Atomic Structure
A = Mass number = protons + neutrons
Z = Atomic number = # of protons
Note: Atomic Weight = weighted average
Scientist Contributions
Rutherford Model: 1911. Electrons surround a nucleus.
BohrModel: 1913.Described orbits in more detail. Farther orbits = ↑Energy
Photon emitted when n↓, absorbed when n↑.
AHED Mnemonic:
Absorb light
Higher potential
Excited
Distant from nucleus
HeisenbergUncertainty: It is impossible to know the momentum and position simultaneously.
Hund’s Rule: e- only double up in orbitals if all orbitals first have 1 e-.
Pauli Exclusion Principle: Paired electrons must be +½, –½.
Constants
Avogadro’s Number: 6.022 × 10²³ = 1 mol
Planck’s (h): 6.626 × 10⁻³⁴ J·s
Speed of Light (c): 3.0 × 10⁸ m/s
Light Energy
E= hc/λ E=hf
f = frequency
h = Planck’s constant
c = speed of light
| Quantum Number | Name | What it Labels | Possible Values | Notes |
| n | Principal | e- energy level or shell number | 1, 2, 3, … | Except for d- and f-orbitals, the shell # matches the row of the periodic table. |
| l | Azimuthal | 3D shape of orbital | 0, 1, 2, …, n-1 | 0 = s orbital 1 = p orbital 2 = d orbital 3 = f orbital 4 = g orbital |
| mi | Magnetic | Orbital sub-type | ntegers –l→ +l | |
| ms | Spin | Electron spin | +½, –½ |
Maximum e- in terms of n = 2n²
Maximum e- in subshell = 4l + 2
Free Radical: An atom or molecule with an unpaired electron.
Diamagnetic vs. Paramagnetic
Diamagnetic: All electrons are paired
↑↓ REPELLED by an external magnetic field
Paramagnetic: 1 or more unpaired electrons
↑ PULLED into an external magnetic field
Follow Hund’s rule to build the atom’s electron configuration. If 1 or more orbitals have just a single electron, the atom is paramagnetic. If there are no unpaired electrons, then the atom is diamagnetic.
Examples:
He = 1s² = diamagnetic and will repel magnetic fields.
C = 1s²2s²2p² = paramagnetic and will be attracted to magnetic fields.
3D shapes of s, p, d, and f orbitals
The Periodic Table
Bonding and Chemical Interactions
Covalent Bonds
Covalent Bond:
Formed via the sharing of electrons between two elements of similar EN.
Bond Order:
Refers to whether a covalent bond is a single, double, or triple bond. As bond order increases → bond strength ↑, bond energy ↑, bond length ↓.
Nonpolar Bonds:
ΔEN < 0.5.
Polar Bonds:
ΔEN is between 0.5 and 1.7.
Coordinate Covalent Bonds:
A single atom provides both bonding electrons. Most often found in Lewis acid-base chemistry.
Intermolecular Forces
Intermolecular Forces
Hydrogen O-H, N-H, F-H
Dipole-Dipole
London Dispersion
Strength ↑
Note: Van de Waals Forces is a general term that includes Dipole-Dipole forces and London Dispersion forces.
Bond Type According to ΔEN
0 → Nonpolar covalent
0.5 → Polar covalent
1.7 → Ionic
Ionic Bonds
Formed via the transfer of one or more electrons from an element with a relatively low IE to an element with a relatively high electron affinity ΔEN > 1.7.
Cation: POSITIVE +
Anion: NEGATIVE –
Crystalline Lattices: Large, organized arrays of ions.N
Sigma and Pi Bonds
— 1 σ
═ 1 σ 1 π
≡ 1 σ 2 π
Formal Charge
Formal Charge = valence e⁻ – dots – sticks
Dots: Nonbonding e⁻
Sticks: Pair of bonding electrons
Valence Shell Electron Pair Repulsion Theory (VSEPR)
Electronic Geometry: Bonded and lone pairs treated the same.
