Chemical Kinetics How quickly does that chemical reaction occur?

Goals  Determine factors affecting reaction rates.  Experimentally measure rates of reaction.  Determine how to mathematically describe and predict rates of reaction.  Be able to use data to propose mechanisms for chemical reactions.  Understand how catalysts can change the rate of chemical reactions

Chemical Reaction Rates  Chemical reactions occur at different rates.  Ex. Oxidation of steel wool   How are the rates of chemical reactions measured?

Factors Affecting the Rates of Reaction  The physical state of the reactants  The concentration of the reactants  The temperature at which the reaction occurs  The presence of a catalyst

Reaction Rates  Rate = change in concentration / change in time  What unit is used?

Calculating an Average Reaction Rate  Imagine a hypothetical reaction in which A  B Calculate the average rate at which A disappears over the time interval from 20 sec to 40 sec. Time (sec)[A] (M)[B] (M)

Rates change over time  Look at the following reaction: C 4 H 9 Cl (aq) + H 2 O (l)  C 4 H 9 OH (aq) + HCl (aq)  What happens to the rate of the chemical reaction over time?  Why?

Instantaneous Rates of Chemical Reaction  To find the instantaneous rate of a chemical reaction at a particular time interval, find the slope of the tangent line at the point of interest.  Calculus is often used to do this, You will sometimes see this infomation written using calculus notation.

Finding instantaneous rate graphically  Determine the instantaneous rate of reaction for butyl chloride at t = 0 sec.

Instantaneous Reaction Rates  In chemical kinetics we will always assume rate to mean instantaneous reaction rate.

Stoichiometric Relationships in Kinetics  Imagine the following reaction C 4 H 9 Cl (aq) + H 2 O (l)  C 4 H 9 OH (aq) + HCl (aq)  How does the rate of decrease of butyl chloride (C 4 H 9 Cl) compare to the rate of increase of butyl alcohol (C 4 H 9 OH)?

Stoichiometric Relationships in Kinetics  Imagine the following reaction 2 HI (g)  H 2(g) + I 2(g)  How is the rate of formation of iodine related to the rate of HI decrease

General Stoichiometric Relationships  For the general reaction: aA + bB  cC + dD

Sample Problem  The decomposition reaction of N 2 O 5 is represented in the following equation. 2 N 2 O 5 (g)  4 NO 2 (g) + O 2 (g) If the rate of disappearance of N 2 O 5 = 4.2x10 -7 M/sec, what is the rate of appearance of each of the products?

Rate Laws Mathematical Expressions to Predict Reaction Rates

Rate of Reaction is Dependent on Concentration  Examine the reaction between nitrogen monoxide and hydrogen 2 NO (g) + 2 H 2 (g)  N 2 (g) + 2 H 2 O (g) The initial rates of reaction under varying concentrations: Exp. #[NO] (M)[H 2 ] (M)Initial Rate (M/sec) x x x10 -3

Determining rate law  What happens to the rate when [NO] doubles?  What happens to the rate when [H 2 ] doubles?

Using the information give, determine k Exp. #[NO] (M)[H 2 ] (M)Initial Rate (M/sec) x x x10 -3

Using the information we have calculated so far …  Determine the initial rate of reaction when [NO] = M and [H 2 ] = M.

A note about rate laws  You cannot determine a rate law by looking at an equation.  You must use experimental data to determine a rate law.  The most common exponents are 1 and 2. It also possible to have exponents of 0, ½, and 3.  We will discuss the physical reason for exponents later in the unit.

Rate Laws and Reaction Order  First order reactions: Reactions whose rate depends on the concentration of only one reactant raised to the first power.  Imagine the reaction A  B where the rate of the reaction is dependent on [A] so that The rate law in this form is called the differential rate law.

Integrated rate law  Integrating the rate law gives us:  This can be manipulated to fit the form of y = mx + b  Or expressed as:

1 st Order Rate Law Practice Problem  The decomposition of an insecticide in water follows first order reaction kinetics with a k = 1.45/yr at 12 o C. A quantity of insecticide washes into the lake so that the [insecticide] in the lake = 5.00x10 -7 g/cm 3. Assume that the average temp of the lake is 12 o C.  A. What is the [insecticide] after one year?  B. How long will it take for [insecticide] to decrease to 3.0x10 -7 g/cm 3 ?

Second order reactions  Reactions in which two reactants react with and each reactant reacts has an exponent of one in the rate law. OR  Reactions with one reactant reacts and has an exponent of 2 in the rate law.

Second Order Reactions  Consider the reaction: A  B Where the reaction order is 2 so that the differential rate law is:

Integrated Rate Law: 2 nd order reaction  Integration of the previous equation yields  Notice the y = mx + b format of the resulting equation.

Sample Problem  In the following reaction NO 2 (g)  NO (g) + ½ O 2 (g) the decomposition of NO 2 is second order with k = 0.543/M sec. If the initial [NO 2 ] = M, what is the remaining concentration after hour?

Using Kinetic Data to Determine Reaction Order  Cyclopentadiene (C 5 H 6 ) reacts with itself to form dicyclopentadiene (C 10 H 12 ). A M solution of C 5 H 6 was monitored as a function of time as the reaction proceeded and the following data was collected.  From this data determine the order of the reaction. Time (s)[C 5 H 6 ] (M)

How to solve this kind of problem? Examine the integrated rate law equations 1 st order 2 nd order If it is first order, what will a graph of ln [C 5 H 6 ] v. time look like? If it is second order, what will a graph of 1/[C 5 H 6 ] v. time look like?

Determine the value of the rate constant (k) from this data.  For the slope of the line is equal to k

What happens in a chemical reaction?  Molecules involved must collide with one another.  For the reaction to occur, the molecules must  Collide at the with the correct orientation  Collide with sufficient energy. d

Remember the Reaction Profile

Effects of temperature  Increasing temperature increases the energy at which collisions occur.  This means that there will be a greater chance that molecules will collide with sufficient activation energy.

Relating E a to temperature  The fraction of molecules with sufficient energy to react is given by the equation  Note: If all other factors are equal, the primary determinant of reaction rate is activation energy.

Arrhenius Equation  Arrhenius noted this relationship and noted the effect of collision frequency.  Modified equation to find the rate constant (k)  A is the frequency factor and is nearly constant as temperature varries.

Arrhenius Equation in Point-Slope format  With this equation, a graph of ln k vs. 1/T will give a line with slope = -E a /R. From this E a can be easily determined.

Sample Problem  The following values of k were determined at different temperatures for a chemical reaction.  Find the activation energy. Temperature (OC)K (s -1 ) x x x x10 -3

Solving  Arrange so that you can graph. T (K)1/T (K -1 )ln k x x x x

 Slope is equal to –Ea/R.  For R, use J/mol K  Find Ea Ea = -slope R = -(-19105K)(8.314J/mol K) = 1.6 kJ/mol

Reaction Mechanisms  See notes and handouts from class.