Exhaustive Study Guide: Structure and Properties of Matter (SCH 4U Unit 1)

Course Schedule and Overview

• Course Schedule: Structure and Properties of Matter

  • Day 1: Introduction and Safety | Textbook Reading: N/A | Homework and Practice Questions: Online Safety Training, Grade 11 Review Assignment

  • Day 2: Grade 11 Review Assignment | Textbook Reading: N/A | Homework and Practice Questions: Grade 11 Review Assignment

  • Day 3: Grade 11 Review Assignment | Textbook Reading: N/A | Homework and Practice Questions: Grade 11 Review Assignment

  • Day 4: Grade 11 Review Assignment Due, Probing the Atom Activity | Textbook Reading: N/A | Homework and Practice Questions: Probing the Atom Activity

  • Day 5: Components of Atoms and Atomic Models | Textbook Reading: Pg 164 – 172 | Homework and Practice Questions: Pg 164 – 172

  • Day 6: Quantum Mechanical Model | Textbook Reading: Pg 174 – 178 | Homework and Practice Questions: Pg 179 PP# 1 – 10

  • Day 7: Communicating Where Electrons Are | Textbook Reading: Pg 181 – 186 | Homework and Practice Questions: Worksheet

  • Day 8: Patterns in the Periodic Table | Textbook Reading: Pg 187 – 192 | Homework and Practice Questions: Chapter 3 Review Pg 199 Q# 1, 5, 6, 19, 22, 24, 27, 32, 33, 35, 36, Worksheet, Study for Quiz

  • Day 9: Types of Chemical Bonds | Textbook Reading: N/A | Homework and Practice Questions: Worksheet, Study for Quiz

  • Day 10: Quiz 1: Learning Targets #1 – 3; Lab 1: Observing Types of Solids | Textbook Reading: Pg 208 – 220 | Homework and Practice Questions: Lab Write Up

  • Day 11: Drawing Lewis Structures of Molecular Compounds | Textbook Reading: Pg 228 – 231 | Homework and Practice Questions: Worksheet

  • Day 12: Determining Molecular Shape | Textbook Reading: Pg 232 – 235 | Homework and Practice Questions: Worksheet

  • Day 13: Determining Molecular Polarity, VSEPR Whiteboard Practice | Textbook Reading: Pg 238 – 239 | Homework and Practice Questions: Worksheet, Study for Quiz

  • Day 14: Types of Intermolecular Forces | Textbook Reading: Pg 241 – 245 | Homework and Practice Questions: Worksheet

  • Day 15: Types of Solids | Textbook Reading: Pg 212 – 214, 216 – 218, 224 – 225 | Homework and Practice Questions: Worksheet, Study for Quiz

  • Day 16: Quiz 2: Learning Target #4; Lab 2: Determining Solid Type & Explain Properties | Textbook Reading: N/A | Homework and Practice Questions: Lab Write Up, Study for Test

  • Day 17: Unit Review | Textbook Reading: N/A | Homework and Practice Questions: Unit Review Pg 263 Q# 3, 4, 6, 9–15, 17, 22, 31, 33, 35, 36, 41, 44a), 45, 46, Study for Test

  • Day 18: Unit Test

• Big Ideas

  • What does an atom look like, and how do scientists know?

  • How do bonding and intermolecular forces affect the properties of a substance?

• Unit Learning Targets

  • #1: Describe the components of an atom and discuss the experimental evidence and theory that supports their existence, charge, and location.

  • #2: Describe the number and location of orbitals and electrons using quantum numbers, orbital diagrams, and electron configurations.

  • #3: Explain why the shape of the periodic table is determined by the quantum mechanical model of the atom, and use the position of an element on the table to determine its electron configuration.

  • #4: Determine the geometric arrangement, shape, bond angles, and polarity of a molecule by drawing a proper Lewis diagram and using VSEPR theory.

  • #5: Determine the difference between atomic, molecular (both polar and non-polar), ionic, metallic, and network solids, and predict their properties based on the structure’s intermolecular forces.

Development of Atomic Theory and Atomic Models

• Experimental Inquiry into Atomic Structure

  • Atoms are extremely small, preventing direct visual imaging of individual subatomic particles and their dynamic behaviors within an atom using existing microscopy technology.