Molecular Shape: Lone pairs take up more space than a bond to another atom.
| Hybridization | e⁻ Groups Around Central Atom | Bonded Pairs | Lone Pairs | Electronic Geometry | Molecular Shape | Bond Angle |
| sp | 2 | 2 1 | 0 1 | Linear | Linear | 180° |
| sp² | 3 | 3 2 1 | 0 1 2 | Trigonal Planar | Trigonal Planar, Bent, Linear | 120° |
| sp³ | 4 | 4 3 2 1 | 0 1 2 3 | Tetrahedral | Tetrahedral, Trigonal Pyramidal, Bent, Linear | 109.5° |
| sp³d | 5 | 5 4 3 2 | 0 1 2 3 | Trigonal Bipyramidal | Trigonal Bipyramidal, Seesaw, T-Shaped, Linear | 90° & 120° |
| sp³d² | 6 | 6 5 4 | 0 1 2 | Octahedral | Octahedral, Square Pyramidal, Square Planar | 90° |
Compounds and Stoichiometry
Equivalents & Normality
Equivalent Mass: Mass of an acid that yields 1 mole of H⁺ or mass of a base that reacts with 1 mole of H⁺.
GEW = molar mass / mol H⁺ or e⁻
Equivalents = mass of compound / GEW
Normality = Eq / L
For acids, the # of equivalents (n) is the # of H⁺ available from a formula unit.
Molarity = normality / mol H⁺ or e⁻
Compound Formulas
Empirical: Simplest whole-number ratio of atoms.
Molecular: Multiple of empirical formula to show exact # of atoms of each element.
Types of Reactions
Combination: Two or more reactants forming one product
2H₂(g) + O₂(g) → 2H₂O(g)
Decomposition: Single reactant breaks down
2HgO(s) → 2Hg(l) + O₂(g)
Combustion: Involves a fuel, usually a hydrocarbon, and O₂(g). Commonly forms CO₂ and H₂O.
CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(g)
Single-Displacement: An atom/ion in a compound is replaced by another atom/ion
Cu(s) + 2AgNO₃(aq) → Ag(s) + Cu(NO₃)₂(aq)
Double-Displacement (metathesis): Elements from two compounds swap places
CaCl₂(aq) + 2AgNO₃(aq) → Ca(NO₃)₂(aq) + 2AgCl(s)
Neutralization: A type of double-replacement reaction
Acid + base → salt + H₂O
HCl(aq) + NaOH(aq) → NaCl(aq) + H₂O(l)
Naming Ions
For elements (usually metals) that can form more than one positive ion, the charge is indicated by a Roman numeral in parentheses following the name of the element.
Fe²⁺ Iron(II) Fe³⁺ Iron(III)
Cu⁺ Copper(I) Cu²⁺ Copper(II)
Older method: –ous and –ic to the atoms with lesser and greater charge, respectively.
Fe²⁺ Ferrous Fe³⁺ Ferric
Cu⁺ Cuprous Cu²⁺ Cupric
Monatomic anions drop the ending of the name and add –ide.
H⁻ Hydride
F⁻ Fluoride O²⁻ Oxide
S²⁻ Sulfide N³⁻ Nitride P³⁻ Phosphide
Oxyanions = polyatomic anions that contain oxygen.
- MORE Oxygen = –ate
- LESS Oxygen = –ite
NO₃⁻ Nitrate NO₂⁻ Nitrite
SO₄²⁻ Sulfate SO₃²⁻ Sulfite
In extended series of oxyanions, prefixes are also used.
- MORE Oxygen = Hyper- (per–)
- LESS Oxygen = Hypo–
ClO⁻ Hypochlorite
ClO₂⁻ Chlorite
ClO₃⁻ Chlorate
ClO₄⁻ Perchlorate
Polyatomic anions that gain H⁺ to form anions of lower charge add the word Hydrogen or Dihydrogen to the front.
HCO₃⁻ Hydrogen carbonate or bicarbonate
HSO₄⁻ Hydrogen sulfate or bisulfate
H₂PO₄⁻ Dihydrogen phosphate
Acid Names
–ic: Have one MORE oxygen than –ous.
–ous: Has one FEWER oxygen than –ic.
Chemical Kinetics
| m | Order | Rate Law | Integrated Rate Law | Half-Life | Units of Rate Constant |
| 0 | Zeroth Order | R = k | [A] = [A]₀ − kt | t½ = [A]₀ / 2k | M/s |
| 1 | First Order | R = k[A] | [A] = [A]₀ · e^(-kt) | t½ = ln(2) / k | 1/s |
| 2 | Second Order | R = k[A]² | 1/[A] = 1/[A]₀ + kt | t½ = 1 / (k[A]₀) | 1/m s |
Reaction Order and Michaelis-Menten Curve:
At low substrate concentrations, the reaction is approximately first order. At very high substrate concentrations, the reaction approximates zero order, since the rate no longer depends on substrate concentration.
