We know that chemical reactions proceed at widely differing rates.

1. Rates of Chemical Reactions • We know that chemical reactions proceed at widely differing rates. • Some reactions take place very slowly, e.g., corrosion • Some reactions are of intermediate rate • S2O32-(aq) + 2H+(aq) = H2O(l) + SO2(g) + S(s) • Some reactions take place very rapidly • H+(aq) + OH-(aq) = H2O(l) • Balanced chemical equation gives no information on rates.

2. Why Reaction Rates Matter? • If we wish to synthesize a new compound, or design a process such as dyeing of a textile material, we would need to ensure that the reaction/s concerned take place at a reasonable rate. • Studies of the rates of chemical reactions can tell us an enormous amount about exactly how the reactions take place at the molecular level, i.e., such studies provide information about the reaction mechanism. To measure the rates of reactions, the most usual way is tofollow the changes in concentration of the substances involved.

3. Measuring Reaction Rates • The rate of a reaction could be monitored by measuring the increase in the concentration of a reaction product with time.For a reaction A  B we have:

4. At t = 0 (time zero) there was 1.00 mol A (100 red spheres) and no B present • At t = 10 min, there was 0.74 mol A and 0.26 mol B. • At t = 20 min, there was 0.54 mol A and 0.46 mol B.

5. At t = 0 (time zero) there was 1.00 mol A (100 red spheres) and no B present • At t = 10 min, there was 0.74 mol A and 0.26 mol B. • At t = 20 min, there was 0.54 mol A and 0.46 mol B. Reaction rates are different at different times!

6. Real World Example • In practice we measure concentrations and changes in concentration rather than moles and changes in moles • We measure concentration in terms of molarity. If the volume is constant, molarity and moles are directly proportional to one another. • Consider the following chemical reaction: • C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq) • The substance chlorobutane reacts with water to form butanol and hydrochloric acid

8. Reaction Rate and Stochiometry • For a general chemical reaction • aA + bB cC + dD • we could choose to measure reaction rate as: • Decrease in [reactant] per unit time: • Increase in [product] per unit time: • Minus signs are attached to the change of reactants toensure that rates of reaction are always positive quantities. Inversed stochiometric coefficients ensure the same value of the reaction rate.

9. Definition of Reaction Rate The RATE OF REACTION, r, is defined as the instantaneous rate of decrease in the concentration of a reactant, or increase in the concentration of a product, divided by the stoichiometric coefficient of the reactant or product concerned.

10. Factors that Affect Reaction Rates • There are 4 important factors which affect rates of reactions: • concentrations of reactants, • temperature, • action of catalysts, and • surface area of solid reactants.

11. Concentration and Rate In general reaction rates increase as concentrations increase. NH4+(aq) + NO2-(aq)  N2(g) + 2H2O(l)

12. Rate Law • For a general reaction with 2 reactants the rate law is: • we say the reaction is mth order in reactant 1 and nth order in reactant 2. • The overall order of reaction is m + n + …. • A reaction can be zeroth order if m, n, … are zero. • Note the values of the exponents (orders) have to be determined experimentally. They are not simply related to stoichiometry.

13. Examples of Rate Laws for Chemical Reactions

14. Integrated Form of the 1st Order Rate Law [A]t represents the [A] at time t [A]0 represents the [A] at time t = 0, i.e., initially k represents the rate constant. ln represents the natural logarithm, i.e., log to base e.

15. First Order Reactions

16. Half-Life The half-life of a reaction is the time taken for the concentration of a reactant to drop to half its original value. For the 1st order reaction: The half-life for a 1st order reaction has a constant value, i.e., a value that does not change as the reaction proceeds. This provides a simple way of recognizing that a specific reaction follows 1st order kinetics.

18. Temperature and Rate • Most reactions speed up as temperature increases (e.g. food spoils when not refrigerated, dyeing proceeds faster at elevated temperatures) • It is commonly observed that the rates of chemical reactions are very sensitive to temperature • As a rough rule of thumb, the rates of many chemical reactions approximately double for every 10°C rise in temperature.

19. As temperature increases, the rate constant for the reaction increases quite dramatically.

20. Arrhenius Equation • Arrhenius found that most reaction-rate data obeyed the Arrhenius equation: • k is the rate constant, Eais the activation energy, R is the gas constant (8.314 J/K-mol) and T is the temperature in K. • A is called the frequency factor. • A is a measure of the probability of a favorable collision. • Both A and Ea are specific to a given reaction.