  • Conceptual understandings of atomic structure are established through empirical observations, experimental results, and theoretical modeling.

• John Dalton (1803)

  • Experiment: Conducted chemical reactions using various atmospheric gases.

  • Observations: Observed that gases reacted in definite, fixed whole-number proportions by mass. For example, nitrogen and oxygen react to yield $NO_2$ and $NO_3$, with no intermediate compounds existing between these ratios.

  • Inferences: Matter consists of distinct fundamental building blocks possessing definite and characteristic masses.

  • Atomic Model: Postulated that matter consists of minute, indestructible spherical units called atoms, defined by four central postulates:

  1. All matter is composed of indivisible particles called atoms.

  2. Atoms belonging to the same element share identical average mass, size, and unique chemical properties.

  3. Atoms cannot be subdivided, created, or converted into atoms of a different element via chemical reactions.

  4. Atoms of different elements combine in fixed, specific whole-number ratios to form chemical compounds.

• Joseph Thompson (1897)

  • Experiment: Investigated electrical discharges using cathode ray tubes, which project a stream of microscopic particles that produce luminescence upon colliding with a coated screen. Applied electric fields across the particle beam using charged plates.

  • Observations: The particle beam consistently deflected toward the positively charged electrode.

  • Inferences: The beam consists of negatively charged subatomic particles because opposite electrical charges attract. Because intact atoms are electrically neutral, they must contain negative particles that can be detached from a bulk positive framework.

  • Atomic Model: Proposed the Plum Pudding Model, defining atoms as uniform spheres of positive electric charge embedded with negatively charged electrons.

• Ernest Rutherford (1911)

  • Experiment: Directed positively charged alpha particles emitted from radioactive sources at an ultra-thin sheet of gold foil to test Thompson's distributed charge model. Expected the alpha particles to pass through unhindered.

  • Observations: The vast majority of alpha particles passed straight through the foil unimpeded. A small fraction deflected at sharp angles, and occasionally particles bounced directly backward toward the emitter source. Subsequent experiments involving nuclear reactions with nitrogen revealed the ejection of small positive particles.

  • Inferences: Because most particles traversed the foil without interaction, the atom consists predominantly of empty space. The severe deflections indicate that the positive charge and mass are concentrated within an extraordinarily dense core that repels incoming alpha particles.

  • Atomic Model: Proposed the Planetary Model, describing an atom as containing a small, highly dense, positively charged nucleus surrounded by electrons moving through empty space. Identified the individual fundamental positive units of the nucleus as protons, which carry an absolute charge equal and opposite to that of an electron.

• Niels Bohr (1913)

  • Theoretical Foundations: Synthesized Max Planck's quantum hypothesis (energy transfer occurs exclusively in discrete, fixed quanta) and Albert Einstein's photon concept (light energy consists of discrete packets called photons) to mathematically model electronic locations and account for atomic emission spectra (unique discrete color patterns produced when element vapors are heated).

  • Observations: Accurately calculated the precise energy values of moving electrons and predicted the exact emission spectrum wavelengths produced during electronic transitions, but only for single-electron chemical species.

  • Inferences: Classical electrodynamics predicts that orbiting charged particles must continuously emit electromagnetic radiation, causing electrons to rapidly spiral into the nucleus and undergo atomic collapse. Because atoms are stable, subatomic particles do not obey classical macroscopic physical laws.

  • Atomic Model: Defined fixed electron orbits governed by three principles:

  1. Electrons exist only within specific allowable energy levels representing fixed, circular orbits around the central nucleus.

  2. An electron residing within a defined stable orbit undergoes no net gain or loss of energy.

  3. Electronic transitions between orbits occur via the absorption or emission of a discrete energy quantum exactly equivalent to the difference in energy between the two involved orbits: $\Delta E = E_{\text{final}} - E_{\text{initial}}$

• Ernest Rutherford (1920)

  • Experiment: Evaluated atomic masses by comparing the measured proton counts required to balance electronic charges against total experimental atomic weights.

  • Observations: Determined that actual atomic masses substantially exceed the combined mass of an atom's protons and electrons.

