# 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) 1 1 1 1 2 1 1 4 1 2 1 2 1 1 2 1
• 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 Type Reaction Order Rate Law(s) Unimolecular 1 r = k[A] Bimolecular 2 r = k[A]2, r = k[A][B] Termolecular 3 r = k[A]3, r = k[A]2[B], r = k[A][B][C] Zero order reaction 0 r = 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
• 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.
• 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.
• 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 reaction Factors 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.