Kinetics

SWBAT Determine how to set up a rate law equation. Determine the order of reaction for each reactant and the overall reaction. Practice solving rate equations.

Reaction Rate Reaction rate is the rate at which reactants disappear and products appear in a chemical reaction. This can be expressed as the change in concentration of reactants and products in a certain amount of time. The rate of reaction cannot be calculated from the balanced chemical equation, it must be found experimentally by measuring the concentration of a reactant and product at various times throughout the reaction.

Reaction Rate t1 is the initial time t2 is the final time Conc of reactant at t1 - conc of reactant at t2 Average rate of reaction = t2 - t1 t1 is the initial time t2 is the final time t1 is subtracted from t2 to yield a positive value The value of the rate at a particular time is the instantaneous rate.

Reaction Rate Since the reactants disappear during a chemical reaction, the rate calculated by measuring a reactant will have a negative sign. (You will be calculating the rate of disappearance) If a product is measured, the calculated rate will have a positive sign. (You will be calculating the rate of appearance) Reaction rates diminish as the concentrations of reactants diminish. After the rate has been measured based on one component of the reaction, the rates of change of the other components may be calculated by a stoichiometric conversion.

Reaction Rates and Stoichiometry If the number of moles of reactants disappearing is not equal to the number of moles of product appearing, use the following equation: aA + bB → cC + dD Rate = – 1 ∆[A] = – 1 ∆[B] = 1 ∆[C] = 1 ∆[D] a ∆t b ∆t c ∆t d ∆t Reactants are negative because they are used up Products are positive because they are created

Rate Law The effect of concentration on the rate of reaction is described using a rate law. The rate law is an equation that can be used to calculate the reaction rate for any given concentration of reactants. The rate law can be determined by keeping the concentrations of all but one reactant constant while measuring the reaction rate for the various concentrations of that reactant.

Rate Laws The rate equation can be expressed as follows: Rate = k [ A]m [ B]n [ A] and [ B] are the molar concentrations of reactants A and B in moles/liters. The exponents “m” and “n” are the powers of the concentrations of the reactants. (In all cases, “m” and “n” must be determined experimentally) The exponents “m” and “n” are usually small, whole numbers. (In more complex rate laws they may be negative numbers or rational fractions.) k is the rate constant. This constant has a fixed value for a reaction at a particular temperature. Do Not use the coefficients in the balanced equation when determining the rate law.

Order of Reaction Rate = k [ A ]m [ B ]n “m” and “n” are the reaction orders You can say: the reaction order in reactant 1 is the “m” th order and the reaction order in reactant 2 is the “n” th order. The overall reaction order is “m” + “n” The values of “m and n” are determined experimentally, not by the coefficients of the reactants.

The Dependence of Rate on Concentration See page 516 in B & L Rate = k [NH4+1] [ NO2-1 ] Use the date in table 14.3 (14.2 new book) to determine the reaction order for both reactants and the overall reaction order for the reaction. The next few slides explains what to do.

The Dependence of Rate on Concentration Use the data in table 14.3 (14.2 new book) by changing the concentration of one reactant while holding the concentration of the other constant. The NH4+1 concentration doubles when comparing experiments 1 and 2 (hold NO2-1 constant) and you will see that the rate doubles.

The Dependence of Rate on Concentration Rate difference = (conc difference )m If the rate doubles, place a “2” in for rate If the conc. of NH4+1 doubles, place a “2” in for conc. Now you have, 2 = [2]m , now solve for “m” m = 1, therefore the reaction order for NH4+1 is first order

Or you can think it through this way: Using the basic form of the rate law, determine the reaction order. Ratef = (concf )m Ratei (conci )m

The Dependence of Rate on Concentration NO2-1 concentration doubles when comparing experiments 6 and 8 (hold NH4+1 constant) and you will see that the rate doubles. Using the basic form of the rate law, determine the reaction order. Rate = [reactant]n If the rate doubles, place a “2” in for rate If the conc. of NO-1 doubles, place a “2” in for conc. Now you have, 2 = [ 2 ] n , solve for “n” n = 1, therefore the reaction order for NO-1 is first order The overall reaction order is 1+ 1 = 2 Therefore, the reaction is second order overall **** Keep reminding yourself that you did not use **** **** stoichiometric coefficients during this process. **** **** The rate law must be determined experimentally. ****

First Order Reactions A first order reaction is one whose rate depends on the concentration of a single reactant raised to the first power. A → products Rate = – ∆[A] = k ∆[A] ∆t

First Order Use calculus to create an equation that relates the concentration at the start of the reaction [A]0 to the concentration at any other time [A] . ln[A]= - kt + ln[A]0 This equation should look similar to y = mx + b Therefore, for a first order reaction a graph of ln [A] vs time gives a straight line with a slope of –k and a “y” intercept of ln [A]0.

