Kinetics & Equilibrium

1. Kinetics & Equilibrium Chapter 18

2. A Model for reaction rates

3. Reaction Rates • the _______________ is the change in ______________ (molarity) of a reactant or product per unit ________(units are mol/L*sec) • Some notes: • Brackets around a formula for a substance (ex: [NaCl]) stand for “molar concentration of the substance”) • Reaction rates are calculated experimentally

4. Calculating Average Rate • Generally: • In relation to chemical reactions: Note: this is negative because it calculates the rate of the reaction by calculating the rate of consumption of the reactant – you could also calculate the rate by calculating the rate of production of the products

5. Calculating Average Rate CO (g) + NO2 (g)  CO2 (g) + NO (g)

6. Calculating Average Rate CO (g) + NO2 (g)  CO2 (g) + NO (g) If the concentration of NO is 0.000M at time t1 = 0.00 s, and 0.010M two seconds after the reaction begins, what is the rate of the reaction?

7. Collision Theory • Atoms, ions, and molecules must _________ in order to react • Reacting substances must collide in the correct _______________ • Reacting substances must collide with sufficient energy to form an ______________ • Sometimes called the “transition state” • A temporary, unstable arrangement of atoms in which old bonds are breaking and new bonds are forming

8. Activation Energy and Reaction Rate • The minimum amount of energy that reacting particles must have to form the activated complex and lead to a reaction is called the ____________________ (Ea) • A high Eameans few collisions have enough energy to produce the activated complex and the reaction rate is _______ • A low Eameans less energy is required for the reaction to occur and the reaction rate is _______

9. Activation EnergyEndothermic Reaction

10. Activation EnergyExothermic Reaction

11. Factors affecting reaction rates

12. What we already know about factors that affect reaction rates… • _____________________ – some substances react more readily than others • _________________ – higher concentration of reactants mean faster rate of reaction (more collisions) • ________________ – greater surface area leads to more collisions and faster rate of reaction • _________________ – increased temperature means more kinetic energy, thus, more collisions and a faster rate of reaction

13. Catalysts and Inhibitors • ______________ are substances that increase the rate of a chemical reaction without being consumed in the reaction (ex: enzymes) • Work by lowering the activation energy • ________________ are substances that slow down, or inhibit, chemical reactions • Can raise the activation energy • Can block a catalyst (ex: bind the enzyme that catalyzes a reaction in a biological system)

14. Catalysts

15. Reaction rate laws

16. Rate Laws A Rate Law expresses the relationship between the rate of a chemical reaction and the concentration of the reactants For a one-step reaction, such as A  B: Where: [A] = concentration of reactant k = specific rate constant

17. Reaction Order • The reaction order for a reactant defines how the rate is affected by the concentration of that reactant • First order reactions: Since the exponent on [H2O2] is a 1, the reaction rate is directly proportional to the concentration of H2O2 raised to the first power Reaction orders are determined experimentally

18. Other-Order Reaction Rate Laws For the reaction: aA + bB products The General Rate Law: Where: [A] and [B] are the concentrations of reactants A and B “m” and “n” are the reaction orders (determined experimentally) – may be equal to “a” and “b” if the reaction occurs in one single step with a single activated complex

19. Reaction Rate Laws 2NO (g) + 2H2 (g)  N2 (g) + 2H2O (g) The reaction occurs in more than one step and has the following rate law: The reaction is: Second order in NO (if [NO] doubles, the rate quadruples) First order in H2 (if [H2] doubles, the rate doubles) Third order overall (sum of the exponents)

20. Determining Reaction Order Method of Initial Rates – determines reaction order by comparing the initial rates of a reaction carried out with varying reactant concentrations Remember: • To determine “m”, compare the concentrations and reaction rates in Trials 1 and 2 (see next slide) • Do same process to determine “n”, but use Trials 2 and 3

21. Determining Reaction Order • Since doubling [A] doubles the rate, the reaction is first order in A • Since doubling [B] quadruples the rate, the reaction is second order in B • The overall reaction is third order (add the exponents 1 + 2 = 3)

22. Half-life of a First-Order Reaction • The time required for a reactant to reach half of its original concentration is called the half-life of a reactant (t1/2) This is the half-life equation for a first-order reaction

23. Half-life of a Second-Order Reaction Where: t1/2 = half-life of reactant k = rate constant [A]0 = concentration of reactant at t = 0

24. Reaction mechanisms

25. Reaction Mechanisms • Most chemical reactions consist of sequences of two or more simpler reactions • A ___________________ is one that consists of two or more elementary steps • A ____________________ is the complete sequence of elementary steps that makes up a complex reaction

26. Reaction Mechanism Elementary Step: Cl + O3 ClO + O2 Elementary Step: O3  O + O2 Elementary Step: ClO + O  Cl + O2 Complex Reaction: 2O3  3 O2 This is the complex reaction for the formation of oxygen from ozone.

