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Chapter 16. Reaction Rate Theory

Recommended Article: 【Chemistry】 Chemistry Table of Contents

1. Reaction Rate

2. Simple Reaction Rate Equation

3. Reaction Mechanism

4. Michaelis-Menten Equation

5. Inorganic Material Equations

6. Reaction Rate Factors

a. Pharmacology

b. Drug Synergy Modeling

c. Electrochemistry reaction rate theory

d. Reaction rate theory problem sets

1. Reaction Rate

⑴ Definition: Rate of change in concentration per unit time. Can be defined by the rate of disappearance or rate of formation.

① (Distinct Concept) Conversion rate = moles of reacted reactants / moles of supplied reactants

⑵ Reaction Equation Example

⑶ Expression of Reaction Rate

① Average Reaction Rate

② Instantaneous Reaction Rate

③ In reaction kinetics, only the instantaneous reaction rate is considered.

⑷ Unique Reaction Rate

⑸ Reaction Rate Measurement Experiment

① When measuring the reaction rate, measure the rate at the initial state.

② Increase the concentration of one substance by 2 or 3 times while keeping the concentration of all other substances fixed.

Figure 1. Example of Reaction Rate Measurement Experiment

2. Simple Reaction Rate Equation

⑴ Reaction Rate Equation: In the chemical reaction aA + bB + ··· → cC + dD, the reaction rate equation is as follows:

① H₂O(l), C(s), etc. always have a degree of 1 as their degree of freedom.

② Order of Reaction Rate = m + n + ···

③ Reaction order can be inferred by examining the trend of half-life.

⑵ Zero-Order Reaction

① Reaction Rate Equation

② Example 1: Reverse reaction of the Haber process

③ Example 2: Reaction of alcohol decomposition in the liver

⑶ First-Order Reaction: Constant Half-Life

① Reaction Rate Equation

② Example 1: Nuclear reaction: Radioactive elements undergo first-order reaction, resulting in constant half-life.

③ Example 2: First-order reaction near equilibrium, rather than at initial reaction

⑷ Second-Order Reaction

① Reaction Rate Equation

② Example 1: Dimerization

Figure 2. Dimerization using Diels-Alder reaction

3. Reaction Mechanism

⑴ Reaction Mechanism: A single reaction is divided into multiple elementary reactions, with each reactant contributing in proportion to its coefficient.

⑵ Elementary Reaction (Unit Step Reaction)

① Molecularity: The number of molecules participating in the reaction.

○ Unimolecular Reaction: Molecularity is 1

○ Bimolecular Reaction: Molecularity is 2

○ Termolecular Reaction: Molecularity is 3

○ Termolecular reactions are rare in nature due to the difficulty in arranging suitable reaction conditions.

○ Combining unimolecular and bimolecular reactions to form a mechanism is more natural.

② Elementary reactions determine the order of the overall reaction.

○ A → P: rate = k [A]

○ A + B → P: rate = k [A][B]

○ A + A → P: rate = k [A]²

○ A + B + C → P: rate = k [A][B][C]

○ A + A + B → P: rate = k [A]²[B]

○ A + A + A → P: rate = k [A]³

⑶ Method 1: Rate-Determining Step (RDS): Included in Method 2 and Method 3

① Reaction Mechanism Example

② Rate-Determining Step: The slowest step in the reaction mechanism, has the greatest impact on the overall reaction rate.

③ Overall Reaction Rate Equation

⑷ Method 2: Quasi-Steady-State Approximation

① Mechanism Example

○ If interpreted as Method 1, the overall reaction rate equation is as follows:

○ Limitation: If the first step is not the rate-determining step, the overall reaction rate equation becomes an expression involving intermediates, making it less useful.

② Assumption: The concentration of intermediate N2O2 reaches a rapid equilibrium in the first step.

③ Overall Reaction Rate Equation

⑸ Method 3: Rapid Equilibrium (Pre-Equilibrium Approximation): Preferred over Method 2

① Mechanism Example: Same as Method 2

② Assumption: Rapid equilibrium is assumed in the first step of the one-step reaction.

③ Overall Reaction Rate Equation

4. Michaelis-Menten Equation

⑴ Michaelis-Menten Equation

① Derivation 1: Quasi-Steady-State

○ k_cat: Reaction rate constant for ES → E + P

○ V: Rate of product formation

○ V_m = k_cat [ES] ≤ k_cat E₀ (where E₀ is total enzyme concentration)

② Derivation 2: Rapid Equilibrium: Mainly adopted. Assumes that the first reaction reaches equilibrium rapidly.

③ Graphical Methods

○ Michaelis-Menten Plot

○ Woolf-Hanes Equation

○ Eadie-Hofstee Equation

○ Lineweaver-Burk Plot: Also known as LB plot

○ x-axis: 1 / [S], y-axis: 1 / V, x-intercept: (-1 / K_m , 0), y-intercept: (0, 1 / V_m)

○ [S] ≫ K_m: V = V_m = k_catE₀

○ [S] ≪ K_m: V = V_m[S] / K_m = k_catE₀[S] / K_m

④ Analysis of Michaelis-Menten Equation

○ Michaelis Constant: Referred to as K_m

○ Meaning of K_m: Substrate concentration corresponding to half of the maximum velocity

○ Higher K_m indicates lower substrate affinity

○ Catalytic Turnover Number: Referred to as k_cat

○ Definition: Number of substrate molecules converted per enzyme molecule per unit time when the enzyme is saturated with substrate (unit: s^-1)

○ Equal to V_max / E_tot.

○ Catalytic Efficiency or Specificity Constant: Referred to as k_cat / K_m.