21. Activation Energy • Molecules must possess a minimum amount of energy to react. Why? • In order to form product molecules, chemical bonds must be broken in the reactant molecules. • Bond breakage requires energy. • The minimum energy required by a molecule or by a pair of colliding molecules to lead to chemical reaction is called the Activation Energy of the reaction, Ea. • Example: rearrangement of methyl isonitrile:

23. Reaction Mechanisms • The balanced chemical equation provides information about the initial reactants and final products, i.e., the beginning and end of a reaction. • The reaction mechanism gives the path of the reaction. • Mechanisms provide a very detailed picture of which bonds are broken and formed during the course of a reaction. • An elementary step is any reaction that occurs as a result of a single molecular collision.

24. Multistep Mechanisms • Some reactions proceed through more than one step: • NO2(g) + NO2(g)  NO3(g) + NO(g) • NO3(g) + CO(g)  NO2(g) + CO2(g) • Notice that if we add the above steps, we get the overall reaction: • NO2(g) + CO(g)  NO(g) + CO2(g) • This reaction takes place via a two-step mechanism. • Reactive intermediate: a species which appears in an elementary step but which is not a reactant or product in the overall reaction. Example: NO3 in the previous equations

25. Transition states/ activated complexes Potential energy NO3 NO2 + CO Reactive intermediate NO + CO2 Reaction pathway • PE diagram for a reaction with a two-step mechanism

26. Rate-determining Step • The various elementary steps in the mechanism of a • reaction proceed at different rates • The slowest step in the reaction mechanism is called the rate-determining step or the rate-limiting step in the reaction mechanism. • Example: It has been established experimentally that the rate law for the reaction • NO2(g) + CO(g)  NO(g) + CO2(g) • is r = k[NO2]2. The following 2-step mechanism has been proposed for this reaction:

27. If k1 << k2 , i.e., step 1 is much slower than step 2, then step 1 will be the rate-determining step. What is the molecularity of step 1? Molecularity = 2, therefore step 1 is a bimolecular elementary reaction. So, rStep 1 = k1 [NO2]2. Since step 1 is the rate-determining step, we can say that, for the overall reaction r = k1 [NO2]2.

28. Catalysis A catalyst is a substance that increases the rate of a reaction, without itself being consumed by the reaction. • Homogeneous catalysis: the catalyst and reactants are present in the same phase. • Heterogeneous catalysis: the catalyst and reactants are in different phases.

29. Generally, catalysts operate by lowering the activation energy for a reaction.They do this by changing the mechanism of the reaction.

30. Homogeneous Catalysis: Example • Hydrogen peroxide decomposes very slowly: • 2H2O2(aq)  2H2O(l) + O2(g) • In the presence of the bromide ion, the decomposition occurs rapidly: • 2Br-(aq) + H2O2(aq) + 2H+(aq)  Br2(aq) + 2H2O(l). • Br2(aq) is brown. • Br2(aq) + H2O2(aq)  2Br-(aq) + 2H+(aq) + O2(g). • Br- is a catalyst because it can be recovered at the end of the reaction.

31. Heterogeneous Catalysis • The catalyst is in a different phase than the reactants and products. • Typical example: solid catalyst, gaseous reactants and products (catalytic converters in cars). • Most industrial catalysts are heterogeneous. • First step is adsorption (the binding of reactant molecules onto active sites on the catalyst surface).

33. Heterogeneous Catalysis: Example • Hydrogenation of ethylene: • C2H4(g) + H2(g)  C2H6(g), H = -136 kJ/mol. • The reaction is slow in the absence of a catalyst. • In the presence of a metal catalyst (Ni, Pt or Pd) the reaction occurs quickly at room temperature. • First the ethylene and hydrogen molecules are adsorbed onto active sites on the metal surface. • The H-H bond breaks and the H atoms migrate about the metal surface.

34. Enzymes • Enzymes are biological catalysts. • Most enzymes are protein molecules with large molecular masses (10,000 to 106 amu). • Enzymes have very specific shapes. • Most enzymes catalyze very specific reactions. • Substrates undergo reaction at the active site of an enzyme. • A substrate locks into an enzyme and a fast reaction occurs. • The products then move away from the enzyme.

35. Substrate A makes with the enzyme E reaction intermediate AE, which further decomposes into product B and enzyme E is recovered. Total concentration of enzyme (E0) is a sum of free enzyme concentration (E) and AE [E0]=[E]+[AE]

36. Kinetics of Enzyme Catalysis Fast reaction equilibrium Slower decomposition to product and enzyme is the rate-limiting step: Michaelis and Menten equation

37. The Freundlich isotherm is described by where K is the partition coefficient, S is the amount sorbed, C is concentration of the solution and n 1. Freundlich Sorption Isotherm When n < 1, the plot is concave with respect to the C axis. When n = 1, the plot is linear. In this case, K is called the distribution coefficient (Kd ).

38. The Langmuir isotherm describes situation where the number of sorption sites is limited, so a maximum sorptive capacity (S max) is reached. Langmuir Sorption Isotherm The governing equation for Langmuir isotherms is: