Determining activation energy graphically

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. Apply market research to generate audience insights. Measure content performance. Develop and improve products. List of Partners vendors. Share Flipboard Email.

By Todd Helmenstine Todd Helmenstine. Todd Helmenstine is a science writer and illustrator who has taught physics and math at the college level.

He holds bachelor's degrees in both physics and mathematics. Learn about our Editorial Process. Featured Video. Cite this Article Format. Helmenstine, Todd. A larger proportion of the collisions that occur between reactants now have enough energy to overcome the activation energy for the reaction.

As a result, the rate of reaction increases. To illustrate how a catalyst can decrease the activation energy for a reaction by providing another pathway for the reaction, let's look at the mechanism for the decomposition of hydrogen peroxide catalyzed by the I - ion. In the presence of this ion, the decomposition of H 2 O 2 doesn't have to occur in a single step.

It can occur in two steps, both of which are easier and therefore faster. Because there is no net change in the concentration of the I - ion as a result of these reactions, the I - ion satisfies the criteria for a catalyst.

Because H 2 O 2 and I - are both involved in the first step in this reaction, and the first step in this reaction is the rate-limiting step, the overall rate of reaction is first-order in both reagents. Determining the Activation Energy of a Reaction. The rate of a reaction depends on the temperature at which it is run.

As the temperature increases, the molecules move faster and therefore collide more frequently. The molecules also carry more kinetic energy. Thus, the proportion of collisions that can overcome the activation energy for the reaction increases with temperature. The only way to explain the relationship between temperature and the rate of a reaction is to assume that the rate constant depends on the temperature at which the reaction is run.

Calculate the a activation energy and b high temperature limiting rate constant for this reaction. All reactions are activated processes. Rate constant is exponentially dependent on the Temperature. We know the rate constant for the reaction at two different temperatures and thus we can calculate the activation energy from the above relation.

First, and always, convert all temperatures to Kelvin, an absolute temperature scale. Then simply solve for E a in units of R. Now that we know E a , the pre-exponential factor, A , which is the largest rate constant that the reaction can possibly have can be evaluated from any measure of the absolute rate constant of the reaction. The infinite temperature rate constant is 4.