Chemical Kinetics: Reaction Rate & Rate Law

Chemical Kinetics

Reaction Rate

• Reaction rate refers to the alteration in reactant or product concentration per unit of time.

Rate Law

• The rate law describes how reaction rates are related to reactant concentrations.
• The rate law for the reaction $aA + bB \rightarrow cC + dD$ is $rate = k[A]^m[B]^n$.
• $k$ represents the rate constant.
• [A] and [B] denote reactant concentrations.
• $m$ and $n$ are reaction orders relative to A and B.

Reaction Order

• The reaction order equals the sum of exponents in the rate law, which is m + n.
  • Zero order: The rate equals to $k$, indicating it's unrelated to reactant concentration.
  • First order: The rate equals to $k[A]$, meaning it's directly proportional to A's concentration.
  • Second order: The rate equals to $k[A]^2$ or $k[A][B]$. This is when rate equals the constant times the concentration of $A$ squared or, the constant times the concentration of $A$ and $B$.

Factors Affecting Reaction Rate

Temperature

• The Arrhenius Equation describes how temperature affects reaction rate.
  • $k = Ae^{-E_a/RT}$ is the Arrhenius Equation
  • $k$ is the rate constant.
  • $A$ is the pre-exponential factor.
  • $E_a$ denotes activation energy.
  • $R$ represents the gas constant, equivalent to 8.314 J/(mol⋅K).
  • $T$ is the temperature measured in Kelvin.

Catalysts

• Catalysts accelerate reactions by reducing their activation energy ($E_a$).

Reaction Mechanisms

Elementary Steps

• An elementary step constitutes a single stage within a reaction mechanism.

Rate-Determining Step

• The rate-determining step is the slowest within a reaction mechanism and establishes the reaction's overall rate.

Equilibrium

Equilibrium Constant

• For the reversible reaction $aA + bB \rightleftharpoons cC + dD$, the equilibrium constant ($K_c$) is:
  • $K_c = \frac{{[C]^c[D]^d}}{{[A]^a[B]^b}}$

Le Chatelier's Principle

• Le Chatelier's Principle dictates that a system at equilibrium adjusts to counteract any applied changes.
  • Concentration: Increasing reactants favors product formation; the reverse occurs with product increase.
  • Pressure: Increasing system pressure moves the equilibrium towards the side with fewer gas moles, and vice versa.
  • Temperature: Raising temperature favors endothermic reactions, and decreasing temperature favors the opposite.

Acid-Base Chemistry

Definitions

• Definitions for acids and bases according to different theories:
  • Arrhenius Acid: Generates $H^+$ ions in water.
  • Arrhenius Base: Generates $OH^-$ ions in water.
  • Bronsted-Lowry Acid: Donates a proton ($H^+$).
  • Bronsted-Lowry Base: Accepts a proton ($H^+$).
  • Lewis Acid: Accepts an electron pair.
  • Lewis Base: Donates an electron pair.

pH Scale

• Describe the acidity or basicity of a solution:
  • $pH = -log[H^+]$
  • $pOH = -log[OH^-]$
  • $pH + pOH = 14$ at $25^\circ C$

Acid-Base Strength

• Strong acids and bases:
  • Strong Acids: Fully dissociate in water (e.g., $HCl, H_2SO_4$)
  • Strong Bases: Fully dissociate in water (e.g., $NaOH, KOH$)
  • Weak Acids/Bases: Partially dissociate in water.

Acid Dissociation Constant ($K_a$)

• For a weak acid $HA$:
  • $HA \rightleftharpoons H^+ + A^-$
  • $K_a = \frac{{[H^+][A^-]}}{{[HA]}}$
  • $pK_a = -log(K_a)$

Base Dissociation Constant ($K_b$)

• For a weak base $B$:
  • $B + H_2O \rightleftharpoons BH^+ + OH^-$
  • $K_b = \frac{{[BH^+][OH^-]}}{{[B]}}$
  • $pK_b = -log(K_b)$

