (E a_ 2 ) is \_\_\_\_ kJ mol ^ -1 . (Nearest Integer)

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Correct answer: A. A

From the Arrhenius equation: _ 10 k = _ 10 A - E_a 2.303RT . Comparing with given equation _ 10 k_1 = 14.34 - 1.5 10^4 T , we get: E_ a_1 2.303R = 1.5 10^4 K E_ a_1 = 1.5 10^4 2.303 8.314 = 1.5 10^4 0.01913 = 287 kJ/mol Since E_ a_2 = 1 5 E_ a_1 : E_ a_2 = 287 5 = 57.4 57 kJ/mol

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