HESI Chemistry Comprehensive Study Guide: General and Atomic Chemistry and Electrochemistry

Atomic Theory and Subatomic Structure

• The atom is the smallest unit of matter and consists of three primary sub-atomic particles: protons, neutrons, and electrons.
• Nucleus: A dense, positively charged core at the center of the atom composed of protons and neutrons.
• Electron Cloud: The region around the nucleus where negatively charged electrons are found.
• Protons:     - Determine the type of element (e.g., all atoms with one proton are hydrogen).     - Carry an electrical charge of $+1$.     - Relatively heavy with a mass of approximately $1\,amu$ (atomic mass unit).
• Neutrons:     - Located inside the nucleus.     - Mass of approximately $1\,amu$.     - Carry no electrical charge (neutral particles).     - Isotopes: Atoms of the same element that have the same number of protons but different numbers of neutrons. For example, carbon isotopes always have $6$ protons, but can have $6, 7,\text{ or } 8$ neutrons. These react chemically the same but differ in nuclear stability.
• Electrons:     - Negatively charged particles ($-1$ charge).     - Found in clouds surrounding the nucleus.     - Extremely small; the mass of an electron is almost $1,000$ times smaller than a proton.
• Subatomic Particle Data Table:     - Electrons: Charge = $-1$; Mass = $9.1094 \times 10^{-28}\,g$     - Protons: Charge = $+1$; Mass = $1.6726 \times 10^{-24}\,g$     - Neutrons: Charge = $0$; Mass = $1.6749 \times 10^{-24}\,g$
• Atomic Number (Z): The number of protons in the nucleus of an atom; also the number of electrons in a neutral atom. It provides each atom its unique identity.
• Mass Number (A): The sum of the number of protons and the number of neutrons in an individual atom.

Historical Atomic Models

• Democritus Atomic Theory (approx. 400 BC):     - Proposed by Leucippus and Democritus.     - All matter consists of invisible, indestructible, solid, and homogenous particles called atoms.     - Atoms differ in size, shape, mass, position, and arrangement.     - Specific shapes were hypothesized: solids (small, pointy atoms), liquids (large, round atoms), and oils (fine, small atoms that slip past each other).
• Dalton's Atomic Theory (John Dalton, 1766-1844):     1. All substances are composed of atoms, the building blocks of matter.     2. Atoms of a given element are identical in mass and properties; atoms of different elements are different.     3. Compounds form when atoms of different elements combine in fixed proportions. This is the Law of Constant Composition (or Law of Definite Proportions).     4. Atoms are neither created nor destroyed in chemical reactions; they are rearranged. This is the Law of Conservation of Mass (Total mass of products = total mass of reactants).
• Thomson Atomic Model (Sir Joseph J. Thomson, 1856-1940):     - Discovered the electron in 1897 using high-vacuum cathode tubes.     - Proposed the "Plum-pudding model" in 1904: atoms are spheres of uniformly distributed positive matter with electrons positioned by electrostatic forces.
• Rutherford Atomic Model (Ernest Rutherford, 1871-1937):     - Conducted the gold-foil experiment firing positively charged alpha-particles (alpha) at thin gold foil.     - Observations: Most passed through undeflected; some had little deflection; a few bounced back.     - Conclusions: Atoms contain a dense, positively charged nucleus at the center; the rest is mostly empty space. Electrons circulate the nucleus like planets (Planetary or Nuclear model).
• Modern Evidence: Scientific instruments like the scanning tunneling microscope provide actual images of atoms (e.g., Au(111) and Graphite) that support these historical models.

