Question

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.

Answer 1

Answer:

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