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

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

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, 8.314 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 Tro: Chemistry: A Molecular Approach, 2/e

Tro: Chemistry: A Molecular Approach, 2/e

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 Tro: Chemistry: A Molecular Approach, 2/e

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 Tro: Chemistry: A Molecular Approach, 2/e

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 Tro: Chemistry: A Molecular Approach, 2/e

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 Tro: Chemistry: A Molecular Approach, 2/e

Tro: Chemistry: A Molecular Approach, 2/e

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) Tro: Chemistry: A Molecular Approach, 2/e

Example 13.7: Determine the activation energy and frequency factor for the reaction O3(g)  O2(g) + O(g) given the following data: Tro: Chemistry: A Molecular Approach, 2/e

Example 13.7: Determine the activation energy and frequency factor for the reaction O3(g)  O2(g) + O(g) given the following data: Tro: Chemistry: A Molecular Approach, 2/e

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 Tro: Chemistry: A Molecular Approach, 2/e

Arrhenius Equation: Two-Point Form If you only have two (T,k) data points, the following forms of the Arrhenius Equation can be used: Tro: Chemistry: A Molecular Approach, 2/e

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: Tro: Chemistry: A Molecular Approach, 2/e

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 Tro: Chemistry: A Molecular Approach, 2/e

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 Tro: Chemistry: A Molecular Approach, 2/e

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 Tro: Chemistry: A Molecular Approach, 2/e

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 Tro: Chemistry: A Molecular Approach, 2/e

Effective Collisions Orientation Effect Tro: Chemistry: A Molecular Approach, 2/e

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 Tro: Chemistry: A Molecular Approach, 2/e

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 Tro: Chemistry: A Molecular Approach, 2/e

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 Tro: Chemistry: A Molecular Approach, 2/e

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 Tro: Chemistry: A Molecular Approach, 2/e

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 Tro: Chemistry: A Molecular Approach, 2/e

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 Tro: Chemistry: A Molecular Approach, 2/e

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 Tro: Chemistry: A Molecular Approach, 2/e

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 Tro: Chemistry: A Molecular Approach, 2/e