Mass and Identification of Atoms

• Atomic Mass Scale:     - Dalton originally used hydrogen as the standard ($1\,amu$).     - The modern scale is based on Carbon-12: one atom of carbon-12 has a mass of exactly $12\,amu$.
• Determining Atomic Mass:     - Chemical Means: Combining an element with oxygen and calculating the mass ratios of the resulting compound.     - Physical Means: Using a mass spectrometer to measure ion currents and compensate for magnetic field fluctuations.
• Symbolic Notation: ${}_{Z}^{A}X$     - $X$: Element symbol.     - $Z$: Atomic number (subscript, front bottom).     - $A$: Mass number (superscript, front top).
• Isobars: Atoms with the same mass number but different atomic numbers (e.g., Carbon-14 and Nitrogen-14).
• Isotopes of Hydrogen:     - Protium: $1$ proton.     - Deuterium: $1$ proton, $1$ neutron.     - Tritium: $1$ proton, $2$ neutrons.

Atomic Spectrum and Light

• Spectrum: The spreading of light into colored bands. Red has the longest wavelength and least deviation; violet has the shortest wavelength and most deviation.
• Continuous Spectrum: A spectrum without gaps from violet to red (e.g., a rainbow).
• Absorption Spectrum:     - Observed when light passes through a gas.     - Appears as a spectrum with black bars known as absorption lines.     - These gaps identify what elements are present (e.g., identifying hydrogen or helium in the Sun).
• Emission Spectrum:     - Observed when gas is heated; the gas emits light as electrons return to lower energy states.     - Only specific colors correspond to the elements in the gas.
• Energy and Light: Light with longer wavelengths (red) has lower energy; shorter wavelengths (blue/violet) have higher energy.

Electron Orbitals and Quantum Numbers

• Bohr Model (Niels Bohr): Electrons exist at fixed radii (quantized energy). High energy electrons are further from the nucleus. Accurate only for single-electron systems.
• Schrodinger Wave Equation (Erwin Schrodinger): Electrons behave like waves. The probability of finding an electron is proportional to the square of its wave function ($\Psi^{2}$).
• Orbitals: Regions of high probability for finding an electron (represented as clouds).
• Quantum Numbers:     1. Principal Quantum Number (n): Determines orbital size and energy. Values: $n = 1, 2, 3...$ (Shells $K, L, M, N...$).     2. Azimuthal Quantum Number (l): Defines the 3D shape (sublevel). Values: $0$ to $n - 1$.         - $l = 0$: s (spherical)         - $l = 1$: p (peanut/dumbbell)         - $l = 2$: d (double dumbbell)         - $l = 3$: f (flower)     3. Magnetic Quantum Number (ml): Defines spatial orientation. Values: $-l \dots 0 \dots l$.         - $s$ has $1$ orbital, $p$ has $3$, $d$ has $5$, $f$ has $7$.     4. Spin Quantum Number (ms): Defines electron spin angular momentum. Values: $+1/2$ (spin-up) or $-1/2$ (spin-down). Proposed by Goudsmit and Uhlenbeck.

The Periodic Table

• Mendeleev’s Periodic Law (1905): Properties of elements are a periodic function of their atomic weights.
• Modern Periodic Law (Henry Moseley): Properties of elements are a periodic function of their atomic numbers.
• Organization:     - Periods: 7 horizontal rows organized by principal energy level ($n$).     - Groups: Vertical columns organized by outermost electronic configuration ($nl^{e}$).
• Classification Blocks:     - Aufbau Principle: Electrons fill the lowest energy levels first (e.g., $1s$ before $2s$).     - s-block: Groups 1 and 2. Reactive metals, lose electrons readily. Reactivity increases down the group.     - p-block: Groups 13 to 18. Includes metals, non-metals, and noble gases. Metallic character increases down a group; non-metallic character increases left to right.     - d-block: Groups 3 to 12 (Transition metals). All metals, form colored ions, variable oxidation states, and act as catalysts.     - f-block: Inner-transition elements (Lanthanides and Actinides). Elements after uranium are "Transuranium elements."

