Calculate rate constant of a first order reaction having pre exponential factor 1.6 10¹³ ~s ⁻¹ ( E _ a / 2.303 RT =21 )

Step-by-step solution

The rate constant k for a first-order reaction follows the Arrhenius equation: k = A e^ -E_a / RT . Taking natural logarithms yields k = A - E_a RT , which converts to base 10 as k = A - E_a 2.303 RT . Given A = 1.6 10¹³ s ⁻¹ and E_a 2.303 RT = 21 , substitution gives k = (1.6 10¹³) - 21 . Evaluating the logarithm: (1.6 10¹³) = 1.6 + 10¹³ 0.2041 + 13 = 13.2041 . Thus, k = 13.2041 - 21 = -7.7959 . Taking the antilogarithm: k = 10^ -7.7959 1.6 10⁻⁸ s ⁻¹ , which corresponds to option D. Final answer: D