Rate Processes in Chemical Reactions - Kinetics and Equilibrium

Reaction rates

  • The reaction rate is defined as the rate of change in the concentration of reactants or products. ie. how fast a reactant gets used up, and how fast a product gets produced.
  • Rate = -ΔReactant/ΔTime = how fast a reactant disappears.
  • Rate = ΔProduct/ΔTime = how fast a product forms.
  • The unit for rate is molarity per second, or M/s.

Dependence of reaction rate upon concentration of reactants; rate law

  • The rate law is the equation that describes the rate = the product of reactants raised to some exponents.
  • aA + bB → cC + dD
    • If the above reaction is single-step, then rate = k[A]a[B]b
    • If the above reaction is the rate-determining step of a multi-step reaction, then the rate of the multi-step reaction = k[A]a[B]b
    • If the above reaction is a multi-step reaction, then rate = k[A]x[B]y, where x and y are unknowns that correspond to the rate-determining step.
  • To determine the rate law, you refer to a table of rates vs reactant concentrations.
    • [A] (M)[B] (M)[C] (M)rate (M/s)
    • r = k[A]x[B]y[C]z
    • From this table, a 2x increase in [A] corresponds to a 4x increase in the rate. 2x = 4, so x = 2.
    • A 2x increase in [B] corresponds to a 2x increase in the rate. 2y = 2, so y = 1.
    • A 2x increase in [C] corresponds to 1x (no change) in rate. 2z = 1, so z = 0.
    • r = k[A]2[B]1[C]0
    • r = k[A]2[B]
  • rate constant
    • The k in the rate law is the rate constant.
    • The rate constant is an empirically determined value that changes with different reactions and reaction conditions.
  • reaction order
    • Reaction order = sum of all exponents of the concentration variables in the rate law.
    • Reaction order in A = the exponent of [A]
    • Reaction TypeReaction OrderRate Law(s)
      Unimolecular1r = k[A]
      Bimolecular2r = k[A]2, r = k[A][B]
      Termolecular3r = k[A]3, r = k[A]2[B], r = k[A][B][C]
      Zero order reaction0r = k

Rate determining step

  • The slowest step of a multi-step reaction is the rate determining step.
  • The rate of the whole reaction = the rate of the rate determining step.
  • The rate law corresponds to the components of the rate determining step.

Dependence of reaction rate on temperature

  • Activation energy
    • Activated complex or transition state
      • Activated complex = what's present at the transition state.
      • In the transition state, bonds that are going to form are just beginning to form, and bonds that are going to break are just beginning to break.
      • The transition state is the peak of the energy profile.
      • The transition state can go either way, back to the reactants, or forward to form the products.
      • You can't isolate the transition state. Don't confuse the transition state with a reaction intermediate, which is one that you can isolate.
    • Interpretation of energy profiles showing energies of reactants and products, activation energy, ΔH for the reaction
      • reaction energy profile
      • The activation energy is the energy it takes to push the reactants up to the transition state.
      • ΔH is the difference between the reactant H and the product H (net change in H for the reaction).
      • H is heat of enthalpy.
      • Exothermic reaction = negative ΔH
      • Endothermic reaction = positive ΔH
  • Arrhenius equation
    • k = Ae-Ea/RT
    • k is rate constant, Ea is activation energy, T is temperature (in Kelvins), R is universal gas constant, A is a constant.
    • What this equation tells us: Low Ea, High T → large k → faster reaction.
    • reaction rate vs activation energy
    • reaction rate vs temperature
    • When activation energy approaches zero, the reaction proceeds as fast as the molecules can move and collide.
    • When temperature approaches absolute zero, reaction rate approaches zero because molecular motion approaches zero.

Kinetic control versus thermodynamic control of a reaction

  • A reaction can have 2 possible products: kinetic vs thermodynamic product.
    • Kinetic product = lower activation energy, formed preferentially at lower temperature.
    • Thermodynamic product = lower (more favorable/negative) ΔG, formed preferentially at higher temperature.
  • kinetics vs thermodynamics
  • Thermodynamics tells you whether a reaction will occur. In other words, whether it is spontaneous or not.
    • A reaction will occur if ΔG is negative.
    • ΔG = ΔH - TΔS
      Factors favoring a reactionFactors disfavoring a reaction
      Being exothermic (-ΔH)Being endothermic (+ΔH)
      Increase in entropy (positive ΔS)Decrease in entropy (negative ΔS)
      Temperature is a double-edged sword. High temperatures amplify the effect of the ΔS term, whether that is favoring the reaction (+ΔS) or disfavoring the reaction (-ΔS)
  • Kinetics tells you how fast a reaction will occur.
    • A reaction will occur faster if it has a lower activation energy.