Periodic Trends (Physical Properties)

• Atomic Radius: Measure of atom size.     - Decreases across a period (increased nuclear charge pulls electrons closer).     - Increases down a group (increased number of shells).
• Ionic Radius:     - Cations are smaller than their parent atoms (fewer electrons, same charge).     - Anions are larger (added electrons increase repulsion and decrease effective nuclear charge).
• Ionization Energy: Energy required to remove an electron from a gaseous atom.     - Increases across a period (closer to stability/octet rule).     - Decreases down a group (valence electrons farther from nucleus).     - Noble gases have the highest ionization energy.
• Electron Affinity: Energy released when an electron is added to a gaseous atom.     - Increases across a period.     - Decreases slightly down a group.
• Electronegativity: Tendency of an atom to attract bonding electrons.     - Increases across a period.     - Decreases down a group.
• Metallic Character: Ability to lose an electron.     - Increases down a group (size increases, less attraction).     - Increases right to left across a period.

Chemical Properties and Bonding

• Valence/Oxidation Number: Maximum number of bonds an atom can form. Determined by electrons in the outermost orbital ($8$ minus outermost electrons).
• Chemical Reactivity:     - In metals, reactivity increases down a group.     - In non-metals, reactivity increases up a group.
• Types of Chemical Bonds:     - Ionic Bond: Electrostatic attraction between ions (e.g., $NaCl$).     - Covalent Bond: Sharing of electron pairs between atoms (e.g., $Cl_{2}$).     - Metallic Bond: Attraction between delocalized electron cloud ("sea of electrons") and positive metal ions.     - Dispersion (van der Waal’s) Force: Weakist intermolecular force; temporary induced dipole.     - Macromolecular (Network) Bonding: Continuous network of covalent bonds (e.g., Diamond, Quartz/$SiO_{2}$, Graphite).     - Hydrogen Bonding: Electromagnetic attraction between polar molecules where H is bound to O or N.

Polarity and Bond Character

• Dipole Moment (D): Product of charge ($Q$) and distance of separation ($r$).     - $\mu = Q \times r$     - $1\,D = 3.33564 \times 10^{-30}\,Coulomb-meters (C\,m)$.
• Molecular Dipole Moments:     - $H_{2}O$: Bent structure, angle $104.5^{\circ}$, net dipole $6.17 \times 10^{-30}\,C\,m$.     - $BeF_{2}$: Linear, net dipole is zero (dipoles cancel).     - $BF_{3}$: Tetra-atomic, net dipole is zero ($120^{\circ}$ orientation).     - $NH_{3}$ vs $NF_{3}$: $NH_{3}$ has a larger dipole because the orbital dipole of the lone pair is in the same direction as the N-H bond dipoles.
• Covalent Character of Ionic Bonds (Fajans' Rules):     1. Small cation and large anion increase covalent character.     2. Higher charge on the cation increases covalent character.     3. Transition electronic configuration is more polarizing than noble gas configuration.

Valence Bond Theory and Hybridization

• Valence Bond (VB) Theory: Developed by Heitler and London (1927), modified by Pauling. Bonds form through the overlap of atomic orbitals.
• Hybridization: Mixing atomic orbitals to form equivalent hybrid orbitals.     - sp: 1 s + 1 p orbital. Linear, $50\%\,s$ and $50\%\,p$ character.     - sp2: 1 s + 2 p orbitals. Trigonal planar.     - sp3: 1 s + 3 p orbitals. $25\%\,s$ and $75\%\,p$ character.
• Sigma (sigma) and Pi (pi) Bonds:     - Sigma (sigma): End-to-end overlap along the internuclear axis (s-s, s-p, or p-p). Stronger than pi bonds.     - Pi (pi): Lateral overlap where axes are parallel and perpendicular to the internuclear axis.

Scientific Method and Laboratory Measurements

• Scientific Method: Observation -> Question -> Hypothesis -> Experiment -> Data Collection -> Refine/Reject -> Develop Theories.
• Experimental Design:     - Aim (goal/objective).     - Reproducibility (precision).     - Error analysis.
• Precision vs. Accuracy:     - Precision: Repeatability/consistency of measurements.     - Accuracy: Correctness/closeness to the actual value.

