Kinetics

1. Kinetics Reaction Rates, Rate Law, Collision Theory and Activation Energy (PLN 7-10)

2. PLN 7 • Important Concepts: • Reactions can occur at different rates • Factors that help determine the reaction rate • Reaction characteristics: • Mechanism of reaction (PLN 11) • Rate of Reaction • Rate Law (PLN 8)

3. Basic Kinetics • Reaction Rate – Speed that reactants disappear and products form • How fast reactants become/form products

4. Examples: • Very Fast Rates (Almost Instantaneous): • Most Acid-Base Reactions • Some Precipitation Reactions • Slower Reaction Rates: • Rusting

5. What Determines the Rate? • Temperature • Pressure • Concentration • Catalyst (PLN 12) • Lowers activation energy • Surface Area • Not going to be covered on this test

6. Mechanism of Reaction • Lists the individual steps of a reaction • Describe reactions at a molecular level • Not all reactions occur in one step or all at once • Chemical equation is overall summary of the reaction

7. Rate of Reaction • The calculated rate at which reactants are used up/disappear or products are formed/appear • For general reaction: Wherea, b, c and d are coefficients,

8. Rate Law • Mathematic expression for the rate of reaction • Expressed in terms of the concentrations of the reactants • For a reaction: A + B  C + D

9. Reaction Rates • Definition: • The rate of a reaction is the change in molar concentration of a reactant or product per unit of time in a reaction • Example: • Rate of decomposition of • However, this gives the average rate over the period of time Δt • The instantaneous rate can be calculated as the slope of the tangent line at a given point

10. Overall Rate of Reaction • The rate of reaction is more commonly described in terms of the equation • For the reaction: • For every 2 moles of N2O5 lost: • 4 moles of NO2 is formed • And 1 mole of O2 is formed Note: The negative sign placed in front of the reactants is to count for the fact that their concentrations are decreasing

11. PLN 8 • Important Concepts: • Rate Laws • Rate Constant (k) • Order of Reaction • Initial Rate Method

12. Rate Laws for Chemical Reactions • Rates depend on concentrations of certain reactants and the concentration of the catalyst, if there is one • Definition: • A Rate Law is an equation that relates the rate of a reaction to the concentrations of the reactants (and catalyst, if used) raised to various powers, or exponents.

13. Rate – Expressed in mol/L/time or M/time • k – Rate constant • Specific to a certain reaction at a specific temperature • Units depend on the overall reaction order (explained later) • [A] & [B] – Concentrations of reactants as mol/L or M • m & n – Orders of reaction with respect to reactants

14. k • The reaction constant, k, is called the rate constant and is dependent on the particular reaction as well as the specific temperature at which the reaction takes place • The units of k depend on the order of reaction

15. Orders of Reaction • The rate law exponents are determined using experimental data • Examples: • The overall order of reaction is the sum of all orders with respect to each reactant • So for the example, where the rate is 2nd order with respect to NO and first order with respect to H2: • The overall order of reaction is 2 + 1 = 3, or a 3rd order reaction

16. Determining the Rate Law Experimentally • The Initial Rate Method • Uses the relationship between the measured initial rate of a reaction and the concentrations of each reactant • The Integrated Rate Law Method • Uses the relationship between reactant or product concentration and its changes over time

17. The Initial Rate Method • By determining the ratio of Δrate to Δ[reactant] between 2 experiments • Solve for the exponents for each reactant

18. The Initial Rate Method – Data Collection • Determine the initial rate of reaction, fixing the concentration of all reactants except one • Repeat step 1, fixing the concentration of each reactant in turn Example:

19. The Initial Rate Method – Calculations • The reaction is 2nd order with respect to NH4NCO • The reaction is also 2nd order overall, since NH4NCO is the only reactant and there is no catalyst

20. Initial Rate Method – Rate Law and k • Given NH4NCO is 2nd order, we can now determine the rate law to be: • Using this rate law and the experimental data, the rate constant can also be calculated:

21. PLN 9 • Important Concepts: • Integrated Rate Law Method • 0th, 1st and 2nd order reactions • Half-Life • 0th, 1st and 2nd order reactions • Units for k • 0th, 1st and 2nd order reactions

