Chemical Kinetics The study of rates of chemical reactions, the factors that affect the rates, and the sequence of steps by which a reaction occurs. The study of rates of chemical reactions, the factors that affect the rates, and the sequence of steps by which a reaction occurs.

In some situations, it is important that reaction rates are very fast. An airbag will deploy in 1/25 of a second.

Some reactions occur very slowly over time such as the reaction of pigments and varnish with light and pollutants in the air paintings are exposed to.

Some reactions are so slow that for all intents and purposes, the reactants are completely stable and no reaction takes place. For example, the combustion of diamond is a spontaneous process at room temperature, but a diamond will remain stable in air at room temperature for what seems like forever. The combustion of diamond is said to be kinetically stable but thermodynamically unstable.

Rate – How much something changes in a unit of time. Rate of Rxn – Change in concentration per unit of time. A + B  C + D A + B  C + D Rate = Rate of Disappearance = _ [A] 2 - [A] 1 = _ ∆[A] t 2 – t 1 ∆t t 2 – t 1 ∆t Rate = Rate of Appearance = [C] 2 - [C] 1 = ∆[C] t 2 – t 1 ∆t t 2 – t 1 ∆t [ ] = concentration = M t = time ( s = seconds) M s -1 = M/s M s -1 = M/s

Calculate the rate of reaction in M/s for the reaction below where the concentration of B is initially 0.35M and 10 minutes later the concentration of B is 0.10M. Calculate the rate of reaction in M/s for the reaction below where the concentration of B is initially 0.35M and 10 minutes later the concentration of B is 0.10M. A + B  C + D A + B  C + D

rate of disappearance of reactant or of formation of product stoichiometric coefficient of that reactant or product in the balanced equation General rate of reaction = The stoichiometry dictates the relationship between the rates of appearance and disappearance for each reactant or product. aA + bB  cC + dD General Rate of Rxn : An overall rate for the entire reaction. The general rate has the same value regardless of which reactant or product we investigate because it considers the stoichiometric relationship between reactants and products. General Rate = _ 1 ∆[A] = _ 1 ∆[B] = 1 ∆[C] = 1 ∆[D] a ∆t b ∆t c ∆t d ∆t a ∆t b ∆t c ∆t d ∆t

General Rate = _ 1 ∆[A] = _ 1 ∆[B] = 1 ∆[C] = 1 ∆[D] a ∆t b ∆t c ∆t d ∆t a ∆t b ∆t c ∆t d ∆t The decomposition of N 2 O 5 proceeds as follows: 2N 2 O 5  4 NO 2 + O 2 If the rate of decomposition of N 2 O 5 at a particular instant in a reaction vessel is 4.2 x M/s, what is the rate of appearance of NO 2 ? O 2 ? What is the general rate for this reaction? NO 2 = 8.4 x M/s O 2 = 2.1 x M/s

If the rate of consumption of H 2 O 2 is 4.6 M/h, then … … the rate of formation of H 2 O must also be 4.6 M/h, and … … the rate of formation of O 2 is 2.3 M/h

Measuring Reaction Rates  In general, the greater the concentration of a reactant, the faster the reaction goes.  When we calculate change in concentration over change in time, we calculate the average rate of reaction. At the beginning of a time interval for a reaction, rate is faster and the end rate is slower.  The rate of reaction at a given point in time is an instantaneous rate of reaction.  The instantaneous rate of reaction at the beginning of a reaction is called the initial rate of reaction.

Average vs. Instantaneous Rate Instantaneous rate is the slope of the tangent to the curve at a particular time. We often are interested in the initial instantane- ous rate; for the initial concentrations of reactants and products are known at this time.

Collision Theory Collisions are vital for chemical change, either to provide the energy required for a particle to change (a bond to break) and/or to bring the reactants into contact. (As particles approach each other there is a repulsion of the electron clouds of the particles.) Activation Energy (E a ) – the minimum amount of energy required in a collision to allow a reaction to take place.

Collision Theory In order to react, the two colliding particles must: Collide with each other Must collide with enough energy to overcome the activation energy of the reaction Must collide with the correct geometrical alignment - the reactive parts of the molecule must come in contact in the correct way. (This is often called the steric factor and is very important in large organic molecules)

Importance of Orientation One hydrogen atom can approach another from any direction … … and reaction will still occur; the spherical symmetry of the atoms means that orientation does not matter. Effective collision; the I atom can bond to the C atom to form CH 3 I Ineffective collision; orientation is important in this reaction.