Catalysts; the special case of enzyme catalysis

  • Catalysts speed up a reaction without getting itself used up.
  • Enzymes are biological catalysts.
  • Catalysts/enzymes act by lowering the activation energy, which speeds up both the forward and the reverse reaction.
  • Catalysts/enzymes alter kinetics, not thermodynamics.
  • Catalysts/enzymes help a system to achieve its equilibrium faster, but does not alter the position of the equilibrium.
  • Catalysts/enzymes increase k (rate constant, kinetics), but does not alter Keq (equilibrium).

Equilibrium in reversible chemical reactions

  • Law of Mass Action
    • The Law of Mass Action is the basis for the equilibrium constant.
    • What the Law of Mass Action says is basically, the rate of a reaction depends only on the concentration of the pertinent substances participating in the reaction.
    • Using the law of mass action, you can derive the equilibrium constant by setting the forward reaction rate = reverse reaction rate, which is what happens at equilibrium.
      • For the single-step reaction: aA + bB <--> cC + dD
      • rforward = rreverse
      • kforward[A]a[B]b = kreverse[C]c[D]d
      • kforward/kreverse = [C]c[D]d/[A]a[B]b
      • Keq = [C]c[D]d/[A]a[B]b
      • This holds true for single and multi-step reactions, the MCAT will not ask you to prove why this is so.
  • the equilibrium constant
    • There are 2 ways of getting Keq
      • From an equation, Keq = [C]c[D]d/[A]a[B]b
      • From thermodynamics, ΔG° = -RT ln (Keq)
        • Derivation: ΔG = 0 at equilibrium.
        • ΔG = ΔG° + RT ln Q
        • 0 = ΔG° + RT ln Qat equilibrium
        • ΔG° = -RT ln Qat equilibrium
      • At equilibrium:
        • ΔG = 0
        • rforward = rbackward
        • Q = Keq
    • Keq is a ratio of kforward over kbackward
      • If Keq is much greater than 1 (For example if Keq = 103), then the position of equilibrium is to the right; more products are present at equilibrium.
      • If Keq = 1, then the position of equilibrium is in the center, the amount of products is roughly equal to the amount of reactants at equilibrium.
      • If Keq is much smaller than 1 (For example if Keq = 10-3), then the position of equilibrium is to the left; more reactants are present at equilibrium.
    • The reaction quotient, Q, is the same as Keq except Q can be used for any point in the reaction, not just at the equilibrium.
      • If Q < Keq, then the reaction is at a point where it is still moving to the right in order to reach equilibrium.
      • If Q = Keq, the reaction is at equilibrium.
      • If Q > Keq, then the reaction is too far right, and is moving back left in order to reach equilibrium.
    • The reaction naturally seeks to reach its equilibrium
  • application of LeChatelier's principle
    • LeChatelier's principle: if you knock a system off its equilibrium, it will readjust itself to reachieve equilibrium.
    • A reaction at equilibrium doesn't move forward or backward, but the application of LeChatlier's principle means that you can disrupt a reaction at equilibrium so that it will proceed forward or backward in order to restore the equilibrium.
    • Reaction at equilibriumWhat will induce the reaction to move forwardWhat will induce the reaction to move backward
      A (aq) + B (aq) <--> C (aq) + D (aq)Add A or B. Remove C or D.Remove A or B. Add C or D.
      A (s) + B (aq) <--> C (l) + D (aq)Add B. Remove D. Adding or removing solids or liquids to a reaction at equilibrium doesn't do anything that will knock the system off its equilibrium. So, altering A and C won't make a difference.Remove B. Add D.
      A (s) + B (aq) <--> C (l) + D (g)Add B. Remove D. Remove (decrease) pressure.Remove B. Add D. Add (increase) pressure.
      A (s) + B (g) <--> C (l) + D (g)Add B. Remove D. Since both side of the balanced equation contains the same mols of gas products, modifying pressure is of no use.Remove B. Add D.
      A (s) + B (aq) <--> C (l) + D (aq) ΔH < 0Add B. Remove D. Removing heat by cooling the reaction.Remove B. Add D. Add heat by heating the reaction.

Relationship of the equilibrium constant and standard free energy change

  • ΔG = ΔG° + RT ln Q
    • Set ΔG = 0 at equilibrium.
    • Q becomes Keq at equilibrium.
  • 0 = ΔG° + RT ln (Keq)
  • ΔG° = -RT ln (Keq)