1. Rates of Reactions

2. Collision Theory
The amount of time required for a chemical rxn to come to completion can vary tremendously
When you strike a match it seems flame up instantly
Coal is made over millions of years from very slow chemical reactions
Chemists find it useful, although difficult, to study a reactions progress over a period of time, which is called Kinetics.

3. Collision Theory The concept of rate is familiar
A fast sprinter may cover 100 m in 11.5 s
A slower sprinter may take 15 s to run the same distance
On average the 1st sprinter runs at a speed of 8.7m/s
The 2nd runs at a speed of 6.7m/s
Both speeds are expressions of rates of travel

4. Collision Theory The word rate can be used as a synonym of speed
Rates measure the speed of any change that occurs within an interval of time
The interval of time may range from fractions of a second to centuries
Rates of chemical change usually are expressed as the amount of reactant forming products per unit time.

6. Collision Theory
Rates of chem rxns are related to the properties of atoms, ions, and molecules through a model called collision theory
According to collision theory, atoms, ions, and molecules can react to form products when they collide
provided that the particles have enough kinetic energy

8. Collision Theory
The minimum amount of energy that the particles or reactants must have in order to react is called the rxn’s activation energy.
In a sense the activation energy is a barrier that reactants must get over to be converted to products
The higher the barrier the larger the investment of energy in order to get the rxn to proceed

9. Activated complex

10. Collision Theory
During a rxn, a particle that is neither reactant nor product forms momentarily, called an activated complex
if there is sufficient energy
and if the atoms are oriented properly
An activated complex is a kind of transition molecule which has similarities to reactants & products
An activated complex is the arrangement of atoms at the peak of the activation-energy barrier.

11. Collision Theory
Collision theory explains why some naturally occurring rxns are immeasurably slow at room temp.
Carbon and Oxygen react when charcoal burns, but this reaction has a high activation energy
At room temp, the collisions of oxygen and carbon molecules aren’t energetic enough to react
But the rxn can be helped along a number of ways

12. Reaction Rates
It is possible to vary the conditions of the rxn, the rate of almost any rxn can be modified
collision theory can help explain why the rates can be modified
Several strategies can be used:
Increase the temperature
Increase the concentration
Decrease the particle size
Employ a catalyst

13. Temperature
Increasing the temp speeds up the rxn, while lowering the temp slows down the rxn
Increasing the temp increases the frequency of the collisions
Collisions taking place more often more likely they are to stick
And the extra energy increases the power of the collisions
Also increasing the likelihood of a successful collision

14. Just sitting out, charcoal does not react at a measurable rate
However, when a starter flame touches the charcoal, atoms of reactants collide with higher energy and greater frequency
Some of the collisions are high enough in energy that the product CO2 is formed
The energy released by the rxn then supp-lies enough energy to get more C and O2 over the activation-energy barrier
Evidence of this would be if you remove the starter flame, the rxn will continue on its own.

15. Concentration
The more reacting particles you have in a given volume, the higher the rate of rxn.
Cramming more particles into a fixed volume increases the concentration of reactants,
Increasing the concentration, increases the frequency of the collisions, and therefore increasing the reaction rate.

16. Particle Size
The smaller the particle size, the larger the surface area for a given mass of particles
The total surface area of a solid or liquid reactant has an important effect on the rate of reaction.
An increase in surface area increases the amount of the reactant exposed for collision to take place…
Which increases the collision frequency and the reaction rate.

17. Particle Size
One way to increase the surface area of solid reactants is to dissolve them
which separates the particles and makes them more accessible to other reactants.
Grinding solids into a fine powder also increases the surface area of reactants
Small dust-like particles can be very dangerous, can be highly explosive

18. Catalyst
An increase in temp is not always the best way to increase the rate of rxn
A catalyst is often better.
A catalyst is a substance that increases the rate of a rxn without being changed during the rxn
They permit rxns to proceed at lower energy than is normally required
With a lower activation energy more reactants can form products in a given amount of time.

20. Catalyst

22. Catalyst
Since catalysts are not consumed during a rxn, they do not appear as reactants or products in the chem eqn
Often written above the rxn arrow(s)
Catalysts are crucial for many life processes.
Your body temp is only 37°C and cannot be raised significantly without danger
Without catalysts, few rxns in the body would proceed fast enough at that temp
Enzymes, biological catalysts, increase the rates of biological rxns

23. When you eat a meal containing protein, enzymes in your digestive tract break down the protein molecules in a few hrs..
Without enzymes, the digestion of proteins at 37C takes yrs
An inhibitor is a substance that interferes with the action of a catalyst
An inhibitor could work by reacting with or “poisoning” the catalyst itself

24. Rate Laws
The rate of a rxn depends in part on the concentration of the reactants
Concentration is a measure of how much stuff is available to react
For a rxn in which reactant A reacts to form product B in 1 step, you can write a simple rxn eqn: A  B
The speed that A forms B is dependent on how the conc of A changes over time
As the conc of A decreases the rate of the rxn generally decreases

25. Rate Laws Rate = k•[A] DA Dt
You can express the rate as the change in A (DA) with respect to the change in time (Dt)
Rate = DA Dt
The rate of disappearance of A is proportional to the concentration or mol-arity (# of moles/Liter) of reactant A
This proportionality can be expressed as a constant (k) multiplied by the concentration of reactant A
k•[A]

26. Rate Laws This mathematical expression is an example of a rate law
An expression which relates the rate of a rxn to the conc of reactants
The magnitude of the rate constant (k) depends on the conditions at which the rxn is conducted
If reactant A reacts to form product B quickly, the value of k will be large
If reactant A reacts to form B slowly, the value of k will be small

27. Rate Laws
Rxns are classified as either zero-order, first-order, second-order, or mixed order (higher order) rxns.
The rate of chemical rxns and the size of the rate constant (k) is dependent on the “order” of the rxn
Zero-Order Rxns
(Order = 0) have a constant rate This rate is independent of the conc of the reactants. The rate law is: k, with k having the units of M/sec.