  • Inferences: Unidentified particles possessing mass comparable to protons must exist within the nucleus to account for the missing mass. These particles must carry zero net electrical charge to maintain atomic neutrality.

  • Atomic Model: Re-defined the atomic nucleus as containing both positive protons and uncharged neutrons, encircled by orbiting electrons occupying discrete Bohr orbits.

Quantum Mechanical Model of the Atom

• Limitations of the Bohr Model

  • Fails to accurately predict emission spectra for multi-electron atoms. Multi-electron spectra exhibit fine structure—tightly clustered groups of spectral lines alongside broad gaps—indicating the presence of electronic sublevels within principal energy shells.

  • Violates fundamental principles of quantum physics regarding simultaneous positioning and velocity measurement.

• Heisenberg Uncertainty Principle (Werner Heisenberg, 1927)

  • Asserts that it is physically impossible to measure both the position and momentum of a subatomic particle simultaneously with absolute precision.

  • Increasing the measurement precision of one canonical variable increases the uncertainty of the conjugate variable.

  • Invalidates Bohr's model by establishing that fixed circular trajectories and exact velocities cannot coexist for electrons.

• Wave-Particle Duality (Louis de Broglie, 1924)

  • Hypothesized that all moving matter exhibits wave-like characteristics, defined by the de Broglie wavelength equation: $\lambda = \frac{h}{p} = \frac{h}{m v}$

  • Macroscopic objects possess momentum values so large that their associated wavelengths are infinitesimally small and undetectable.

  • Microscopic entities like electrons possess observable wavelengths. For instance, an electron moving at a velocity of $5.9 \times 10^6\,m/s$ has an associated wavelength of $1 \times 10^{-10}\,m$, which exceeds the physical radius of a ground-state Hydrogen atom.

  • Experimental verification of electron wave properties is demonstrated by electron diffraction patterns in double-slit experiments.

• Quantum Mechanical Model (Erwin Schrödinger, 1926)

  • Incorporated wave-particle duality into structural atomic theory using wave mechanics.

  • Formulated the Schrödinger wave equation to calculate electronic energy levels and probabilistic distributions around the nucleus.

  • Replaced deterministic circular paths with three-dimensional spatial probability regions designated as orbitals, defined by a mathematical boundary enclosing a $95\%$ probability of locating the electron.

Quantum Numbers and Quantum Orbitals

• System of Quantum Numbers

  • Quantum orbitals vary in energy, scale, and spatial orientation. A set of four quantum numbers specifies the exact quantum state of an electron.

• Principal Quantum Number ($n$)

  • Defines the principal energy level and overall physical dimension of the orbital.

  • Allowed values are positive integers: $n \in \{1, 2, 3, 4, \dots\}$

  • Higher $n$ values correspond to larger spatial distributions and higher potential energy levels.

  • The maximum electron capacity of a principal energy level $n$ is given by: $\text{Maximum Capacity} = 2 n^2$

• Orbital Shape Quantum Number ($l$)

  • Also termed the angular momentum quantum number; dictates the three-dimensional geometry of the orbital subshell.

  • Allowed values range from $0$ to $(n - 1)$.

  • Subshell designation letter assignments:

  • $l = 0$ corresponds to the $s$ orbital (spherical shape).

  • $l = 1$ corresponds to the $p$ orbital (dumbbell shape).

  • $l = 2$ corresponds to the $d$ orbital (cloverleaf shape).

  • $l = 3$ corresponds to the $f$ orbital (complex multi-lobed shape).

• Magnetic Quantum Number ($m_l$)

  • Specifies the spatial orientation of an orbital relative to the standard Cartesian coordinate axes ($x, y, z$).

  • Allowed integral values range from $-l$ through $0$ to $+l$: $m_l \in \{-l, \dots, 0, \dots, +l\}$

  • The total number of available orbital orientations for a given subshell value $l$ is: $\text{Orientations} = 2 l + 1$

• Spin Quantum Number ($m_s$) and Pauli Exclusion Principle (Wolfgang Pauli, 1924)

  • Specifies the intrinsic angular momentum (spin orientation) of an electron on its internal axis.