Any factor that either increases the frequency of the collisions or increases the energy with which they collide will make the reaction go faster. Factors mainly affecting the number of collisions Factors mainly affecting the proportion of collisions with the required E a Concentration/Pressure (for gases) Temperature Surface AreaCatalyst

Grain Silo Explosion 1977 Mineapolis Grain Elevator Explosion

The rate of reaction between two reactants, A & B, can be followed experimentally. The rate will be found to be proportional to the concentration of A raised to some power and also to the concentration of B raised to a power.

Rate Law (Rate Expression)- Shows how the concentration of reactants affect the rate of the reaction. Rate of Reaction = k [Reactant 1] m [Reactant 2] n k = rate constant: the constant of proportionality The value of K changes with changing temperature. Reaction Order – The power to which the concentration of a reactant is raised in a rate law. m & n = reaction orders for reactants – these are determined by examining experimental data. If no number is shown, m & n = 1. The sum of m + n = the overall reaction order. The order of reaction and the rate law can only be determined using experimental data.

To determine reaction order, examine experimental data: IF: Rate does not change with changing concentration: Rxn Order = 0 IF: Rate doubles with double in concentration, triples with triple concentration, etc. In other words, the changes in concentration produce proportional changes in rate: Rxn Order = 1 IF: Doubling concentration increases rate by factor of 2 2 = 4 or tripling increases rate by 3 2 = 9 and so on, in other words, the changes in concentration produce exponential changes in rate: Rxn Order = 2

Method of Initial Rates The method of initial rates is a method of establishing the rate law for a reaction—finding the values of the exponents in the rate law, and the value of k. A series of experiments is performed in which the initial concentration of one reactant is varied. Concentrations of the other reactants are held constant. When we double the concentration of a reactant A, if: –there is no effect on the rate, the reaction is zero-order in A. –the rate doubles, the reaction is first-order in A. –the rate quadruples, the reaction is second-order in A. –the rate increases eight times, the reaction is third- order in A.

The concentration of NO was held the same in Experiments 1 and 2 … … while the concentration of Cl 2 in Experiment 2 is twice that of Experiment 1. The rate in Experiment 2 is twice that in Experiment 1, so the reaction must be first order in Cl 2. Which two experiments are used to find the order of the reaction in NO? How do we find the value of k after obtaining the order of the reaction in NO and in Cl 2 ?

O Order Rxn: The rate of reaction does not depend on concentration of reactant but rather some other factor such as the absorption of light or the amount of surface area a reactant has. Rate Law: Rate = K

1st Order Rxn: Rate depends on the concentration of a single reactant raised to the 1st power. Rate Law: Rate = k[A] K = Rate = mol dm -3 s -1 = s -1 [A] mol dm -3

2nd Order Reaction: Rate depends on the reactant concentration raised to the second power or on the concentrations of two different reactants, each raised to the first power. Rate Law: Rate = k[A] 2 or k[A][B] K = rate = mol dm -3 s -1 = dm 3 mol -1 s -1 [A] 2 (mol dm -3 ) 2

3rd Order Reaction Rate depends on the concentration of one reactant raised to the second power and the concentration of another reactant raised to the first power. Rate = k[A] 2 [B] or rate = k[A][B] 2 K = rate = mol dm -3 s -1 = dm 6 mol -2 s -1 [A] 2 [B] (mol dm -3 ) 3

The following data were measured for the reaction of nitric oxide with hydrogen: Exp. # [NO](M)[H 2 ] (M)Initial Rate (M/s) x x x a. Determine the rate law for this reaction. b. Calculate the rate constant. c. Calculate the rate when [NO] = 0.050M and[H 2 ] = 0.150M.

Example 13.3 For the reaction 2 NO(g) + Cl 2 (g)  2 NOCl(g) described in the text and in Table 13.2, (a) what is the initial rate for a hypothetical Experiment 4, which has [NO] = M and [Cl 2 ] = M? (b) What is the value of k for the reaction?

Half Life t (1/2) Half life is the time it takes for the concentration of a reactant to fall to half its initial value. By viewing a graph of time vs. concentration the half life for a reaction can be determined and this allows us to determine the order of the reaction.

Half Life t (1/2) Zero Order Each t (1/2) is half the preceding t (1/2) First Order Constant half-life = t (1/2) Second Order Each t (1/2) is double the preceding t (1/2)

Shown here are graphs of [A] versus time for two different experiments dealing with the reaction A  products. What is the order of this reaction?

The first order rate constant for the decomposition of a certain insecticide in water at 12°C is 1.45/yr. A quantity of this insecticide is washed into a lake on June 1, leading to a concentration of 5.0 x 10 –7 g/ml of water. Assume that the average temperature of the lake is 12°C. What is the concentration of the insecticide on June 1st of the following year? How long will it take for the concentration of the insecticide to drop to 3.0 x 10 – 7g/cm3?