Bond Cleavage and Reactions

• Heterolytic Cleavage (Ionic Fission): Shared pair stays with one fragment, forming ions (Electrophile/Nucleophile).
• Homolytic Cleavage (Radical Fission): Electrons divided equally, forming free radicals.
• Collision Theory:     - Molecules must collide.     - Collisions must be energetic enough to disrupt bonds.     - Threshold Energy: Minimum energy required for a reaction.     - Activation Energy: Difference between threshold and normal state energy.

Acid-Base Theories

• Arrhenius Theory:     - Acid: Increases $H^{+}$ ($H_{3}O^{+}$) concentration in water.     - Base: Increases $OH^{-}$ concentration in water.
• Bronsted-Lowry (Proton Theory):     - Acid: Proton donor.     - Base: Proton acceptor.     - Conjugate Pair: Two species differing by a single proton (e.g., $HCl/Cl^{-}$, $NH_{3}/NH_{4}^{+}$).
• Lewis Theory:     - Acid: Electron pair acceptor (Electrophile).     - Base: Electron pair donor (Nucleophile).
• Acid Strength: Measured by Ka. Strong acids have large Ka; weak acids have small Ka.
• Amphoterism: Ability to act as either an acid or a base (e.g., Water).

Coordination Complexes

• Coordination Complex: Product of Lewis acid-base reaction.
• Ligands: Lewis bases (donors) attached to a central metal.
• Donor Atom: Atom within the ligand directly bonded to the metal.
• Coordinate Covalent Bond: Bond where one atom supplies both electrons.
• Coordination Number: Number of donor atoms bonded to the central metal (e.g., $Zn(CN)_{4}^{2-}$ has a coordination number of $4$).

Precipitation Reactions and Solubility Rules

• Precipitation: Mixing soluble reactants to form an insoluble product.
• Net Ionic Equation: Shows only the ions forming the precipitate (e.g., $Pb^{2+}(aq) + 2I^{-}(aq) \rightarrow PbI_{2}(s)$).
• Solubility Rules:     - Soluble: $NH_{4}^{+}$, Group IA cations, Nitrates ($NO_{3}^{-}$), Acetates ($CH_{3}CO_{2}^{-}$).     - Mostly Soluble: Chlorides/Bromides/Iodides (Except Ag, Pb, Hg(I)), Sulfates (Except Ag, Pb, Hg(I), Ba, Sr, Ca).     - Mostly Insoluble: Carbonates, Sulfites, Phosphates, Hydroxides, Sulfides (with Group IA and specific exceptions).

Oxidation-Reduction (Redox)

• Oxidation: Loss of electrons; increase in oxidation number.
• Reduction: Gain of electrons; decrease in oxidation number.
• Agents:     - Oxidizing Agent: Accepts electrons (gets reduced).     - Reducing Agent: Donates electrons (gets oxidized).
• Rules for Oxidation Numbers:     - Total oxidation number equals the charge of the species.     - Hydrogen = $+1$ (except hydrides).     - Oxygen = $-2$ (except peroxides).     - Group IA = $+1$, IIA = $+2$, VIIA = $-1$ (common).

Electrochemistry

• Electrolytic Cell: Uses electrical energy to cause chemical change or generates electricity from spontaneous redox.
• Voltaic (Galvanic) Cell:     - Converts chemical energy to electrical energy.     - Anode: Oxidation occurs; negatively charged.     - Cathode: Reduction occurs; positively charged.     - Salt Bridge: Maintains electrical neutrality by allowing flow of ions ($K^{+}$ and $NO_{3}^{-}$).
• Standard Half-Cell Potential (E0): Measured at unit concentration, $25\,^{\circ}C$, against a Standard Hydrogen Electrode ($0\,V$).
• Nernst Equation: Calculates cell voltage under non-standard conditions.     - $E_{cell} = E^{\circ}_{cell} - \frac{0.06}{n} \ln(Q)$
• Faraday’s Constant (F): $96,486\,C/mol$.