1. The relationship between concentration and time can be derived from the rate law and calculus
Integration of the rate laws gives the integrated rate laws
Integrate laws give concentration as a function of time
Integrated laws can get very complicated, so only a few simple forms will be considered

2. First order reactions Rate law is: rate = k [A]
The integrate rate law can be expressed as:
[A]0 is [A] at t (time) = 0
[A]t is [A] at t = t
e = base of natural logarithms = …

3. Graphical methods can be used to determine the first-order rate constant, note

4. A plot of ln[A]t versus t gives a straight line with a slope of -k
The decomposition of N2O5. (a) A graph of concentration versus time for the decomposition at 45oC. (b) A straight line is obtained from a logarithm versus time plot. The slope is negative the rate constant.

5. The simplest second-order rate law has the form
The integrated form of this equation is

6. Graphical methods can also be applied to second-order reactions
A plot of 1/[B]t versus t gives a straight line with a slope of k
Second-order kinetics. A plot of 1/[HI] versus time (using the data in Table 15.1).

7. The amount of time required for half of a reactant to disappear is called the half-life, t1/2
The half-life of a first-order reaction is not affected by the initial concentration

8. First-order radioactive decay of iodine-131
First-order radioactive decay of iodine-131. The initial concentration is represented by [I]0.

9. The half-life of a second-order reactions does depend on the initial concentration

10. One of the simplest models to explain reactions rates is collision theory
According to collision theory, the rate of reaction is proportional to the effective number of collisions per second among the reacting molecules
An effective collision is one that actually gives product molecules
The number of all types of collisions increase with concentration, including effective collisions

11. There are a number of reasons why only a small fraction of all the collisions leads to the formation of product:
Only a small fraction of the collisions are energetic enough to lead to products
Molecular orientation is important because a collision on the “wrong side” of a reacting species cannot produce any product
This becomes more important as the complexity of the reactants increases

12. The key step in the decomposition of NO2Cl to NO2 and Cl2 is the collision of a Cl atom with a NO2Cl molecules. (a) A poorly orientated collision. (b) An effectively orientated collision.

13. The minimum energy kinetic energy the colliding particles must have is called the activation energy, Ea
In a successful collision, the activation energy changes to potential energy as the bonds rearrange to for products
Activation energies can be large, so only a small fraction of the well-orientated, colliding molecules have it
Temperature increases increase the average kinetic energy of the reacting particles

14. Kinetic energy distribution for a reaction at two different temperatures. At the higher temperature, a larger fraction of the collisions have sufficient energy for reaction to occur. The shaded area under the curves represent the reacting fraction of the collisions.

15. Transition state theory explains what happens when reactant particles come together
Potential-energy diagrams are used to help visualize the relationship between the activation energy and the development of total potential energy
The potential energy is plotted against reaction coordinate or reaction progress

16. The potential-energy diagram for an exothermic reaction
The potential-energy diagram for an exothermic reaction. The extent of reaction is represented as the reaction coordinate.

17. A successful (a) and unsuccessful (b) collision for an exothermic reaction.

18. Activation energies and heats of reactions can be determined from potential-energy diagrams
Potential-energy diagram for an endothermic reaction. The heat of reaction and activation energy are labeled.

19. Reactions generally have different activation energies in the forward and reverse direction
Activation energy barrier for the forward and reverse reactions.

20. The brief moment during a successful collision that the reactant bonds are partially broken and the product bonds are partially formed is called the transition state
The potential energy of the transition state is a maximum of the potential-energy diagram
The unstable chemical species that “exists” momentarily is called the activated complex

21. Formation of the activated complex in the reaction between NO2Cl and Cl.
NO2Cl+ClNO2+Cl2

22. The activation energy is related to the rate constant by the Arrhenius equation
k = rate constant
Ea = activation energy
e = base of the natural logarithm
R = gas constant = J mol-1 K-1
T = Kelvin temperature
A = frequency factor or pre-exponential factor

23. The Arrhenius equation can be put in standard slope-intercept form by taking the natural logarithm
A plot of ln k versus (1/T) gives a straight line with slope = -Ea/RT

24. The activation energy can be related to the rate constant at two temperatures
The reaction’s mechanism is the series of simple reactions called elementary processes
The rate law of an elementary process can be written from its chemical equation

25. The overall rate law determined for the mechanism must agree with the observed rate law
The exponents in the rate law for an elementary process are equal to the coefficients of the reactants in chemical equation

26. Multistep reactions are common
The sum of the element processes must give the overall reaction
The slow set in a multistep reaction limits how fast the final products can form and is called the rate-determining or rate-limiting step
Simultaneous collisions between three or more particles is extremely rate

27. A reaction that depended a three-body collision would be extremely slow
Thus, reaction mechanism seldom include elementary process that involve more than two-body or bimolecular collisions
Consider the reaction
The mechanism is thought to be

28. The second step is the rate-limiting step, which gives
N2O2 is a reactive intermediate, and can be eliminated from the expression

29. The first step is a fast equilibrium
At equilibrium, the rate of the forward and reverse reaction are equal

30. Substituting, the rate law becomes
Which is consistent with the experimental rate law

31. Thus a larger fraction of the collisions are effective
A catalyst is a substance that changes the rate of a chemical reaction without itself being used up
Positive catalysts speed up reactions
Negative catalysts or inhibitors slow reactions
(Positive) catalysts speed reactions by allowing the rate-limiting step to proceed with a lower activation energy
Thus a larger fraction of the collisions are effective

32. (a) The catalyst provides an alternate, low-energy path from the reactants to the products. (b) A larger fraction of molecules have sufficient energy to react when the catalyzed path is available.

33. Catalysts can be divided into two groups
Homogeneous catalysts exist in the same phase as the reactants
Heterogeneous catalysts exist in a separate phase
NO2 is a homogeneous catalyst for the production of sulfuric acid in the lead chamber process
The mechanism is:

34. The second step is slow, but is catalyzed by NO2:

35. Heterogeneous catalysts are typically solids
Consider the synthesis of ammonia from hydrogen and nitrogen by the Haber process
The reaction takes place on the surface of an iron catalyst that contains traces of aluminum and potassium oxides
The hydrogen and nitrogen binds to the catalyst lowering the activation energy

36. The Haber process. Catalytic formation of ammonia molecules from hydrogen and nitrogen on the surface of a catalyst.