Chemical Kinetics: Rate Laws and Reaction Order

Chemical Kinetics

• Reaction rate defined as the change in concentration of reactants or products per unit time.

Rate Law

• The rate law ($rate = k[A]^m[B]^n$) expresses the relationship between the rate of a reaction and the concentrations of the reactants.
  • $k$ is the rate constant.
  • [A] and [B] are concentrations of reactants.
  • $m$ and $n$ are reaction orders with respect to A and B.

Reaction Order

• Reaction order is the sum of the exponents in the rate law (m + n).
  • Zero order: rate = k (rate is independent of reactant concentration).
  • First order: rate = k[A] (rate is directly proportional to the concentration of A).
  • Second order: rate = k[A]^2 or rate = k[A][B].

Factors Affecting Reaction Rate

Temperature

• Temperature affects reaction rate

• Arrhenius Equation: $k = Ae^{-E_a/RT}$

  • $k$ is the rate constant
  • $A$ is the pre-exponential factor
  • $E_a$ is the activation energy
  • $R$ is the gas constant ($8.314 J/(mol \cdot K)$)
  • $T$ is the temperature in Kelvin

Catalysts

• Catalysts lower the activation energy ($E_a$) of a reaction, and increasing the reaction rate.

Reaction Mechanisms

Elementary Steps

• Elementary step constitutes a single step in a reaction mechanism

Rate-Determining Step

• Rate-determining step involves the slowest step in a reaction mechanism which determine the overall rate of the reaction.

Equilibrium

Equilibrium Constant

• For a 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 states that if a change of condition is applied to a system in equilibrium, the system will shift in a direction that relieves the stress.

Changes in Condition

• Concentration: Adding reactants will shift the equilibrium towards products, and vice versa.
• Pressure: Increasing pressure will shift the equilibrium towards the side with fewer moles of gas, and vice versa.
• Temperature: Increasing temperature will favor the endothermic reaction, and vice versa.

Acid-Base Chemistry

Definitions

• Arrhenius Acid: Produces $H^+$ ions in water.
• Arrhenius Base: Produces $OH^-$ 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

• $pH = -log[H^+]$
• $pOH = -log[OH^-]$
• $pH + pOH = 14$ at $25^\circ C$

Acid-Base Strength

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

Acid Dissociation Constant ($K_a$)

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

Base Dissociation Constant ($K_b$)

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

Relationship between $K_a$ and $K_b$

• For a conjugate acid-base pair, $K_a \cdot K_b = K_w$, where $K_w$ is the ion product of water ($1.0 \times 10^{-14}$ at $25^\circ C$)

Buffers

• A buffer is a solution that resists changes in pH when small amounts of acid or base are added.

Henderson-Hasselbalch Equation

• For acidic buffer: $pH = pK_a + log \frac{{[A^-]}}{{[HA]}}$
• For basic buffer: $pOH = pK_b + log \frac{{[BH^+]}}{{[B]}}$

Titration

• Titration involves a process used to determine the concentration of a solution by reacting it with a solution of known concentration.

Equivalence Point

• Equivalence point denotes the point in a titration where the acid and base have completely reacted.

Endpoint

• Endpoint is the point in a titration where the indicator changes color.

Indicators

• Indicators are substances that change color depending on the pH of the solution.

Biochemistry I

Amino Acids

• Amino acids are the building blocks of proteins and proteins being involved in almost every function of the human body.
• There are 20 common amino acids.

General Formula

• The general formula of an amino acid is $NH_2-CHR-COOH$, with each amino acid has a different "R" group.

Classes of Amino Acids

Nonpolar, Aliphatic R Groups

• These are hydrophobic, including Glycine, Alanine, Proline, Valine, Leucine, Isoleucine, Methionine.

Aromatic R Groups

• These are relatively nonpolar, which include Phenylalanine, Tyrosine, Tryptophan.

Polar, Uncharged R Groups

• These are hydrophilic, including Serine, Threonine, Cysteine, Asparagine, Glutamine.

Positively Charged R Groups

• These are hydrophilic and involves Lysine, Arginine, Histidine.

Negatively Charged R Groups

• These are hydrophilic, involving Aspartate, Glutamate.

Titration of Amino Acids

• Amino acids are weak acids having at least two dissociable protons, $H^+$.
• Titration curve reveals two distinct stages of deprotonation when an amino acid is titrated with a base, such as $NaOH$.

Peptide Bond Formation

• Amino acids can be linked together through peptide bonds to form peptides and proteins.
• A peptide bond is an amide bond between the $\alpha$-carboxyl group of one amino acid and the $\alpha$-amino group of another.
• The formation of a peptide bond involves the loss of a molecule of water.

Protein Structure

Primary Structure

• It represents the linear sequence of amino acids.
• It is determined by by the sequence of the amino acids in the polypeptide chain.
• It determines the higher levels of protein structure.

Secondary Structure

• Secondary structure: local spatial arrangement of the polypeptide backbone.
• The two most common types of secondary structure: $\alpha$-helix and $\beta$-sheet.

Tertiary Structure

• Tertiary Structure involves the overall three-dimensional arrangement of all the atoms in the protein.
• Variety of interactions stabilizees the tertiary structure, involving hydrophobic interactions, hydrogen bonds, disulfide bonds, and ionic interactions.

Quaternary Structure

• Quaternary structure represents the arrangement of multiple polypeptide chains in a multi-subunit protein.
• Proteins with quaternary structure have two or more polypeptide chains, called subunits, which are held together by the same types of interactions that stabilize tertiary structure.

Protein Folding

• Protein folding involves the process in which a protein acquires its native three-dimensional structure.
• This is driven by the hydrophobic effect, where nonpolar amino acids will cluster in the interior of the protein.
• Protein folding is often assisted by chaperone proteins, which prevent misfolding and aggregation.

Protein Misfolding and Disease

• Protein misfolding can lead to a variety of diseases, including Alzheimer's disease, Parkinson's disease, and Huntington's disease.
• In these diseases, misfolded proteins aggregate to form amyloid plaques.

Enzymes

• Enzymes biological catalysts that speed up the rate of chemical reactions in living organisms.
• Enzymes made of proteins.

Enzyme Kinetics

• Enzyme kinetics involves the study of the rates of enzyme-catalyzed reactions.

• Michaelis-Menten equation constitutes a mathematical model that describes the kinetics of many enzymes, where $V = \frac{V_{max}[S]}{K_m + [S]}$

  • $V$ is the initial reaction rate
  • $V_{max}$ is the maximum reaction rate
  • $[S]$ is the substrate concentration
  • $K_m$ is the Michaelis constant

Enzyme Inhibition

• Enzyme inhibitors are molecules that reduce the activity of enzymes and can be competitive, uncompetitive, or noncompetitive. Enzymes can be inhibited by molecules.

Regulation of Enzyme Activity

• Enzyme activity can be regulated by a variety of mechanisms, including:
  • Allosteric control
  • Covalent modification
  • Proteolytic cleavage
  • Changes in enzyme concentration

Understand chemical kinetics, rate laws, and reaction orders. Explore how temperature affects reaction rates, including the Arrhenius equation. Learn about activation energy and catalysts.