Arrhenius and Activation Energy

A change in the reaction temperature affects the rate constant k. As the temperature increases, the value of the rate constant increases and the reaction is faster. The Swedish scientist, Arrhenius, derived a relationship that related the rate constant and temperature. The Arrhenius equation has the form k = Ae-E /RT. In this equation, k is the rate constant and A is a term called the frequency factor that accounts for molecular orientation. The symbol e is the natural logarithm base and R is universal gas constant. Finally, T is the Kelvin temperature and Ea is the activation energy, the minimum amount of energy needed to initiate or start a chemical reaction. 

We commonly use the Arrhenius equation to calculate the activation energy of a reaction. One way to do this is to plot the In of k versus 1/T. This gives a straight line whose slope is EJR. Knowing the value of R, we can calculate the value of Ea. 

Another method for determining the activation energy involves using a modification of the Arrhenius equation. If we try to use the Arrhenius equation directly, we have one equation with two unknowns (the frequency factor and the activation energy). The rate constant and the temperature are experimental values, while R is a constant. One way to prevent this difficulty is to perform the experiment twice. We determine experimental values of the rate constant at two different temperatures. We then assume that the frequency factor is the same at these two temperatures. We now have a new equation derived from the Arrhenius equation that allows us to calculate the activation energy. This equation is  

Remember that the k in the denominator, k2, goes with the first temperature, T2. 

The two rate constant values, k2 and k2, are the values determined at two different temperatures, Tx and T2. The temperatures must be in Kelvin. The units on the rate constants will cancel, leaving a unitless ratio. R is 8.314 J/mol-K. The activation energy will have units of joules/mol. 

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