  • Allowed values are restricted to: $m_s \in \left\{+\frac{1}{2}, -\frac{1}{2}\right\}$

  • By convention, assignment of quantum states fills the positive spin value ($+\frac{1}{2}$) prior to assigning the negative value ($-\frac{1}{2}$).

  • Pauli Exclusion Principle: No two electrons within a single atom can possess an identical set of all four quantum numbers $(n, l, m_l, m_s)$. Consequently, an individual orbital box can accommodate a maximum of two electrons, which must possess paired, anti-parallel spins.

• Single-Electron vs. Multi-Electron Orbital Energies

  • In single-electron systems (such as Hydrogen), orbital energies depend purely on the principal quantum number $n$; subshells sharing an $n$ level are degenerate (equal energy).

  • In multi-electron systems, inter-electronic repulsions cause energetic splitting among subshells belonging to the same principal shell, causing subshell energies to increase in the sequence $s < p < d < f$.

Communicating Electron Configurations

• Quantum Numbers Assignment Examples (Ground State)

  • Hydrogen ($H$, $1\,e^-$): $(n = 1, l = 0, m_l = 0, m_s = +\frac{1}{2})$

  • Helium ($He$, $2\,e^-$):

  • Electron 1: $(n = 1, l = 0, m_l = 0, m_s = +\frac{1}{2})$

  • Electron 2: $(n = 1, l = 0, m_l = 0, m_s = -\frac{1}{2})$

  • Lithium ($Li$, $3\,e^-$):

  • Electron 1: $(n = 1, l = 0, m_l = 0, m_s = +\frac{1}{2})$

  • Electron 2: $(n = 1, l = 0, m_l = 0, m_s = -\frac{1}{2})$

  • Electron 3: $(n = 2, l = 0, m_l = 0, m_s = +\frac{1}{2})$

  • Beryllium ($Be$, $4\,e^-$):

  • Electron 1: $(n = 1, l = 0, m_l = 0, m_s = +\frac{1}{2})$

  • Electron 2: $(n = 1, l = 0, m_l = 0, m_s = -\frac{1}{2})$

  • Electron 3: $(n = 2, l = 0, m_l = 0, m_s = +\frac{1}{2})$

  • Electron 4: $(n = 2, l = 0, m_l = 0, m_s = -\frac{1}{2})$

• Rules for Constructing Orbital Diagrams and Configurations

  • Aufbau Principle: Electrons sequentially populate the lowest available energetic orbital state before occupying higher energy levels.

  • Hund's Rule: When filling degenerate orbitals (orbitals of equal energy, such as $2p_x, 2p_y, 2p_z$), electrons occupy each orbital singly with parallel spins ($m_s = +\frac{1}{2}$) before pairing up.

• Electron Configuration Formats

  • Full Configuration: Denotes occupied subshells sequentially with superscript electron counts.

  • Example (Phosphorus, $Z = 15$): $P = 1s^2 2s^2 2p^6 3s^2 3p^3$

  • Condensed (Abbreviated) Configuration: Replaces core electrons with the bracketed noble gas symbol representing the preceding filled shell, followed by outer shell valence electrons.

  • Example (Phosphorus, $Z = 15$): $P = [Ne]3s^2 3p^3$

  • Last Electron Quantum Numbers for Phosphorus ($P$): $n = 3, l = 1, m_l = +1, m_s = +\frac{1}{2}$

• Excited States vs. Ground State Anomalies

  • Excited State Configurations: Absorption of energy promotes valence electrons to higher available orbitals.

  • Example (Excited Phosphorus): $\text{Excited } P = [Ne]3s^2 3p^2 4s^1$

• Ground State Anomalies: Certain transition elements shift an $s$ electron into the $d$ subshell to achieve half-filled or fully filled subshell stability.

