Chemical Kinetics: Rate Laws, Reaction Orders

Chemical Kinetics

• Reaction rate represents the change in concentration of reactants or products over time.

Rate Law

• This law shows relationship between reaction rate and reactant concentrations.
  • For the reaction $aA + bB \rightarrow cC + dD$, the rate law is $rate = k[A]^m[B]^n$
  • $k$ is the rate constant, $[A]$ and $[B]$ are reactant concentrations.
  • $m$ and $n$ are reaction orders with respect to A and B.

Reaction Order

• Reaction order involves sum of exponents in reaction rate law; $m + n$ in $rate = k[A]^m[B]^n$.
  • Zero order: rate = k, so rate doesn't depend on reactant concentration.
  • First order: rate = k[A], rate directly proportional to A concentration.
  • Second order: rate = k[A]^2 or rate = k[A][B].

Factors Affecting Reaction Rate

• Temperature affects reaction rate.
  • Arrhenius Equation: $k = Ae^{-E_a/RT}$.
  • $k$ = rate constant, $A$ = pre-exponential factor,.
  • $E_a$ = activation energy, $R$ = gas constant ($8.314 J/(mol \cdot K)$).
  • $T$ = temperature in Kelvin.
• Catalysis increases reaction rate.
  • Catalysts operating by lowering the activation energy ($E_a$).
• Catalyst function is to lower activation energy of reaction.

Reaction Mechanisms

• Elementary Step: A single step in reaction mechanism.
• Rate-Determining Step: The slowest step that dictates overall reaction rate.

Equilibrium

• For reversible reaction $aA + bB \rightleftharpoons cC + dD$, equilibrium constant ($K_c$) is $K_c = \frac{{[C]^c[D]^d}}{{[A]^a[B]^b}}$
• Le Chatelier's Principle: A system at equilibrium shifts to relieve stress from changed conditions.

Changes in Condition

• Concentration: Increase in reactants shifts equilibrium to products, and vice versa.
• Pressure: Higher pressure shifts equilibrium to side with fewer gas moles, and vice versa.
• Temperature: Higher temperature favors endothermic reaction, and vice versa.

Acid-Base Chemistry

Definitions

• Arrhenius Acid: Produces $H^+$ in water.
• Arrhenius Base: Produces $OH^-$ in water.
• Bronsted-Lowry Acid: Donates $H^+$ proton.
• Bronsted-Lowry Base: Accepts $H^+$ proton.
• Lewis Acid: Accepts electron pair.
• Lewis Base: Donates electron pair.

pH Scale

• Formula to calculate pH is $pH = -log[H^+]$.
• Formula to calculate pOH is $pOH = -log[OH^-]$.
• The pH + pOH = 14 at $25^\circ C$.

Acid-Base Strength

• Strong acids fully dissociate in water ($HCl, H_2SO_4$).
• Strong bases are fully dissociate in water ($NaOH, KOH$).
• Weak acids/bases only partially dissociate in water.

The Dissociation Constant ($K_a$)

• For weak acid $HA$, $HA \rightleftharpoons H^+ + A^-$.
• Determined by the formula $K_a = \frac{{[H^+][A^-]}}{{[HA]}}$
• $pK_a = -log(K_a)$.

Base Dissociation Constant ($K_b$)

• For weak base $B$, $B + H_2O \rightleftharpoons BH^+ + OH^-$.
• Determined by the formula $K_b = \frac{{[BH^+][OH^-]}}{{[B]}}$
• $pK_b = -log(K_b)$

Relationship between $K_a$ and $K_b$

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

Buffers

• Resists pH changes when small amounts of acid or base added.

Henderson-Hasselbalch Equation

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

Titration

• Process to determine solution concentration by reacting it with known concentration.

Equivalence Point

• In acid-base titration: the point when two reactants have reacted.

Endpoint

• In acid-base titration: the point when the indicator changes color.

Indicators

• Substances that change color depending on solution pH.

Biochemistry I

Amino Acids

Introduction

• Amino acids are protein building blocks.
• Proteins are vital for most bodily functions.
• Includes 20 common types.

General Formula

• Has the structure $NH_2-CHR-COOH$
• Different R group for each amino acid.

Classes of Amino Acids

Nonpolar, Aliphatic R Groups

• They're hydrophobic
• Includes: Glycine, Alanine, Proline, Valine, Leucine, Isoleucine, Methionine.

Aromatic R Groups

• Are relatively nonpolar
• Includes Phenylalanine, Tyrosine, Tryptophan.

Polar, Uncharged R Groups

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

Positively Charged R Groups

• These are Hydrophilic
• Includes Lysine, Arginine, Histidine.

Negatively Charged RGroups

• These are hydrophilic
• Includes Aspartate, Glutamate.

Titration of Amino Acids

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

Peptide Bond Formation

• Amino acids are linked together by peptide bonds.
• A peptide bond is an amide bond between the $\alpha$-carboxyl group of one amino acid and the $\alpha$-amino group of another.
• Formation requires water loss.

Protein Structure

Primary Structure

• Linear amino acid sequence determines the structure.

Secondary Structure

• The local spatial arrangement of the polypeptide backbone
• Includes $\alpha$-helix and $\beta$-sheet.

Tertiary Structure

• Overall 3D arrangement of all atoms.
• Stabilized by hydrophobic interactions, hydrogen/disulfide bonds, and ionic interactions.

Quaternary Structure

• Protein arrangement of multiple polypeptide chains.
• Not all proteins have quaternary structure.
• Held together by same interactions stabilizing tertiary structure.

Protein Folding

• It's the acquiring of 3D structure.
• Driven by hydrophobic effect, causing nonpolar amino acids to cluster in the protein's interior.
• Assisted by chaperone proteins to prevent misfolding and aggregation.

Protein Misfolding and Disease

• It Can lead to diseases, like Alzheimer's, Parkinson's, and Huntington's.
• Misfolded proteins aggregate, which results in the formations of amyloid plagues.

Enzymes

• The activity of these biological catalysts speed up reactions in living organisms.
• Consists of proteins.

Enzyme Kinetics

• Involves study of rates of enzyme-catalyzed reactions.
• Described mathematically with by the Michaelis-Menten equation: $V = \frac{V_{max}[S]}{K_m + [S]}$
• Where V is the reaction rate, $V_{max}$ is the maximum rate.
• $[S]$ is the substrate concentration and $K_m$ is the Michaelis constant.

Enzyme Inhibition

• Reduce the activity of enzymes.
• They can be competitive, uncompetitive, or noncompetitive.

Regulation of Enzyme Activity

• Can be regulated by: allosteric control, covalent modification, proteolytic cleavage, changes in enzyme concentration.

Explore chemical kinetics, including reaction rates, rate laws, and reaction orders. Understand zero, first, and second-order reactions. Learn about factors affecting reaction rates, like temperature and the Arrhenius Equation.