Chapter 12 Chemical Kinetics

Chapter 12 Chemical Kinetics

12.1 – Reaction rates • Thermodynamics answers the question: “Will this reaction proceed?” • Kinetics answers the question: “How quickly/slowly will the reaction proceed?”

12.1 – Reaction rates • The rate of a reaction is the rate at which reactants are consumed, or products are formed. • The rate is measured by considering the change in concentration of reactants/products over time. It is always positive.

12.1 – Reaction rates • For the reaction, • In most cases, the rate of the reaction decreases with time (because reactants are being used up).

12.1 – Reaction rates • Recall from math/calculus: rate is related to the slope of the tangent on a graph • A small slope indicates a low rate of reaction • A steep slope indicates a high rate of reaction

12.1 – Reaction rates

12.1 – Reaction rates • Techniques for measuring rates: • Titration • Increase/decrease in pressure • Light absorption • Conductivity • Clock techniques

12.2 – Rate laws • If only life were so easy! • Because what happens when you have a reversible reaction? Then it’s not so clear… • The rate depends on the difference in rates of the forward and reverse reactions

12.2 – Rate laws • A rate law that expresses how the rate depends on concentration is known as a differential rate law, or simply a rate law. (In 12.4, we will look at integrated rate laws)

12.2 – Rate laws For the reaction: A + B  C + D The differential rate law is calculated by: - k is a constant, that depends solely on temp. - m and n are integers that tell you how the rate changes when [A] and [B] change

12.2 – Rate laws • The value of m and n must be determined experimentally. • We say the reaction is “mth order with respect to A” and “nth order with respect to B” • The overall order of the reaction is given by m + n.

12.2 – Rate laws • Example, for the reaction… • Experiments show that the rate law is… • So we say that the reaction is: • First order, with respect to H2 • Third order, with respect to NO • Fourth order, overall

12.3 – Determining the form of the rate law • The method of initial rates can be used to determine m, n, and k experimentally: • The initial rate is the rate of the reaction just after t = 0.

12.3 – Determining the form of the rate law • Example 1, for the reaction 2ICl + H2 I2 + 2HCl, the following data are collected:

12.3 – Determining the form of the rate law • Example 2, for the reaction: (CH3)3Br + OH- (CH3)3COH + Br-, the following data are collected:

12.3 – Determining the form of the rate law • Note: • If a reaction is zero order with respect to A, it means A is either: • A catalyst (chapter 12.7) • Does

12.3 – Determining the form of the rate law • Note: • The units of [A], [B], etc… are always moles/liter (M) • The units of rate are always M/time • Therefore, the units of k are variable • Example, for a 4th order reaction,

12.4 – Integrated rate laws • First this section, we will consider the reaction: • We said earlier that the rate can be expressed as • We will consider the case where n = 1 (first order), 2 (second order), and 0 (zero order)

12.4 – Integrated rate laws • First order reactions: • Example, the decomposition of hydrogen peroxide is a first order reaction: • We saw earlier that if the concentration of H2O2 were doubled, the rate of production of H2O and O2 would double.

12.4 – Integrated rate laws • First order reactions: • Graphically,

12.4 – Integrated rate laws • First order reactions: • Deriving equations Differential Rate Law Integrated Rate Law

12.4 – Integrated rate laws • First order reactions: • Which can be linearized to create the following graph: Whose x-value is t, y-value is ln[A], slope is -k, and y-intercept is ln[A]0

12.4 – Integrated rate laws • First order reactions: • Example, a fellow researcher is studying the decomposition of N2O5at constant temperature. They approach you to confirm their findings that the reaction is indeed first order. They also want you to find the rate constant, k (include the units). They collected the following data:

12.4 – Integrated rate laws • The same can be repeated for 2nd and 0th order reactions to obtain these results: • Chemical kinetics handout

12.4 – Integrated rate laws • First order reactions: • Half-life (t1/2) equation • Half-life is the time required for a reactant to reach half of its original concentration • Note that half life of a first order reaction does not depend on [A]

12.4 – Integrated rate laws • First order reactions: • Half-life (t1/2) graph • Notice that half life does not depend on [A] in the equation or the graph

12.4 – Integrated Rate Laws • Zero order reactions • Half-life:

12.4 – Integrated Rate Laws • Second order reactions • Half-life:

12.4 – Integrated Rate Laws • Altogether now,

12.4 – Integrated rate laws • Pseudo-first order reactions • Until now, we’ve only considered simple decomposition (or dimerization) reactions: A  B + C or 2A  B

12.4 – Integrated rate laws • Pseudo-first order reactions • For the reaction, A + B  P • If [A] >> [B], then [A] will not measurably change during the reaction. So the rate can be written as,

12.4 – Integrated rate laws • Pseudo-first order reactions • Equivalently, the integrated rate law is given by:

12.4 – Integrated rate laws • Example,

12.5 – Reaction mechanisms • One of the biggest reasons chemists study kinetics is to gain a better understanding of reaction mechanisms. • A balanced chemical equation does not tell us how the reactants become products. • A reaction mechanism is a series of intermediate steps, called elementary steps, reactions, processes.

12.5 – Reaction mechanisms • Elementary steps • A reaction whose rate law can be written from its molecularity– the number of species that must collide to produce the reaction indicated by that step. Can be unimolecular, bimolecular, termolecular, etc…

12.5 – Reaction mechanisms • Intermediate • A species that is created in an early elementary step, and used up in a later one • It is never seen in the final product • Example, NO3 is an intermediate in the reaction below • The overall reaction is

12.5 – Reaction mechanisms • Rate-determining step • A reaction is only as fast as its slowest elementary step, called the rate-determining step. • Experiments show that the rate of the reaction is:

12.5 – Reaction mechanisms (two requirements: must fit balanced chemical equation and must fit experimental rate law)

12.6 – A model for chemical kinetics • Collision model: • Says that molecules must collide in order to react • Activation energy: • The other half of the story, explained by Arrhenius. • Minimum energy required to have a reaction take place (Ea)

12.6 – A model for chemical kinetics • Reaction coordinate (energy level) diagrams:

Exothermic Reaction transition state Ea Energy reactants ΔE products Reaction Coordinate

Endothermic Reaction transition state Ea Energy products ΔE reactants Reaction Coordinate

Multi-step Reactions transition states Energy intermediate products reactants Note: Here, first reaction is slow (RDS) Reaction Coordinate

12.6 – A model for chemical kinetics • Two methods for finding activation energy • 1. Graphing the Arrhenius equation: • A is called the frequency factor of this equation. It takes into account the collision frequency and the fraction of collisions with the correct orientation. • Plot x (1/T) vs y (ln k) and the slope will be given by –(Ea/R)

12.6 – A model for chemical kinetics • Two methods for finding activation energy • 1. Graphing the Arrhenius equation: • Example,

Chapter 12 Chemical Kinetics