Types of Reactions
Combination: Two or more reactants forming one product.
2H₂(g) + O₂(g) → 2H₂O(g)
Decomposition: Single reactant breaks down.
2HgO(s) → 2Hg(l) + O₂(g)
Combustion: Involves a fuel, usually a hydrocarbon, and O₂(g). Commonly forms CO₂ and H₂O.
CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(g)
Single-Displacement: An atom or ion in a compound is replaced by another atom or ion.
Cu(s) + AgNO₃(aq) → Ag(s) + CuNO₃(aq)
Double-Displacement (metathesis): Elements from two compounds swap places.
CaCl₂(aq) + 2AgNO₃(aq) → Ca(NO₃)₂(aq) + 2AgCl(s)
Neutralization: A type of double-replacement reaction.
Acid + base → salt + H₂O
HCl(aq) + NaOH(aq) → NaCl(aq) + H₂O(l)
Hydrolysis: Using water to break the bonds in a molecule.
Gibbs Free Energy
ΔG = Eₐ – Eₐrev
- -ΔG = Exergonic
- +ΔG = Endergonic
Reaction Mechanisms
Overall Reaction: A₂ + 2B → 2AB
Step 1: A₂ + B → A₂B (slow)
Step 2: A₂B + B → 2AB (fast)
A₂B is an intermediate.
Slow step is the rate-determining step.
Arrhenius Equation
Arrhenius: k = A × e^(-Eₐ / RT)
k = rate constant
A = frequency factor
Eₐ = activation energy
R = gas constant = 8.314 J/(mol·K)
T = temp in K
Trends:
↑T ⇒ ↑k
↑T ⇒ ↑k (Exponent gets closer to 0. Exponent becomes less negative)
Equilibrium
Equilibrium Constant
General reaction:
aA + bB ↔ cC + dD
Equilibrium constant (Keq):
[C]c · [D]d [A]a · [B]b Keq
Reaction quotient (Qc):
[C]c · [D]d [A]a · [B]b Qc
Note: Exclude pure solids and pure liquids from the expression.
Reaction Quotient
- Q < Kₑq: ΔG < 0, reaction →
- Q = Kₑq: ΔG = 0, equilibrium
- Q > Kₑq: ΔG > 0, reaction ←
Kinetic (Eₐ) and Thermodynamic (ΔG) Control
Kinetic Products: HIGHER in free energy than thermodynamic products and can form at lower temperatures.
“Fast” products because they can form more quickly under such conditions.
Thermodynamic Products: LOWER in free energy than kinetic products, more stable. Slower but more spontaneous (more negative ΔG).
Le Châtelier’s Principle
If a stress is applied to a system, the system shifts to relieve that applied stress.
Example: Bicarbonate Buffer
CO₂(aq) + H₂O ⇌ H₂CO₃(aq) ⇌ H⁺(aq) + HCO₃⁻(aq)
- ↓pH → ↑respiration to blow off CO₂
- ↑pH → ↓respiration, trapping CO₂
Thermochemistry
Systems and Processes
- Isolated System: Exchange neither matter nor energy with the environment.
- Closed System: Can exchange energy but not matter with the environment.
- Open System: Can exchange BOTH energy and matter with the environment.
- Isothermal Process: Constant temperature.
- Adiabatic Process: Exchange no heat with the environment.
- Isobaric Process: Constant pressure.
- IsoVolumetric (Isochoric): Constant volume.
States and State Functions
State Functions: Describe the physical properties of an equilibrium state. Are pathway independent. Pressure, density, temp, volume, enthalpy, internal energy, Gibbs free energy, and entropy.
Standard Conditions: 298 K, 1 atm, 1 M
(Note: In gas law calculations, Standard Temperature and Pressure (STP) is 0°C, 1 atm.)
Phase Changes:
- Fusion: Solid → liquid
- Freezing: Liquid → solid
- Vaporization: Liquid → gas
- Sublimation: Solid → gas
- Deposition: Gas → solid
- Triple Point: Point in phase diagram where all 3 phases exist.
