In , a Swedish scientist named Svante Arrhenius proposed an equation that relates these concepts with the rate constant:. The Arrhenius equation allows us to calculate activation energies if the rate constant is known, or vice versa. As well, it mathematically expresses the relationships we established earlier: as activation energy term E a increases, the rate constant k decreases and therefore the rate of reaction decreases.
We can graphically determine the activation energy by manipulating the Arrhenius equation to put it into the form of a straight line.
Taking the natural logarithm of both sides gives us:. We can obtain the activation energy by plotting ln k versus , knowing that the slope will be equal to. First determine the values of ln k and , and plot them in a graph:. The activation energy can also be calculated algebraically if k is known at two different temperatures:. Determine the value of E a given the following values of k at the temperatures indicated:.
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