22. The Integrated Rate Law Method • Initial Rate Method describes change of rate as we change initial reactant concentrations • Using integral calculus, we can convert Rate Laws into equations that can give us concentrations of the reactant(s) or product(s) at anytime during the reaction • The Integrated Rate Law Method fits experimental data to a mathematical relationship

23. First Order Reactions • Basic Example: • Which can be rewritten as: • And simply by cross-multiplying, you can get:

24. First Order Reactions (cont.) • This setup allows integration of both sides: Note: The k can be pulled out of the integral since it is a constant. • Rearranging: Note: The next two slides detail all the steps in the integration process and may be skipped if you already understand the integration done here.

25. Explaining the Integration: 1st Order • Beginning with: • The integral of is written as: • And is solved as: Note: In calculus, the notation “”means that you plug in b for x and plug in a for x and subtract the second equation (one with the a’s) from the first (one with the b’s) • So, using our equation, the integration of just the left side looks like this:

26. Explaining the Integration: 1st Order (cont.) • Beginning with: • The integral of 1 on the interval from a to b is written as: • And is solved as: • So, using our equation, the integration of just the right side looks like this: • The final equation:

27. Half-Life of a Reaction • Definition • The half-life of a first order reaction is the time taken for the reactant amount to reach one-half of its initial (or previous) value • This is saying that • Using substitution into the integrated rate law for 1st order reactions, we get time of half life :

28. For only 1st order reactions: The half-life doesn’t depend on the initial concentration Rate Law, k, Integrated Rate Law and Half-Life for 1st, 2nd and 3rd Order

29. PLN 10 • Important Concepts: • Collision Theory • Pre-exponential constant (A) • fKE • Importance of Correct Orientation • Arrhenius Equation • Activation Energy (EA) • Transition State Theory • Potential Energy Diagrams

30. What Affects Reaction Rates, Again? • Reaction rates are dependent upon: • Temperature • Pressure • Concentration • Catalyst • Surface Area

31. How Temperature influences Reaction Rates • Sometimes the influence temperature has on the rate of reaction can be quite dramatic, for: • Data: At 25°C: At 35°C:

32. Collision Theory • The Collision Model says that, in order to react, molecules have to collide, both: • With enough energy • And with correct orientation • In the Collision Model, kdepends on 3 factors: • Z = Collision frequency • fraction of collisions that occur with the molecules properly oriented • fraction of molecules having or exceeding the required activation energy

33. Changes in Temperature • Z and forient are generally combined into one • Pre-exponential constant = A • A is essentially independent of any temperature change, so fKE is the critical factor of k when it comes to changes in temperature • where: • R = ideal gas constant in terms of • 8.314 • T = temperature in kelvin • EA = Activation Energy for the process

34. Importance of Correct Orientation • For the reaction: • Consider two possible ways for the reactant molecules to collide:

35. Arrhenius Equation • Taking the natural log of both sides: • Rearranged: looks somewhat similar to: • In fact, it is a linear equation if you plot • Where the • And the

36. Calculating EA for an Equation • By subtracting: • From: • We get: • (lnA – lnA) = 0, simplify lnx – lny and combine like terms :

37. Example • For: • Plug in values for k1, k2, T1 and T2 into the equation: • Solve for EA:

38. Transition State Theory • Transition State Theory describes what happens to the reactant molecules as a reaction proceeds • When the reactants collide, they form a temporary “substance” composed of a combination of the two reactants • This temporary “substance” is called the transition state or activated complex

39. Transition State • For: • Where a temporary complex: • Is formed, before the • bond is broken • and the bond • is completely formed

40. Transition States (cont.) • The double dagger (‡) indicates a transition state • The transition state is a step in-between forming a bond and breaking another • Can be thought of as one half broken bond and one half formed bond • The partially formed and partially broken bonds are denoted with ()

41. Potential Energy Diagrams • A graph of Potential Energy vs. the Reaction Coordinate • The reaction coordinate is essentially the progress of the reaction Endothermic Reaction Exothermic Reaction