- Supercritical Fluid: Density of gas = density of liquid, no distinction between those two phases.
Gibbs Free Energy (G)
ΔG=ΔH−TΔS
| ΔH | ΔS | Outcome |
|---|---|---|
| + | + | Spontaneous at HIGH temps |
| + | – | Non-spontaneous at all temps |
| – | + | Spontaneous at all temps |
| – | – | Spontaneous at LOW temps |
Note: Temperature dependent when ΔH and ΔS have same sign.
Temperature (T) and Heat (q)
Temperature (T): Scaled measure of average kinetic energy of a substance.
- Celsius vs Fahrenheit:
0°C = 32°F (Freezing Point H₂O)
25°C = 75°F (Room Temp)
37°C = 98.6°F (Body Temp)
°F = ( 9⁄5 °C ) + 32
Heat (q): The transfer of energy that results from differences of temperature. Hot transfers to cold.
Enthalpy (H)
Enthalpy (H): A measure of the potential energy of a system found in intermolecular attractions and chemical bonds.
Phase Changes:
- Solid → Liquid → Gas: ENDOTHERMIC (absorbs heat).
- Gas → Liquid → Solid: EXOTHERMIC (releases heat).
Hess’s Law: Enthalpy changes are additive.
ΔH°rxn from heat of formations
ΔH°rxn = ΔH°products − ΔH°reactants
ΔH°rxn from bond dissociation energies
ΔH°rxn = ΔH°reactants − ΔH°product
Entropy (S)
Entropy (S): A measure of the degree to which energy has been spread throughout a system or between a system and its surroundings.
ΔS = qrev⁄T
Standard Entropy of Reaction:
ΔS°rxn = ΣΔS°products − ΣΔS°reactants
Note: Entropy is maximized at equilibrium.
Entropy (S)
Entropy (S): A measure of the degree to which energy has been spread throughout a system or between a system and its surroundings.
ΔS = qrev⁄T
Standard Entropy of Reaction:
ΔS°rxn = ΔS°f,products − ΣΔS°f,reactants
Note: Entropy is maximized at equilibrium.
Gibbs Free Energy (G)
Gibbs Free Energy (G): Derived from enthalpy and entropy.
ΔG = ΔH − TΔS
Standard Gibbs Free Energy of Reaction:
ΔG°rxn = ΔG°f,products − ΔG°f,reactants
From Equilibrium Constant (Keq):
ΔG°rxn = −RT ln(Keq)
From Reaction Quotient (Q):
ΔGrxn = ΔG°rxn + RT ln(Q)
ΔGrxn = RT ln(Q / Keq)
Interpretation:
- ΔG < 0 : Spontaneous
- ΔG = 0 : Equilibrium
- ΔG > 0 : Non-spontaneous
The Gas Phase
Ideal Gases
Ideal Gas: Theoretical gas whose molecules occupy negligible space and whose collisions are perfectly elastic. Gases behave ideally under reasonably low temperatures and pressures.
- STP: 273 K (0°C), 1 atm
- 1 mol Gas: At STP, 1 mol = 22.4 L
- Units: 1 atm = 760 mmHg = 760 torr = 101.3 kPa = 14.7 psi
Ideal Gas Law
PV = nRT (R = 8.314 J/mol·K)
- Density of Gas: d = PM/RT
- Combined Gas Law: P₁V₁/T₁ = P₂V₂/T₂ (n constant)
- Avogadro’s Principle: V₁/n₁ = V₂/n₂ (T, P constant)
- Boyle’s Law: P₁V₁ = P₂V₂ (n, T constant)
- Charles’s Law: V₁/T₁ = V₂/T₂ (n, P constant)
- Gay-Lussac’s Law: P₁/T₁ = P₂/T₂ (n, V constant)
Other Gas Laws
- Dalton’s Law (Total Pressure): PT = PA + PB + PC + …(total pressure from
- partial pressures)
- Dalton’s Law (Partial Pressure): PA = XAPT (partial pressure from
- total pressure)
- Henry’s Law: [A] = kHPA
Real Gases
Real gases deviate from ideal behavior at low temperature and high pressure.
