Question

The Activation energy of a chemical reaction can be determined by

• A. evaluating rate constant at standard temperature
• B. evaluating velocities of reaction at two different temperatures
• C. evaluating rate constants at two different temperatures
• D. changing concentration of reactants

Answer 1

The Correct Option is C

To determine the activation energy of a chemical reaction, we often utilize the Arrhenius equation. The Arrhenius equation is given by:

k = A e^{-E_a/(RT)}

where:

• k is the rate constant,
• A is the pre-exponential factor (frequency factor),
• E_a is the activation energy,
• R is the universal gas constant, and
• T is the temperature in Kelvin.

The equation can be rearranged to a linear form as follows:

\ln(k) = \ln(A) - \frac{E_a}{R}\left(\frac{1}{T}\right)

This is a straight-line equation of the form y = mx + c, where y = \ln(k), m = -\frac{E_a}{R}, and x = \frac{1}{T}. This means that by plotting \ln(k) against \frac{1}{T}, the slope of the line will be -\frac{E_a}{R}.

Therefore, if you calculate the rate constants k_1 and k_2 at two different temperatures T_1 and T_2, respectively, you can use the following form to determine the activation energy:

\ln\left(\frac{k_2}{k_1}\right) = \frac{E_a}{R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)

Solving this equation for E_a gives:

E_a = R \cdot \ln\left(\frac{k_2}{k_1}\right) \cdot \left(\frac{1}{T_1} - \frac{1}{T_2}\right)^{-1}

Thus, the correct answer is to determine the activation energy by evaluating rate constants at two different temperatures.