27. Intermediates(substance produced in one elementary step and consumed in a subsequent elementary step)

28. Rate-Determining Step • The reaction cannot go faster than its slowest elementary step • The slowest elementary step in a complex reaction is called the ___________________ • This is also the step with the ____________ activation energy

29. Calculating Activation Energies • The Arrhenius Equation Where: k = rate constant A = number of collisions (pre-exponential factor) Ea = activation energy e = mathematical quantity, e R = gas constant (0.08206 Latm/molK) T = temperature in K

30. Calculating Activation Energy Arrhenius Equation Where: k1 and k2 are rate constants measured at temperatures T1 and T2 R = 8.3145 J/K*mol (the gas constant with different units) Ea = activation energy

31. Arrhenius EquationA Sample Problem • At 823 K, the rate constant for a reaction is 1.1 L/mol*s, and at 898 K, the rate constant is 6.4 L/mol*s. Using these values, calculate Ea for the reaction.

32. Chemical Equilibrium

33. Reversible Reactions • A _________________ is a chemical reaction that can occur in both the forward and reverse directions: Forward: N2(g) + 3H2(g)  2NH3(g) Reverse: N2(g) + 3H2(g)  2NH3(g) We will write the complete equation as: N2(g) + 3H2(g) ↔ 2NH3(g)

34. Chemical Equilibrium • __________________is a state in which the forward and reverse reactions balance each other because they take place at equal rates • Only ___________ systems can reach equilibrium! • For a pretty good animation on chemical equilibrium, check out http://www.chm.davidson.edu/ronutt/che115/EquKin/EquKin.htm

35. Equilibrium Expressions • The _____________________________ states that at a given temperature, a chemical system might reach a state in which a particular ratio of reactant and product concentrations has a constant value • While a bit verbose, this definition leads us to writing equilibrium constant expressions…

36. Equilibrium Expressions • For the chemical reaction at equilibrium aA + bB ↔ cC + dD We can write the following expression: Where, [A] and [B] are the molar concentrations of the reactants and [C] and [D] are the molar concentrations of the products (all are raised to their coefficients)

37. The Equilibrium Constant The equilibrium constant, Keq, is the numerical value of the ratio of product concentrations to reactant concentrations, with each concentration raised to the power equal to its coefficient in the balanced equation. The value of Keq is constant only at a specified ________________.

38. The Equilibrium Constant Some additional notes: • Keq > 1: __________are favored at equilibrium • Keq < 1: __________ are favored at equilibrium

39. Homogeneous Equilibrium • If a reaction is a homogeneous equilibrium, all of the reactants and products are in the same physical state, for example H2(g) + I2(g) ↔ 2HI(g) And the equilibrium constant expression would be

40. Heterogeneous Equilibria • If the reactants and products are present in more than one physical state, the equilibrium is called a __________________ equilibrium • Since solids and liquids are considered to be pure substances, their concentrations can be thought of as their densities in units of moles/liter • Density and thus the concentration of solids and liquids are considered ____________ and thus fall out of the equilibrium expression

41. Heterogeneous Equilibria Example 2NaHCO3(s) ↔ Na2CO3(s) + CO2(g) + H2O(g) The general form of this equilibrium expression would be But then omit terms involving solid substances and you get the final equilibrium expression

42. Dynamic Equilibrium • Various “forces” can alter a system’s equilibrium (think of a see-saw that is balanced at one time and unbalanced at another) • ____________________ predicts the position of the equilibrium after a chemical system has been disturbed (by changing temperature, concentration, pressure and/or volume)

43. Applying LeChâtelierChanges in Concentration • Adding reactants will shift the equilibrium toward the ___________ (to the right) until enough products are made to establish a new equilibrium • Removing products will also shift the equilibrium to the __________ (to replenish…) • Adding products will shift the equilibrium toward the ___________ (to the left) and favor the reverse reaction

44. Applying LeChâtelierChanges in Volume and Pressure • REMEMBER – Boyle’s Law – decreasing the volume at constant temperature will increase the pressure – these two are inversely related! • Changing the volume (and pressure) of an equilibrium system shifts the equilibrium only if the number of ________ of gaseous reactants is different from the number of ___________ of gaseous products (look at the coefficients for this!)

45. Applying LeChâtelierChanges in Volume and Pressure • Increasing the pressure will shift the equilibrium toward the side with the _______________________ of gas Example: CO(g) + 3H2(g) ↔ CH4(g) + H2O(g) • Note: you can increase the pressure either by decreasing the volume, or by adding an _____________________ which will not react, but will increase the number of gas particles thereby increasing the pressure

46. Applying LeChâtelierChanges in Temperature • Adding heat to an equilibrium system causes the equilibrium to shift in the direction in which heat is used up • _______________ reactions – consider heat as a reactant (positive ΔH) – more heat shifts equilibrium toward ______________ • _______________ reactions – consider heat as a product (negative ΔH) – more heat shifts equilibrium toward ______________

47. Catalysts and Equilibrium • A _______________speeds up a reaction, but it does so equally in both directions • A catalyzed reaction will reach equilibrium more quickly, but with no change in the amount of product formed (it does not affect the Keq!)

48. Equilibrium Constants • We can find the value of equilibrium constants (Keq) by using concentration data at equilibrium • The concentrations are determined experimentally and will be given to you for this type of calculation.

49. Practice Problem • Calculate the value of Keq for the equilibrium constant expression given concentration data at one equilibrium position: [NH3] = 0.933M, [N2] = 0.533 M, [H2] = 1.600 M.

50. Calculating Equilibrium Concentrations • Just like we calculated Keq, we can calculate any of the equilibrium concentrations from similar data…