- At moderate P, low V, or low T → occupy less volume (attractions)
- At extreme P, low V, or very low T → occupy more volume (particle volume matters)
Van der Waals Equation: (P + n²a/V²)(V – nb) = nRT
- a = corrects for attractive forces
- b = corrects for finite particle volume
Kinetic Molecular Theory
- Average KE: KE = ½mv² = 3/2kBT where kB = 1.38 × 10−23 J/K
- Energy of a gas: (KE ∝ T)
↑T → molecules move faster
↑Molar mass → molecules move slower - Root-Mean-Square Speed: urms = √(3RT/M)
- Diffusion: spreading particles [high] → [low]
- Effusion: The movement of gas from one compartment to another through a small opening under pressure
- Graham’s Law: r₁/r₂ = √(M₂/M₁)
Lower molar mass → diffuses/effuses faster
Higher molar mass → diffuses/effuses slower
Diatomic Gases
Exist as diatomic molecules, never as single atoms.
Includes: H₂, N₂, O₂, F₂, Cl₂, Br₂, I₂
Mnemonic: “Have No Fear Of Ice Cold Beer”
Solutions
Terminology
Solution:
Homogeneous mixture. Solvent particles surround solute particles via electrostatic interactions.
Solvation or Dissolution:
The process of dissolving a solute in a solvent. Most dissolutions are endothermic, although dissolution of a gas into a liquid is exothermic.
Solubility:
Maximum amount of solute that can be dissolved in a solvent at a given temperature.
Molar Solubility:
Molarity of the solute at saturation.
Complex Ions:
Cation bonded to at least one ligand (electron-pair donor). Held together with coordinate covalent bonds. Formation of complex ions ↑ solubility.
Solubility in Water:
- Polar molecules (with +/– charge) are attracted to water molecules → hydrophilic
- Nonpolar molecules are repelled by water molecules → hydrophobic
Polar = Hydrophilic
Nonpolar = Hydrophobic
Solubility Rules
Soluble:
- Na⁺, K⁺, NH₄⁺
- NO₃⁻
- Cl⁻, Br⁻, I⁻ (except with Pb²⁺, Hg₂²⁺, Ag⁺)
- SO₄²⁻ (except with Ca²⁺, Sr²⁺, Ba²⁺, Pb²⁺, Hg₂²⁺, Ag⁺)
Insoluble:
- S²⁻ (except with Na⁺, K⁺, NH₄⁺, Mg²⁺, Ca²⁺, Sr²⁺, Ba²⁺)
- O²⁻ (except with Na⁺, K⁺, Sr²⁺, Ba²⁺)
- OH⁻ (except with Na⁺, K⁺, Ca²⁺, Sr²⁺, Ba²⁺)
- CrO₄²⁻ (except with Na⁺, K⁺, NH₄⁺, Mg²⁺)
- PO₄³⁻ & CO₃²⁻ (except with Na⁺, K⁺, NH₄⁺)
Concentration
% by mass: (mass of solute / mass of solution) × 100%
Mole Fraction (X): XA = moles of solute / total moles
Molarity: M= moles of solute / liters of solution
Molality: Cm = moles of solute / kg of solvent (Can also just be a lowercase m
Normality: N = # of equivalents / liters of solution (For acids, the # of equivalents (n) is the # of H’ available from a formula unit)
Dilutions: M1V1 = M2V2
Solutions Equilibria
Saturated solutions are in equilibrium at that particular temperature.
Solubility Product Constant: Equilibrium expression for something that dissolves.
For substance AaBb, Ksp = [A]a[B]b
Ion Product: IP = [A]a[B]b
IP < Ksp → unsaturated
IP = Ksp → saturated at equilibrium
IP > Ksp → supersaturated, precipitate
Formation or Kf: The equilibrium constant for complex formation.
Stability Constant: Usually much greater than Ksp.
Common Ion Effect: ↓ Solubility of a compound in a solution that already contains one of the ions in the compound. The presence of that ion shifts the dissolution reaction to the left, decreasing its dissociation.
Chelation: When a central cation is bonded to the same ligand in multiple places. Chelation therapy sequesters toxic metals.
Colligative Properties
Colligative Properties: Physical properties of solutions that depend on the concentration of dissolved particles but not on their chemical identity.
Raoult’s Law: Vapor pressure depression.
PA = XAPA°
The presence of other solutes ↓ evaporation rate of solvent, thus ↓Pvap.