29. Rate Laws First-Order Reactions
(order = 1) has a rate proportional to the conc of one of the reactants A common example of a first-order rxn is the phenomenon of radioactive decay. The rate law is: k[A]1 (or B instead of A), with k having the units of sec-1

31. Rate Laws Second-Order Reactions
(order = 2) has a rate proportional to the conc of the square of a single reactant or the product of the conc of two reactants.
Rate law =k[A]2 (or substitute B for A or k multiplied by the concentration of A, [A], times the concentration of B, [B]), with the units of the rate constant M-1sec-1

33. Determining Rate Laws
Rate laws can only be determined experimentally.
It is not an easy process to determine the order of the reaction or the rate constant
Unless you determine a class of rate laws called Integrated Rate Laws.
Integrated Rate Laws are determined by graphing a series of rate data and analyzing the graph looking for a specific pattern.

34. Integrated Rate Law: Zero Order
The Zero order integrated rate law shows that its rate is independent of the [A]
Where [A] vs. t is a straight line with a slope of - k

35. Zero Order
Rate Law k
Rate Constant
Slope = - k
Integrated Rate Law
[A] = -kt + [A]0
Graph
[A] versus t
½ Life
t ½=[A]0/2k

36. Integrated Rate Law: First Order
The first order integrated rate law can be used to determine the concentration of [A] at any time.
It can be determined graphically
Where
y = ln[A]
x = time
m = -k
b = ln[A] 0

37. First Order
Rate Law
k[A]
Rate Constant
Slope = - k
Integrated Rate Law
ln[A] = -kt + ln[A]0
Graph
ln[A] versus t
½ Life
t ½=0.693/k

38. Integrated Rate Law: Second Order m = k b = 1/[A] 0
The second order integrated rate law can be used to determine the concentration of [A] at any time.
It can be determined graphically
Where
y = 1/[A]
x = time
m = k
b = 1/[A] 0

39. Second Order
Rate Law
k[A]2
Rate Constant
Slope = k
Integrated Rate Law
Graph
1/[A] versus t
½ Life
t ½=1/k[A]0

40. Rate Laws Rate = k[A]a[B]b
In some kinds of rxns, such as double replacement, 2 substances react to give products
The coefficients in the eqn for such a rxn can be represented by lower-case letters: aA + bB  cC + dD
For a 1 step rxn of A+B, the rate of rxn is dependent on the concentrations of reactants A & B
It’s rate law would follow the eqn:
Rate = k[A]a[B]b

41. Rate Laws
When each of the exponents a & b in the rate law equals 1, the rxn is said to be 1st order in A, 1st order in B, & 2nd order overall
The overall order of a rxn is the sum of the exponents for the individual reactants
If enough info were available, you could graph all the energy changes that occur as the reactants are converted to products in a chem rxn

42. Rate Laws Such a graph would be called a rxn progress curve
The simplest would be a one-step, elementary rxn
Reactants form products in a single step
1 activated complex
1 energy peak

43. Reaction Mechanism
For a more complex rxn, or a higher order rxn, the rxn progress curve resembles a series of hills & valleys
The peaks correspond to the energies of the activated complexes
Each valley represents an intermediate product which becomes a react of the next stage of the rxn
Intermediates have a significant lifetime compared with an activated complex
They have real ionic or molecular structures and some stability

44. Reaction Mechanism H2(g) + 2ICl(g) <==> I2(g) + 2HCl(g)
Intermediates do not appear in the overall eqn for a rxn
For example in the following overall rxn:
H2(g) + 2ICl(g) <==> I2(g) + 2HCl(g)
This reaction is not exactly accurate
There is an intermediate reaction in between the reactants and products.
1) H2(g) + 2ICl(g)  ICl(g) + HCl(g) + HI(g)
2) ICl(g) + HCl(g) + HI(g)  I2(g) +2HCl(g)

45. Reaction Mechanism

46. Reaction Mechanism
If a chem rxn proceeds in a sequence of steps, the rate law is determined by the slowest step because it has the lowest rate.
The slowest-rate step is called the rate-determining step
Consider this rxn: NO2 + CO  NO + CO2
the rxn is believed to be a 2 step process following this mechanism
Step 1: NO2 + NO2  NO + NO3
SLOW
Step 2: NO3 + CO  NO2 + CO2
FAST

47. Reaction Mechanism In the 1st step
2 molecules of NO2 collide, forming the intermediate NO3.
The NO3 species collides with a molecule of CO and reacts quickly to produce 1 molecules each of NO2 and CO2
The 1st step is the slower of the 2 steps and is therefore the rate-determining step
Its rate law: R=k[NO2]2
The rate determining step and the rate law are both determined experimentally