  • Example (Copper, $Z = 29$): Reorganizes to yield a complete $3d^{10}$ subshell: $\text{Ground State } Cu = [Ar]4s^1 3d^{10}$

• Practice Problems: Orbital Diagrams & Quantum Numbers

  1. Complete and condensed electron configurations:

  • a) Sodium ($Na$): $1s^2 2s^2 2p^6 3s^1 \rightarrow [Ne]3s^1$

  • b) Sulfur ($S$): $1s^2 2s^2 2p^6 3s^2 3p^4 \rightarrow [Ar]3s^2 3p^4$

  • c) Bromine ($Br$): $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^5 \rightarrow [Kr]4s^2 3d^{10} 4p^5$

  • d) Nickel ($Ni$): $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^8 \rightarrow [Ar]4s^2 3d^8$

  • e) Silver ($Ag$): $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^1 4d^{10} \rightarrow [Kr]5s^1 4d^{10}$

  • f) Krypton ($Kr$): $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 \rightarrow [Kr]$

  1. Quantum numbers $(n, l, m_l, m_s)$ for the final added electron:

  • Sodium ($Na$): $(3, 0, 0, +\frac{1}{2})$

  • Sulfur ($S$): $(3, 1, -1, -\frac{1}{2})$

  • Bromine ($Br$): $(4, 1, 0, -\frac{1}{2})$

  • Nickel ($Ni$): $(3, 2, 0, -\frac{1}{2})$

  • Silver ($Ag$): $(4, 2, +2, -\frac{1}{2})$

  • Krypton ($Kr$): $(4, 1, +1, -\frac{1}{2})$

  1. General outer-shell configurations:

  • Group 2: $n s^2$

  • Group 16: $n s^2 n p^4$

  • Group 8: $n s^2 (n-1)d^6$

Modern Periodic Table and Periodic Trends

• Structural Organization of the Periodic Table

  • Elements are arranged sequentially by increasing atomic number ($Z$), reflecting both proton count and progressive electron population according to quantum orbital energetic filling rules.

• Periodic Structural Relationships

  • Periods: Correspond directly to the principal quantum number $n$ of the outermost occupied shell.

  • Period Capacity: Dictated by maximum subshell capacities within that shell. Period 1 contains 2 elements due to the 2-electron capacity of the $1s$ orbital. In Period 4, filling of $3d$ orbitals occurs after $4s$ population because $4s$ possesses lower energy than $3d$ in multi-electron systems.

  • Blocks: Segregated into distinct regions based on the subshell category ($s, p, d, f$) accommodating the final added electron.

  • Valence Electron Groups: Group numbers determine valence electron counts. For main-group elements in Groups 13 through 18, valence electrons correspond to the unit digit of the group number (e.g., Nitrogen in Group 15 possesses 5 valence electrons). Completed inner $d$ or $f$ subshells do not count toward valence totals.

• Summary of Periodic Trends

  • Atomic Radius: Measures half the distance between nuclei of identical bonded atoms. Increases moving down a group (due to additional principal shells) and toward the left across a period (due to decreasing effective nuclear charge).

  • Ionization Energy (IE): The minimal energy required to completely remove an electron from a gaseous atom or ion: $X(g) + \text{IE} \rightarrow X^+(g) + e^-$

  • Increases moving upward within a group and toward the right across a period.

  • Electron Affinity (EA): The energy change associated with the addition of an electron to a gaseous atom: $X(g) + e^- \rightarrow X^-(g) + \text{EA}$

  • Increases in magnitude moving upward within a group and toward the right across a period.

  • Electronegativity (EN): A dimensionless metric representing an atom's relative ability to attract shared electron pairs within a chemical bond. Increases moving upward within a group and toward the right across a period.

