How Do You Calculate the Pre-Exponential Factor?

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The pre-exponential factor, or frequency factor, is an aspect of the Arrhenius equation and is related to collision theory. The value for this factor varies depending on the chemical reaction and is determined through experimental observation. However, if values of the rate constant, k, are known at different temperatures, an Arrhenius plot is used to determine the pre-exponential factor, A.

  1. Rearrange the Arrhenius equation

    Rearrange the Arrhenius equation, k = Ae^(-E_a / RT), to resemble a linear equation, ln(k) = ln(A) - (E_a / R) * (1 / T). E_a is the activation energy, T is the temperature in Kelvin, and R is the gas constant. The values of ln(k) represent the y coordinates, the values of (1 / T) represent the x coordinates, the slope is -(E_a / R), and the y-intercept is ln(A).

  2. Plot the x and y coordinates

    Plot the values of ln(k) and (1 / T) on a graph, and draw a straight line through the points.

  3. Determine the y-intercept, and solve for A

    The y-intercept is determined by extending the line through the y axis and finding where the line crosses over the axis. This coordinate gives the value of ln(A). Raise this value by e to get the value of A, e^(ln(A)) = A.