The rate constant of a reaction is 7.8 * 10-3 s-1 at 25°C, and the activation energy is 33.6 kJ/mol. What is k at 75°C? Enter your answer in scientific notation.

k_2 = 7.815 * 10^-3 s^-1

Explanation:

Given:

- rate constant of reaction k_1 = 7.8 * 10^-3 s^-1 @ T_1 = 25 C

- rate constant of reaction k_2 = ? @ T_2 = 75 C

- The activation energy E_a = 33.6 KJ/mol

- Gas constant R = 8.314472 KJ / mol. K

Find:

- rate of reaction k_2 @ T_2 = 75 C

Solution:

- we will use a combined form of Arrhenius equations that relates rate constants k as function of E_a and temperatures as follows:

k_2 = k_1 * e ^ [ (E_a / R) * (1 / T_1 - 1 / T_2)

- Evaluate k_2 = 7.8 * 10^-3 * e^[ (33.6 / 8.314472) * (1/298 - 1/348)

- Hence, k_2 = 7.815 * 10^-3 s^-1