1. Chapter 13: Chemical Kinetics
CHE 124: General Chemistry II
Dr. Jerome Williams, Ph.D.
Saint Leo University

2. Overview Effect of Temperature on Rate
Activation Energy & Reaction Progress
Arrhenius Equation

3. The Effect of Temperature on Rate
Changing the temperature changes the rate constant of the rate law
Svante Arrhenius investigated this relationship and showed that:
where T is the temperature in kelvins
R is the gas constant in energy units, J/(mol•K)
A is called the frequency factor, the rate the reactant energy approaches the activation energy
Ea is the activation energy, the extra energy needed to start the molecules reacting
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5. Activation Energy and the Activated Complex
There is an energy barrier to almost all reactions
The activation energy is the amount of energy needed to convert reactants into the activated complex
aka transition state
The activated complex is a chemical species with partially broken and partially formed bonds
always very high in energy because of its partial bonds
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6. Isomerization of Methyl Isonitrile
methyl isonitrile rearranges to acetonitrile
for the reaction to occur, the H3C─N bond must break, and a new H3C─C bond form
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7. Energy Profile for the Isomerization of Methyl Isonitrile
As the reaction begins, the C─N bond weakens enough for the CN group to start to rotate
the activated complex is a chemical species with partial bonds
the frequency is the number of molecules that begin to form the activated complex in a given period of time
the activation energy is the difference in energy between the reactants and the activated complex
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8. The Arrhenius Equation: The Exponential Factor
The exponential factor in the Arrhenius equation is a number between 0 and 1
Tt represents the fraction of reactant molecules with sufficient energy so they can make it over the energy barrier
the higher the energy barrier (larger activation energy), the fewer molecules that have sufficient energy to overcome it
That extra energy comes from converting the kinetic energy of motion to potential energy in the molecule when the molecules collide
increasing the temperature increases the average kinetic energy of the molecules
therefore, increasing the temperature will increase the number of molecules with sufficient energy to overcome the energy barrier
therefore increasing the temperature will increase the reaction rate
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10. Arrhenius Plots
The Arrhenius Equation can be algebraically solved to give the following form:
this equation is in the form y = mx + b
where y = ln(k) and x = (1/T)
a graph of ln(k) vs. (1/T) is a straight line
(−8.314 J/mol∙K)(slope of the line) = Ea, (in Joules)
ey–intercept = A (unit is the same as k)
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11. Example 13.7: Determine the activation energy and frequency factor for the reaction O3(g)  O2(g) + O(g) given the following data:
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12. Example 13.7: Determine the activation energy and frequency factor for the reaction O3(g)  O2(g) + O(g) given the following data:
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13. slope, m = 1.12 x 104 K y–intercept, b = 26.8
Example 13.7: Determine the activation energy and frequency factor for the reaction O3(g)  O2(g) + O(g) given the following data:
slope, m = 1.12 x 104 K
y–intercept, b = 26.8
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14. Arrhenius Equation: Two-Point Form
If you only have two (T,k) data points, the following forms of the Arrhenius Equation can be used:
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15. Example 13.8: The reaction NO2(g) + CO(g)  CO2(g) + NO(g) has a rate constant of 2.57 M−1∙s−1 at 701 K and 567 M−1∙s−1 at 895 K. Find the activation energy in kJ/mol
Given:
Find:
T1 = 701 K, k1 = 2.57 M−1∙s−1, T2 = 895 K, k2 = 567 M−1∙s−1
Ea, kJ/mol
Conceptual Plan:
Relationships: Ea
T1, k1, T2, k2
Solution:
most activation energies are tens to hundreds of kJ/mol – so the answer is reasonable
Check:
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16. Hint: make T1 = 300 K, T2 = 310 K and k2 = 2k1
Practice – It is often said that the rate of a reaction doubles for every 10 °C rise in temperature. Calculate the activation energy for such a reaction.
Hint:
make T1 = 300 K, T2 = 310 K
and k2 = 2k1
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17. Practice – Find the activation energy in kJ/mol for increasing the temperature 10 ºC doubling the rate
Given:
Find:
T1 = 300 K, T1 = 310 K, k2 = 2 k1
Ea, kJ/mol
Conceptual Plan:
Relationships: Ea
T1, k1, T2, k2
Solution:
Check:
most activation energies are tens to hundreds of kJ/mol – so the answer is reasonable
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18. Collision Theory of Kinetics
For most reactions, for a reaction to take place, the reacting molecules must collide with each other
on average about 109 collisions per second
Once molecules collide they may react together or they may not, depending on two factors –
1. whether the collision has enough energy to "break the bonds holding reactant molecules together"; and
2. whether the reacting molecules collide in the proper orientation for new bonds to form
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19. Effective Collisions Kinetic Energy Factor
For a collision to lead to overcoming the energy barrier, the reacting molecules must have sufficient kinetic energy so that when they collide the activated complex can form
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20. Effective Collisions Orientation Effect
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21. Effective Collisions
Collisions in which these two conditions are met (and therefore lead to reaction) are called effective collisions
The higher the frequency of effective collisions, the faster the reaction rate
When two molecules have an effective collision, a temporary, high energy (unstable) chemical species is formed – the activated complex
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22. Collision Theory and the Frequency Factor of the Arrhenius Equation
The Arrhenius Equation includes a term, A, called the Frequency Factor
The Frequency Factor can be broken into two terms that relate to the two factors that determine whether a collision will be effective
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23. Collision Frequency
The collision frequency is the number of collisions that happen per second
The more collisions per second there are, the more collisions can be effective and lead to product formation
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24. Orientation Factor
The orientation factor, p, is a statistical term relating the frequency factor to the collision frequency
For most reactions, p < 1
Generally, the more complex the reactant molecules, the smaller the value of p
For reactions involving atoms colliding, p ≈ 1 because of the spherical nature of the atoms
Some reactions actually can have a p > 1
generally involve electron transfer
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25. Orientation Factor
The proper orientation results when the atoms are aligned in such a way that the old bonds can break and the new bonds can form
The more complex the reactant molecules, the less frequently they will collide with the proper orientation
reactions where symmetry results in multiple orientations leading to reaction have p slightly less than 1
For most reactions, the orientation factor is less than 1
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26. Molecular Interpretation of Factors Affecting Rate – Reactant Nature
Reactions generally occur faster in solution than in pure substances
mixing gives more particle contact
particles separated, allowing more effective collisions per second
forming some solutions breaks bonds that need to be broken
Some materials undergo similar reactions at different rates either because they have a (1) higher initial potential energy and are therefore closer in energy to the activated complex, or (2) because their reaction has a lower activation energy
CH4 + Cl2  CH3Cl + HCl is about 12x faster than CD4 + Cl2  CD3Cl + DCl because the C─H bond is weaker and less stable than the C─D bond
CH4 + X2  CH3X + HX occurs about 100x faster with F2 than with Cl2 because the activation energy for F2 is 5 kJ/mol but for Cl2 is 17 kJ/mol
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27. Molecular Interpretation of Factors Affecting Rate – Temperature
Increasing the temperature raises the average kinetic energy of the reactant molecules
There is a minimum amount of kinetic energy needed for the collision to be converted into enough potential energy to form the activated complex
Increasing the temperature increases the number of molecules with sufficient kinetic energy to overcome the activation energy
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28. Molecular Interpretation of Factors Affecting Rate – Concentration
Reaction rate generally increases as the concentration or partial pressure of reactant molecules increases
except for zero order reactions
More molecules leads to more molecules with sufficient kinetic energy for effective collision
distribution the same, just bigger curve
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