Topic: 4. Kinetics
Concept: G. Temperature and reaction rate: Arrhenius Equation
Concept Overview:
As mentioned earlier, temperature does affect how quickly a reaction occurs. In chemical reactions, some bonds are broken, and some new bonds are formed. Bond formation is a favorable process, releasing energy, while bond breaking requires an investment of energy. The easiest energy to apply is usually thermal energy--heat a reaction up, and it will go faster. How much does temperature affect the reaction rate? The credit for this answer goes to Svante Arrhenius, a Swedish chemist. Here is the relationship he discovered, named, of course, the Arrhenius Equation:
Reaction rate constant = k = A e-Ea/RT
Recall from Collision Theory that in order for a reaction to occur, two molecules must collide in the proper orientation and possess a minimum amount of energy to react. This equation accounts for all of the requirements of Collision Theory. The factor A represents the frequency of collisions between two molecules in the proper orientation for reaction to occur. The value of A is determined by experiment and will be different for every reaction.
The value of the exponential term (e-Ea/RT) describes the fraction of molecules with the minimum energy required to react. R is the gas constant, 8.314 J/mol-K, T is the temperature in Kelvin, and Ea is the Activation Energy. Warning! Activation Energy is often given in the units of kJ/mol, while R is in J/mol-K. Don't forget that factor of 1000!
The Arrhenius equation can be used to determine the activation energy for a reaction based on how the rate constant changes with temperature. You will do this for the Bromine Clock experiment in the Chem21 Lab course. Alternatively, you can calculate the rate constant for a reaction at a given temperature if you know the frequency factor, A, and the activation energy.
If you take the log of both sides of the Arrhenius equation, you obtain an equation in the form of a straight line.
ln k = ln a + (-Ea/R)(1/T)
Once you obtain your rate constant over several temperatures, you can plot the natural log of that rate constant (y-axis) versus the reciprocal of your temperature (in Kelvin, of course!) on the x-axis. A straight line will be formed, with the slope being -Ea/R. If you want to know the rate constant at a particular temperature, calculate the reciprocal of your temperature, and use your line to determine the natural log of k, take the antilog (ex), and you've found your rate constant.