Relationship between $K_a$ and $K_b$

• For a conjugate acid-base pair:
  • $K_a \cdot K_b = K_w$
  • $K_w$ represents the ion product of water and equals $1.0 \times 10^{-14}$ at $25^\circ C$

Buffers

• Buffers are solutions resisting pH changes upon adding acid or base.
  • Henderson-Hasselbalch Equation: This equation used to calculate the pH of a buffer solution.
  • $pH = pK_a + log \frac{{[A^-]}}{{[HA]}}$ (acidic buffer)
  • $pOH = pK_b + log \frac{{[BH^+]}}{{[B]}}$ (basic buffer)

Titration

• Titration measures solution concentration via reaction with a known concentration solution.
  • Equivalence Point: The point where equal moles of acid and base have reacted.
  • Endpoint: The point where the indicator changes color during titration.

Indicators

• Indicators undergo color changes responding to solution pH levels.

Biochemistry I

Chapter 1: Amino Acids

• 20 common amino acids form the basis of proteins which are important for body function.
  • General Formula:
  • The general structure of an amino acid is $NH_2-CHR-COOH$
  • Each amino acid has a different "R" group.

Classes of Amino Acids

• Includes multiple classes such as nonpolar, aromatic, polar, positively charged and negatively charged
  • Nonpolar, Aliphatic R Groups
    • Hydrophobic
    • Includes Glycine, Alanine, Proline, Valine, Leucine, Isoleucine, Methionine
  • Aromatic R Groups
    • Relatively nonpolar
    • Includes Phenylalanine, Tyrosine, Tryptophan
  • Polar, Uncharged R Groups
    • Hydrophilic
    • Includes Serine, Threonine, Cysteine, Asparagine, Glutamine
  • Positively Charged R Groups
    • Hydrophilic
    • Includes Lysine, Arginine, Histidine
  • Negatively Charged R Groups
    • Hydrophilic
    • Includes Aspartate, Glutamate

Titration of Amino Acids

• Titration curves reveal two proton dissociation stages because they act as weak acids with multiple dissociable $H^+$.

Peptide Bond Formation

• Amino acids form peptides and proteins via peptide bonds.
• These are amide bonds linking the α-carboxyl of one amino acid to the α-amino of another, releasing water.

Protein Structure

• Includes different structures, primary, secondary, tertiary, quanternary

Primary Structure

• Linear amino acid sequence dictated by amino acid order.
  • The primary structure determines the higher levels of protein structure.

Secondary Structure

• Local spatial organization of the polypeptide backbone such as α-helix and β-sheet.

Tertiary Structure

• Describes overall 3D arrangement stabilized by hydrophobic interactions, hydrogen bonds, disulfide bonds, and ionic interactions.

Quaternary Structure

• Arrangement of polypeptide subunits.
  • Only present in multi-subunit proteins.

Protein Folding

• Is the process where proteins achieve their native 3D structure, driven by hydrophobic effects.
  • It is aided by chaperone proteins to avoid misfolding and aggregation.

Protein Misfolding and Disease

• Can lead to diseases which involve misfolded proteins aggregating into amyloid plaques.

Enzymes

• Biology catalysts, commonly made up of proteins which accelerates the rate in living organisms

Enzyme Kinetics

• Focuses on enzyme-catalyzed reaction rates described mathematically by the Michaelis-Menten equation: $V = \frac{V_{max}[S]}{K_m + [S]}$
  • V represents initial reaction rate.
  • $V_{max}$ is the maximum reaction rate.
  • $[S]$ the substrate concentration is concentration.
  • $K_m$ stands for the Michaelis constant.

Enzyme Inhibition

• Is when molecules reduce the activity of enzymes.
  • This inhibition can be competitive, uncompetitive, or noncompetitive.

Regulation of Enzyme Activity

• Includes multiple mechanisms that can regulate activity
  • Allosteric control
  • Covalent modification
  • Proteolytic cleavage
  • Changes in enzyme concentration

Learn about reaction rates and how they relate to reactant concentrations through the rate law. Explore zero, first, and second-order reactions and how to determine the reaction order. Understand the factors affecting chemical kinetics.