• Practice Problems: Periodic Trends and Configurations

  1. Element identification by terminal configuration:

  • a) $5s^1 \rightarrow Rubidium\ (Rb)$

  • b) $3p^2 \rightarrow Silicon\ (Si)$

  • c) $5p^6 \rightarrow Xenon\ (Xe)$

  • d) $4d^6 \rightarrow Ruthenium\ (Ru)$

  • e) $7s^2 \rightarrow Radium\ (Ra)$

  • f) $4f^2 \rightarrow Praseodymium\ (Pr)$

  1. Condensed electron configurations using periodic positions:

  • a) $Cl \rightarrow [Ne]3s^2 3p^5$

  • b) $Ti \rightarrow [Ar]4s^2 3d^2$

  • c) $Sr \rightarrow [Kr]5s^2$

  • d) $I \rightarrow [Kr]5s^2 4d^{10} 5p^5$

  • e) $Os \rightarrow [Xe]6s^2 4f^{14} 5d^6$

  • f) $U \rightarrow [Rn]7s^2 5f^4$

  1. Location assignments from configuration:

  • a) $[Ne]3s^1 \rightarrow Group\ 1, Period\ 3, s\text{-block}$

  • b) $[He]2s^2 \rightarrow Group\ 2, Period\ 2, s\text{-block}$

  • c) $[Kr]5s^2 4d^{10} 5p^5 \rightarrow Group\ 17, Period\ 5, p\text{-block}$

  • d) $[Xe]6s^2 4f^{14} 5d^3 \rightarrow Group\ 5, Period\ 6, d\text{-block}$

  1. Configuration endings for target positions:

  • a) Group 2, Period 4 $\rightarrow 4s^2$

  • b) Noble gas, Period 6 $\rightarrow 6p^6$

  • c) Group 12, Period 4 $\rightarrow 4s^2 3d^{10}$

  • d) Group 1, Period 2 $\rightarrow 2s^1$

Types of Chemical Bonds and Energetics

• Thermodynamics of Chemical Bonding

  • Chemical systems seek minimal potential energy states to maximize thermodynamic stability. Intramolecular bonding forces restrict particle mobility and release potential energy as kinetic energy dissipates.

  • Stronger chemical bonds release greater energy quantities during formation and require equivalent energy inputs to break.

• Ionic Bonds

  • Electrostatic attractions operating between oppositely charged cations and anions following electron transfer. Typically form between metallic elements (low ionization energy) and non-metallic elements (high electron affinity).

  • Formation Energy Steps:

  1. Ionization Energy Input: Energy required to remove valence electrons from the metal: $Na(g) \rightarrow Na^+(g) + e^-, \quad \Delta H = +496\,kJ/mol\ (118\,kcal/mol)$

  2. Electron Affinity Release: Energy released upon electron capture by the non-metal: $Cl(g) + e^- \rightarrow Cl^-(g), \quad \Delta H = -349\,kJ/mol\ (83\,kcal/mol)$

  3. Lattice Energy Release: Electrostatic stabilization when gaseous ions coalesce into a three-dimensional crystalline lattice: $Na^+(g) + Cl^-(g) \rightarrow NaCl(s), \quad \Delta H = -765\,kJ/mol\ (182\,kcal/mol)$

  • Total energy released in ionic bond formation ranges between $400\,kJ/mol$ and $4000\,kJ/mol$.

• Covalent Bonds (Polar and Non-Polar)

  • Formed via mutual sharing of electron pairs within overlapping atomic orbitals, predominantly between non-metallic atoms. Energy release during covalent bond formation ranges from $150\,kJ/mol$ to $1100\,kJ/mol$.

  • Formation Steps:

  1. Atomic approach enables overlap of partially filled atomic subshells, creating a localized high-density electron zone between nuclei.

  2. Optimal Particle Separation: Nuclei and shared electrons adopt an equilibrium inter-nuclear distance balancing repulsive and attractive forces, releasing energy designated as bond energy (e.g., $H-H$ bond formation releases $436\,kJ/mol$).

• Bond Classification via Electronegativity Difference ($\Delta EN$)

  • The absolute difference in electronegativity dictates bond character: $\Delta EN = |EN_A - EN_B|$

  • Non-Polar Covalent Bond: $\Delta EN \in [0, 0.5)$ — Equal sharing of electrons; zero net charge distribution.

  • Polar Covalent Bond: $\Delta EN \in [0.5, 1.7]$ — Unequal electron sharing; creates partial charges (dipoles $\delta^+, \delta^-$).

  • Ionic Bond: $\Delta EN > 1.7$ — Total electron transfer; forms full discrete ions.