Boiling Point Elevation: ΔTb = i Kb Cm
i = ionization factor
Kb = boiling point depression constant
Cm = molal concentration
Freezing Point Depression: ΔTf = i Kf Cm
Kf = freezing point depression constant
Osmolarity: The number of individual particles in solution.
Example: NaCl dissociates completely in water, so
1 M NaCl = 2 osmol/liter
Osmotic Pressure: “Sucking” pressure generated by solutions in which water is drawn into solution.
π = i M R T
i = van’t Hoff factor
M = molar concentration of solute
R = gas constant
T = temperature
Acids and Bases
Definitions
Arrhenius Acid: Produces H+ (same definition as Brønsted acid)
Arrhenius Base: Produces OH–
Brønsted-Lowry Acid: Donates H+ (same definition as Arrhenius acid)
Brønsted-Lowry Base: Accepts H+
Lewis Acid: Accepts e– pair
Lewis Base: Donates e– pair
Note: All Arrhenius acids/bases are Brønsted-Lowry acids/bases, and all Brønsted-Lowry acids/bases are Lewis acids/bases; however, the converse of these statements is not necessarily true.
Amphoteric Species: Species that can behave as an acid or a base. Amphiprotic = amphoteric species that specifically can behave as a Brønsted-Lowry acid/base.
Polyprotic Acid: An acid with multiple ionizable H atoms.
Properties
Water Dissociation Constant: Kw = 10-14 at 298 K
Kw = Ka × Kb
pH and pOH:
pH = -log [H+] [H+] = 10-pH
pOH = -log [OH–] [OH–] = 10-pOH
pH + pOH = 14
p scale value approximation: -log (A × 10-B)
p value ≈ -(B + 0.A)
Strong Acids/Bases: Dissociate completely
Weak Acids/Bases: Do not completely dissociate
Acid Dissociation Constant: Ka = [H3O+][A–] / [HA] pKa = -log (Ka)
Base Dissociation Constant: Kb = [B+][OH–] / [BOH] pKb = -log (Kb)
pKa + pKb = pKw = 14
Conjugate Acid/Base Pairs: Strong acids & bases / weak conjugate
Weak acids & bases / strong conjugate
Neutralization Reactions: Form salts and (sometimes) H2O
Buffers
Buffer: Weak acid + conjugate salt
Weak base + conjugate salt
Buffering Capacity: The ability of a buffer to resist changes in pH. Maximum buffering capacity is within 1 pH point of the pKa.
Henderson-Hasselbalch Equation:
pH = pKa + log ([A–] / [HA])
pOH = pKb + log ([B+] / [BOH])
When [A–] = [HA] at the half equivalence point, log(1) = 0, so pH = pKa
Polyvalence & Normality
Equivalent: 1 mole of the species of interest.
Normality: Concentration of equivalents in solution.
Polyvalent: Can donate or accept multiple equivalents.
Example: 1 mol H3PO4 yields 3 mol H+. So, 2 M H3PO4 = 6 N.
Titrations
Half-Equivalence Point (midpoint): The midpoint of the buffering region, in which half the titrant has been protonated or deprotonated. [HA] = [A–] and pH = pKa, and a buffer is formed.
Equivalence Point: The point at which equivalent amounts of acid and base have reacted. N1V1 = N2V2
pH at Equivalence Point:
Strong acid + strong base, pH = 7
Weak acid + strong base, pH > 7
Strong base + strong acid, pH < 7
Weak acid + weak base, pH > or < 7 depending on the relative strength of the acid and base
Indicators: Weak acids or bases that display different colors in the protonated and deprotonated forms. The indicator’s pKa should be close to the pH of the equivalence point.
Tests:
Litmus: Acid = red; Base = blue; Neutral = purple
Phenolphthalein: pH < 8.2 = colorless; pH > 8.2 = purple
Methyl Orange: pH < 3.1 = red; pH > 4.4 = yellow
Bromophenol Blue: pH < 6 = yellow; pH > 8 = blue
Endpoint: When indicator reaches full color.
Polyvalent Acid/Base Titrations: Multiple buffering regions and equivalence points.
