The kinetics of this reaction were studied as a function of temperature. (The reaction is first order in each reactant and second order overall.)
C₂H₅Br(aq) + OH^- (aq) → C₂H₅OH(l) + Br^- (aq)
Temperature (°C) k (L,mol •s)
25 8.81⨉10^-5
35 0.000285
45 0.000854
55 0.00239
65 0.00633
a. Determine the activation energy and frequency factor for the reaction.

Verified step by step guidance

1. Identify the Arrhenius equation: $k = A e^{-\frac{E_a}{RT}}$, where $k$ is the rate constant, $A$ is the frequency factor, $E_a$ is the activation energy, $R$ is the gas constant (8.314 J/mol·K), and $T$ is the temperature in Kelvin.
2. Convert the given temperatures from Celsius to Kelvin by adding 273.15 to each temperature value.
3. Take the natural logarithm of both sides of the Arrhenius equation to linearize it: $\ln(k) = \ln(A) - \frac{E_a}{R} \cdot \frac{1}{T}$.
4. Plot $\ln(k)$ versus $\frac{1}{T}$ to obtain a straight line, where the slope of the line is $-\frac{E_a}{R}$ and the y-intercept is $\ln(A)$.
5. Calculate the slope of the line to find $E_a$ using the relation $E_a = -\text{slope} \times R$, and determine $A$ by taking the exponential of the y-intercept: $A = e^{\text{y-intercept}}$.