increase the temperature by 10 °C. To explain the increase of reaction rates with
temperature, we depend on the collision theory of molecules. Collision theory.
12.10 Reaction Rates and Temperature We see in every day circumstances that increasing the temperature increases a chemical reactions rate, whether it s in the frying of an egg, the lighting on fire of a piece of paper, or the setting of an epoxy glue. In general, reaction rates approximately double if you increase the temperature by 10 °C. To explain the increase of reaction rates with temperature, we depend on the collision theory of molecules.
Collision theory The collision theory for molecules is much the same. Let s consider the reaction A + BC
AB + C
If this reaction occurs in a single step, the electron density around the atoms A, B, and C must change as we go from the reactants to products. At some point in time, the B-C bond starts to break, while the A-B bond starts to forms. At this point, all three nuclei and weakly linked together.
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Generally, the molecules A and BC will repel each other as the electrons in each molecule get close to each other. To overcome this repulsion, we must put energy into the molecules to force them to come close enough together so they might be able to react. This energy input is exactly the same thing as what you need to do to get the north poles of two magnets close together, for example. The energy required to overcome the repulsion of the electrons is the kinetic energy of the molecules. This kinetic energy is converted to potential energy as the molecules are forced together against the repulsive force. Consider what happens if you let go of the two magnets you have forced together. They will come apart. The potential energy that was stored is converted back to kinetic energy as the magnets move apart.
At the point where we have the three atoms weakly linked with each other, then, the potential energy is higher than that of the reactants. We call this point where all the atoms are associated in a single structure the transition state or activated complex. This name comes from the fact that this structure comes about as we transition from reactants to products.
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We see an energy hill, where the reactants occur on one side, the products on the other, while the transition state is the top of the hill. Two useful pieces of energy data are shown in the Figure: 1) the energy difference between the reactants side and the transition state, is called Activation Energy 2) the energy difference between the reactants side, and the product side. is the change in energy for the reaction . ( E) The sign can be + or -.
Activation energy The activation energy (Ea) of a reaction is the difference between the energy of the reactants, and the energy of the transition state. This energy will always be positive. The energy required to go from the reactants to the transition state must come from the kinetic energy of the molecules. If the molecules combined have a kinetic energy less than the activation energy, then they cannot reach the transition state and will bounce apart as they fall back down the hill . If the kinetic energy is greater than or equal to the activation energy, then the molecules can reach the transition state, and the reaction between the two molecules might occur.
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From Chapter 8 the kinetic energy of molecule is thermal energy. We measure this thermal energy through temperature, which gives us the average kinetic energy of a molecule. Therefore, if the temperature is higher, the average kinetic energy of a molecule is higher. Therefore, there is a better chance that a collision between molecules has enough energy to overcome the activation energy (Ea).
Collisions Not every collision breaks the activation energy barrier. We can estimate the fraction of collisions (f) that have enough energy to break the activation barrier through the use of :
f = e-Ea/RT where e is approximately 2.718 Ea is the activation energy, T is the temperature in Kelvin, and R is the gas law constant, in units of 8.314 J/(K·mol)
Collisions and energy If we have a reaction at 298 K with an activation energy of 75 kJ/mol, the fraction of collisions (f) with energy greater than the activation energy is:
f = e-Ea/RT f = e(-75000 J/mol)/[8.314 J/(K·mol) (298 K]) f = 7 x 10-14 Only seven collisions in 100 trillion are energetic enough to react! If we repeat the calculation at 308 K (a ten degree increase in temperature)
f = e-Ea/RT f = e(-75000 J/mol)/[8.314 J/(K·mol) (308 K]) f = 1.9 x 10-13 Now about 19 collisions in 100 trillion have enough energy to react. This result is about 2 ½ times larger than for 298 K. Recall that we said that an increase of 10 degrees usually leads to an approximate doubling of rate.
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General reaction A + BC
AB + C
For this reaction to occur, atom A must collide with the B side of BC to form the transition state. If atom A hits the C side, we get a different transition state that might not lead to the same products or might have an even higher activation energy. The activation energy still won t cause the reaction we want because the orientation isn t right.
The number of collisions increases with increasing concentrations of reactants. Therefore, for our general reaction, we can reasonably state that Collision rate = Z [A] [BC] where Z is a constant related to the collision frequency Now the reaction rate would be the same as this collision rate if every collision led to a reaction between the molecules. We have seen that this isn t true. First, only fraction f of reactions have a collision energy greater than or equal to the activation energy. Then, of those reaction, only p collisions have the correct orientation to proceed through the transition state to the products. So Reaction rate = p x f x Collision rate = pfZ [A] [BC] Since for this elementary reaction reaction rate = k [A] [BC] then (rate constant) k = pfZ = pZ e-Ea/RT = A e-Ea/RT
(where A = pZ)
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Arrhenius Equation One form of the rate constant expression is called the Arrhenius Equation . The combined pZ leads to A, which is called the frequency factor, which is named that way because of how often collisions that have the right orientation for reaction occur (their frequency).
k = A e-Ea/RT
ARRHENIUS EQUATION
Key Concept Problem 12.15 The potential energy profile for the one step reaction AB + CD AC +BD is shown (energies in kJ/mol).
A) What is the value of the activation energy for this reaction? B) Is the reaction endothermic or exothermic? What is the energy of the reaction, E ?
Ans: done in class
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