Titration Setup
Titration Curve
When titrating a weak base with a strong acid
Oxidation-Reduction Reactions
Definitions
Oxidation: Loss of e–
Reduction: Gain of e–
With Respect to Oxygen Transfer: Oxidation is GAIN of oxygen
Reduction is LOSS of oxygen
Oxidizing Agent: Facilitates the oxidation of another compound. Is itself reduced
Reducing Agent: Facilitates the reduction of another compound. Is itself oxidized
Balancing via Half-Reaction Method
- Separate the two half-reactions
- Balance the atoms of each half-reaction. Start with all elements besides H and O. In acidic solution, balance H and O using water and H+. In basic solution, balance H and O using water and OH–
- Balance the charges of each half-reaction by adding e– as necessary
- Multiply the half-reactions as necessary to obtain the same number of e– in both half-reactions
- Add the half-reactions, canceling out terms on both sides
- Confirm that the mass and charge are balanced
Oxidation # Rules
- Any free element or diatomic species = 0
- Monatomic ion = the charge of the ion
- When in compounds, group 1A metals = +1; group 2A metals = +2
- When in compounds, group 7A elements = -1, unless combined with an element of greater EN
- H = +1 unless it is paired with a less EN element, then = -1
- O = -2 except in peroxides, when it = -1, or in compounds with more EN elements
- The sum of all oxidation numbers in a compound must = overall charge
Net Ionic Equations
Complete Ionic Equation: Accounts for all of the ions present in a reaction. Split all aqueous compounds into their relevant ions. Keep solid salts intact.
Net Ionic Equation: Ignores spectator ions
Disproportionation Reactions (dismutation): A type of REDOX reaction in which one element is both oxidized and reduced, forming at least two molecules containing the element with different oxidation states
REDOX Titrations: Similar in methodology to acid-base titrations, however, these titrations follow transfer of charge
Potentiometric Titration: A form of REDOX titration in which a voltmeter measures the electromotive force of a solution. No indicator is used, and the equivalence point is determined by a sharp change in voltage
Electrochemistry
Galvanic Cell
Electrolytic Cell
Electrochemical Cells
Anode: Always the site of oxidation. It attracts anions.
Cathode: Always the site of reduction. It attracts cations.
🔴 Red Cat = Reduction at the Cathode
e⁻ Flow: Anode → Cathode
Current Flow: Cathode → Anode
Galvanic Cells (Voltaic): House spontaneous reactions. -ΔG, +Emf, +E°cell
Anode = NEG, Cathode = POS
Electrolytic Cells: House non-spont reactions. +ΔG, -Emf, -E°cell
Anode = POS, Cathode = NEG
Concentration Cells: Specialized form of galvanic cell in which both electrodes are made of the same material. It is the concentration gradient between the two solutions that causes mvmt of charge.
Rechargeable Batteries: Can experience charging (electrolytic) and discharging (galvanic) states.
- Lead-Acid: Discharging: Pb anode, PbO₂ cathode in a concentrated sulfuric acid solution. Low energy density.
- Ni-Cd: Discharging: Cd anode, NiO(OH) cathode in a concentrated KOH solution. Higher energy density than lead-acid batteries.
- NiMH: More common than Ni-Cd because they have higher energy density.
Emf & Thermodynamics
Electromotive force and change in free energy always have OPPOSITE signs.
| Type of Cell | E°cell | ΔG° |
|---|---|---|
| Galvanic | + | – |
| Electrolytic | – | + |
| Concentration | 0 | 0 |
E°cell = E°red,cathode – E°red,anode
ΔG° = -n F E°cell
ΔG° = -R T ln (Keq)
ΔG = ΔG° + R T ln (Q)
Faraday constant (F): 96,485 C
1 C = 1 J/V
Cell Potentials
Reduction Potential: Quantifies the tendency for a species to gain e⁻ and be reduced. More positive Ered = greater tendency to be reduced.
Standard Reduction Potential: E°red. Calculated by comparison to the standard hydrogen electrode (SHE).
Standard Electromotive Force: E°cell. The difference in standard reduction potential between the two half-cells.
Galvanic Cells: +E°cell
Electrolytic Cells: -E°cell
Nernst Equation
Describes the relationship between the concentration of species in a solution under nonstandard conditions and the emf.
When Keq > 1, then +E°cell
When Keq < 1, then -E°cell
When Keq = 1, then E°cell = 0
Ecell = E°cell – (RT / nF) ln (Q)
Ecell = E°cell – (0.0592/n) log (Q)