Chapter 16. Reaction Rate Theory
Recommended Article : 【Chemistry】 Chemistry Table of Contents
2. Simple Reaction Rate Equation
5. Inorganic Material Equations
a. Pharmacology
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.
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
○ kcat : Reaction rate constant for ES → E + P
○ V : Rate of product formation
○ Vm = kcat [ES] ≤ kcat 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 / Km , 0), y-intercept : (0, 1 / Vm)
○ [S] ≫ Km : V = Vm = kcatE0
○ [S] ≪ Km : V = Vm[S] / Km = kcatE0[S] / Km
④ Analysis of Michaelis-Menten Equation
○ Michaelis Constant : Referred to as Km
○ Meaning of Km : Substrate concentration corresponding to half of the maximum velocity
○ Higher Km indicates lower substrate affinity
○ Catalytic Turnover Number : Referred to as kcat
○ Definition : Number of substrate molecules converted per enzyme molecule per unit time when the enzyme is saturated with substrate (unit: s^-1)
○ Equal to Vmax / Etot
○ Catalytic Efficiency or Specificity Constant
: Referred to as kcat / Km
○ kcat ≫ k-1 : kcat / Km ∽ k1
○ When all active sites of the enzyme are filled with substrate, the enzyme is saturated, and the reaction is zero-order with V = Vmax.
○ When determining Vm and Km, 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.
○ Vm remains constant
○ Km 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.
○ Vm decreases
○ Km 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.
○ Vm decreases
○ Km remains constant
○ x-intercept remains the same in Lineweaver plot
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 10^2 s^-1
○ For enzymes, it ranges from 10^3 to 10^7 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, Ea : Arrhenius parameters
○ A : Pre-exponential factor
○ Ea : Activation energy
○ exp (-Ea / RT) : Energy requirement
○ σ vrel NA2 : Collision rate
○ P : Steric requirement
○ kexperiment ＜ kexpected
○ 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 (Note) 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