Half Life The half-life of a reaction, t ½ , is the time required for the concentration of a reactant to drop to one half of its initial value. [A] t ½ = ½ [A]0 If this equation is substituted into the equation ln[A]= - kt + ln[A]0 the resulting equation becomes t ½ = 0.693 k This equation is for a first order reaction.

Half Life The half life of a second order reaction is t ½ = __1__ k [A]0 Unlike the half life of first order reactions, the half life of a second order reaction is dependent on the initial concentration of the reactant.

Second Order Reactions If a reaction is second order in just one reactant the rate law is: rate = k[A]2 Use calculus to create an equation that relates the concentration at the start of the reaction [A]0 to the concentration at any other time [A] . 1 = kt + 1_ [A] [A]0 y = mx + b

Second Order Reactions Therefore, for a second order reaction a graph of 1/ [A] vs t gives a straight line with a slope of k and a “y” intercept of 1 / [A]0.

FACTORS THAT AFFECT REACTION RATES 1. Concentration of reactants 2. Temperature * increasing temperatures increases reaction rates (in most reactions) * decreasing temperatures decreases reaction rates 3. Addition of a catalyst * a catalyst will increase the rate of reaction * a catalyst is a substance that participates in a chemical reaction but does not appear in the balanced equation Surface area * of solid or liquid reactants or catalysts Other experimental factors, as long as they do not affect the concentration, temperature, or catalysts, will have no effect on the rate of a chemical reaction.

Collision Model The Collision Model is based on the Kinetic Molecular Theory. Molecules must collide to react. The greater the number of collisions occurring per second, the greater the reaction rate.

Collision Model - Concentration Increasing the concentration, increases the number of reactant molecules available to collide, thus increasing the probability that collisions will occur which increases the reaction rate.

Collision Model - Temperature Increasing the temperature, increases molecular speeds. As molecules move faster, they collide with more energy and more frequency which increases reaction rates. Not all of these collisions create a reaction. Read on to find out about the minimum energy required for a reaction to occur.

Catalyst A catalyst is a substance that changes the speed of a chemical reaction without undergoing a permanent chemical change itself in the process.

Activation Energy Molecules must have a certain minimum amount of energy in order to react. Upon collision the kinetic energy of the molecules can lead to chemical reactions. Colliding molecules must have a total kinetic energy equal to or greater than some minimum energy value. The minimum energy required to initiate a chemical reaction is called the Activation Energy (Ea ). Ea is different for each reaction.

Making reactions happen Not every collision in which reactants have an energy Ea (or greater) results in reaction. Reactants must collide with sufficient energy to begin to rearrange bonds. Reactants must be oriented in a certain way for the collision to lead to a reaction.

Activation Energy http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch22/rateframe.html Activation Energy is the minimum energy required to initiate a chemical reaction. During the reaction, the arrangement of atoms at the top of the “energy hump” is called the activated complex or transition state. This diagram shows an exothermic reaction. (The reverse reaction would be endothermic.)

Temp and Kinetic Energy Higher Temp, more molecules with higher energy available for the reaction. http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch22/rateframe.html

Activated Complex The fraction of molecules that has an energy equal to or greater than Ea is given by the expression: – Ea /RT f = e R is 8.314 J / mol K T is temp in Kelvins

Arrhenius Equation The Arrhenius Equation is based on three things: 1. the fraction of molecules possessing an energy of Ea or greater 2. the number of collisions occurring per second 3. the fraction of collisions that have the appropriate orientation.

Arrhenius Equation k = A e k is the rate constant – Ea /RT k = A e k is the rate constant Ea is the activation energy R is the gas constant ( 8.314 J/mol K) A is the frequency factor (A is related to the frequency of collisions and the probability that the collisions are favorably oriented for reaction to occur.) (Reaction rates decrease as the energy barrier increases.)

Reaction Order 1 2 Rate Law k k[A] k[A]2 Integrated Rate Law 1 2 Rate Law k k[A] k[A]2 Integrated Rate Law [A]=-kt+[A]0 ln[A]=-kt+ln[A]0 1 - 1 [A] [A]0 =kt Relationship between Concentration and Time [A] 0 -[A] =kt Log10 [A]0 = kt__ [A] 2.30 1 - 1

Equations and Relationships to Remember Reaction Order 1 2 Half-life t ½ = [A]0 2k t ½ = 0.693 k t ½ = _1_ k[A]0 Linear Plot [A] vs t log [A] vs t _1_ vs t [A] Slope -k

Many times a chemical reaction occurs as the result of several steps made up of simple chemical reactions. A series of steps that leads from reactants to products is called a reaction mechanism. Each individual step in a reaction is called an elementary step. Substances that are produced in one step of a reaction but consumed in a later step are called intermediate products. Each elementary step proceeds at its own rate. The rate of the overall reaction is limited by the rate of the slowest elementary step. The slowest elementary step is called the rate-determining step.