How can the activation energy of a reaction be experimentally determined?

The activation energy of a reaction can be experimentally determined using the Arrhenius equation, which is expressed as k = A * e^(-Ea/RT), where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the universal gas constant, and T is the temperature in Kelvin.

By rearranging this equation, you can take the natural logarithm of both sides, resulting in ln(k) = ln(A) - (Ea/R)(1/T). This equation shows that when you plot ln(k) on the y-axis versus 1/T on the x-axis, you will obtain a straight line, where the slope of this line is equal to -Ea/R. Therefore, the slope can be used to determine the activation energy by multiplying the slope by -R.

This method is powerful because it allows for the determination of activation energy from the rate constants of the reaction measured at different temperatures, making it a reliable and indirect approach to assess how temperature influences reaction rates.