The rate constant for the first order dehydration of tert-butyl alcohol at 773 K is 1.20×10⁴ s^{- 1}. The rate constant for this process at 873 K is 6.80×10^{- 3} s^{- 1}. The activation energy for this reaction in kJ/mol is:
(R = 8.314 J/mol × K)

Question

Quizplus · Accepted Answer

The activation energy (Ea) can be calculated using the Arrhenius equation: $k = A \exp\left(-\frac{E_a}{RT}\right)$, where $k$ is the rate constant, $A$ is the pre-exponential factor, $E_a$ is the activation energy, $R$ is the gas constant, and $T$ is the temperature in Kelvin. By taking the natural logarithm of the Arrhenius equation for two different temperatures and rate constants, we can solve for $E_a$. The equation simplifies to: $\ln\left(\frac{k_2}{k_1}\right) = \frac{E_a}{R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)$. Substituting the given values ($k_1 = 1.20 \times 10^{-14}$ at $T_1 = 773$ K and $k_2 = 6.80 \times 10^{-13}$ at $T_2 = 873$ K, with $R = 8.314$ J/mol·K), and solving for $E_a$ gives an activation energy in the range of 226 kJ/mol.

The Rate Constant for the First Order Dehydration of Tert-Butyl