○ k_cat ≫ k_-1: k_cat / K_m ∽ k₁

○ When all active sites of the enzyme are filled with substrate, the enzyme is saturated, and the reaction is zero-order with V = V_max.

○ When determining V_m and K_m, a range should be chosen where the two points are not too close together and the reciprocal values are not too large (to avoid high errors).

⑵ Inhibitors

① Competitive Inhibition: Inhibitor competes with the substrate for the active site, thereby slowing down the enzyme reaction.

○ V_m remains constant.

○ K_m increases.

○ y-intercept remains the same in Lineweaver-Burk plot.

② Uncompetitive Inhibition: Inhibitor binds to the enzyme-substrate complex, slowing down the enzyme reaction.

○ V_m decreases.

○ K_m decreases.

○ Slope remains constant in Lineweaver plot

③ Noncompetitive Inhibition: Inhibitor binds to a site other than the active site (allosteric site), inhibiting the enzyme reaction noncompetitively.

○ V_m decreases.

○ K_m remains constant.

○ x-intercept remains the same in Lineweaver plot

⑶ Cooperativity

① The substrate itself regulates enzyme activity instead of an inhibitor or activator.

② Positive cooperativity: In a multisubstrate enzyme, a substrate that is already bound facilitates the binding of additional substrate molecules.

③ Negative cooperativity: It exists but is extremely rare.

④ Reaction scheme: When cooperativity occurs, $ES_n$ is formed almost immediately after $ES_1$ is formed. Therefore, the intermediate complexes $ES_1, \cdots, ES_{n-1}$ do not need to be considered.

⑤ Example: Oxygen saturation of hemoglobin

○ Hemoglobin consists of four subunits, each with one oxygen-binding site.

○ Hemoglobin exhibits a sigmoidal oxygen-saturation curve.

○ When one oxygen molecule binds to one binding site, the oxygen affinity of the remaining binding sites increases.

○ However, in a region with low oxygen concentration, once one oxygen molecule begins to dissociate, the others also dissociate.

○ Myoglobin consists of a single subunit and therefore shows no cooperativity. Consequently, it exhibits a hyperbolic oxygen-saturation curve.

5. Inorganic Material Equations

⑴ Eley-Rideal Mechanism

Figure 2. Eley-Rideal Mechanism

6. Reaction Rate Factors

⑴ Collision Theory

① Reaction Rate: Assumes that chemical reactions occur when molecules collide.

② Effective Collision: Assumes that reactions actually occur when molecules with sufficient energy collide in the right direction.

③ Activation Energy: Molecules must pass through an unstable state called the transition state to undergo a reaction, and the energy required for reactants to reach the transition state is referred to as activation energy.

⑵ Effective Collision Frequency

① Concentration: Increase in concentration → Increase in effective collision frequency → Increase in reaction rate

② Pressure (Gas): Increase in pressure → Increase in concentration → Increase in reaction rate

③ Surface Area (Solid): Increase in surface area → Increase in effective collision frequency → Increase in reaction rate

⑶ Activation Energy

① Minimum energy required to initiate a reaction.

② Activity

○ Definition: Enhances reaction rate

○ Indicates the extent of reactant conversion

○ Factor 1: Conversion rate / Reaction rate

○ Factor 2: Turnover number (TON) / Turnover frequency (TOF)

○ Definition: Number of reactant molecules converted per active site per unit time (unit: s^-1 or h^-1)

○ Typically ranges from 10^-2 to 10² s^-1.

○ For enzymes, it ranges from 10³ to 10⁷ s^-1.

○ Factor 3: Yield: Selectivity is determined by yield, and activity is determined by conversion rate.

③ Temperature: Increase in temperature → Increase in average kinetic energy → Increase in the number of molecules surpassing activation energy → Increase in reaction rate

○ Typically, reaction rate doubles or triples for every 10°C increase.

④ Catalyst: Does not cause a net change in the amount of reactants before and after the reaction, but alters the reaction pathway, changing activation energy.

○ Positive Catalyst (Catalyst): Decreases activation energy → Increases reaction rate

○ Negative Catalyst (Inhibitor): Increases activation energy → Decreases reaction rate

○ Homogeneous Catalyst: When the reactant and the catalyst are in the same phase (e.g., gas, liquid)

○ Example: 2SO₂(g) + O₂(g) → 2SO₃(g) (Catalyst: NO (g))

○ Heterogeneous Catalyst: When the reactant and the catalyst are in different phases

Table 1. Heterogeneous Catalyst

○ Component 1: Active phase: The metal that provides the active site for chemical reactions

○ Component 2: Support / Carrier: The metal with a high surface area that disperses and stabilizes the active phase. Increases efficiency, physical strength, selectivity, etc.

○ Component 3: Promoter: Enhances catalyst activity, specificity, and lifetime

○ Example: 2SO(g) + O(g) → 2SO₃(g) (Catalyst: Pt (s))

○ Example: 2H₂O₂ (ℓ) → 2H₂O (ℓ) + O₂ (g) (Catalyst: Manganese Dioxide (MnO2) (s))

⑤ Arrhenius Equation

○ A, E_a: Arrhenius parameters

○ A: Pre-exponential factor

○ E_a: Activation energy

○ exp (-E_a / RT): Energy requirement

○ σ v_rel N_A²: Collision rate

○ P: Steric requirement

○ k_experiment ＜ k_expected

○ Factors describing direction and arrangement

○ Always less than 1, sometimes below 10^-6

⑥ Multiplying rate constants adds activation energy, and dividing rate constants subtracts activation energy.

⑦ Brønsted-Evans-Polanyi (BEP) Principle: The free activation energy and the free energy of the reaction are proportional.

○ Like Hammond’s Postulate, it appears to be an empirical rule.

Input: 2018-12-27 18:50

Edited: 2022-04-22 12:10