• Electronegativity Practice Examples:

  • 1) $S\text{ and } O \rightarrow EN_S = 2.5, EN_O = 3.5 \rightarrow \Delta EN = 1.0 \rightarrow Polar\ Covalent$

  • 2) $Na\text{ and } I \rightarrow EN_{Na} = 0.9, EN_I = 2.5 \rightarrow \Delta EN = 1.6 \rightarrow Polar\ Covalent/Ionic$

  • 3) $Br\text{ and } Br \rightarrow EN_{Br} = 2.8, EN_{Br} = 2.8 \rightarrow \Delta EN = 0.0 \rightarrow Non\text{-}Polar\ Covalent$

  • 4) $C\text{ and } H \rightarrow EN_C = 2.5, EN_H = 2.1 \rightarrow \Delta EN = 0.4 \rightarrow Non\text{-}Polar\ Covalent$

  • Metallic Bonds (Arnold Sommerfeld, 1927)

• Free Electron Model: Describes solid metals as regular arrays of fixed metal cations immersed within a delocalized, mobile sea of electrons composed of shed valence electrons occupying interstitial crystal spaces.

• Bonding Force: Non-directional electrostatic attraction between fixed cations and the surrounding electron cloud.

• Bond energy released ranges from $75\,kJ/mol$ to $1000\,kJ/mol$. Metallic bond strength increases with smaller cation ionic radii and higher numbers of delocalized valence electrons.

• Practice Problems: Bonding and Properties

  1. Bond types formed between:

  • a) $S\text{ and } S \rightarrow Non\text{-}Polar\ Covalent\ (\Delta EN = 0)$

  • b) $Rb\text{ and } Cl \rightarrow Ionic\ (\Delta EN = 2.2)$

  • c) $P\text{ and } F \rightarrow Polar\ Covalent\ (\Delta EN = 1.9)$

  • d) $S\text{ and } Cl \rightarrow Polar\ Covalent\ (\Delta EN = 0.5)$

  • e) $F\text{ and } F \rightarrow Non\text{-}Polar\ Covalent\ (\Delta EN = 0)$

  • f) $S\text{ and } F \rightarrow Polar\ Covalent\ (\Delta EN = 1.5)$

  1. Polarity comparison in chemical bonds:

  • a) $C-H\ (\Delta EN = 0.4), Si-H\ (\Delta EN = 0.3), Ge-H\ (\Delta EN = 0.1) \rightarrow C-H\text{ is most polar.}$

  • b) $C-O\ (\Delta EN = 1.0), C-H\ (\Delta EN = 0.4), C-N\ (\Delta EN = 0.5) \rightarrow C-O\text{ is most polar.}$

  1. Lewis structures of Bromine bonds: Ionic ($NaBr$), Non-polar covalent ($Br_2$), Polar covalent ($BrCl$). Ionic bonds are generally most stable due to high lattice energy release.

  2. Metallic melting point trends: Increases moving left-to-right across a period as elements contribute more delocalized electrons to the electron sea, strengthening electrostatic cohesive forces.

Drawing Lewis Structures of Molecular Compounds

• Systematic 5-Step Method for Complex Lewis Structures

  1. Position the atom with the lowest electronegativity as the central atom (Hydrogen is always terminal). Connect surrounding atoms to the central atom using single covalent bonds.

  2. Calculate the total available valence electrons ($V$). Add electrons for negative net charges; subtract electrons for positive net charges.

  3. Calculate total electrons required for all constituent atoms to achieve individual stable octets ($T$) (2 electrons for Hydrogen).

  4. Compute shared bonding electrons ($S$) and total bonding pairs ($BP$): $S = T - V, \quad BP = \frac{S}{2}$

  5. Compute unshared electrons ($U$) and total lone pairs ($LP$): $U = V - S, \quad LP = \frac{U}{2}$

  • Distribute lone pairs to satisfy outer atom octets first, placing any remaining pairs on the central atom.

• Structural Classifications

  • Standard Octet Molecules: Example: Formaldehyde ($CH_2O$)

  • $V = 4(C) + 2(1)(H) + 6(O) = 12\,e^-$

  • $T = 8(C) + 2(2)(H) + 8(O) = 20\,e^-$

  • $S = 20 - 12 = 8\,e^- \rightarrow BP = 4$

  • $U = 12 - 8 = 4\,e^- \rightarrow LP = 2$

  • Polyatomic Ions: Example: Ammonium ($NH_4^+$)

  • $V = 5(N) + 4(1)(H) - 1(\text{charge}) = 8\,e^-$

  • $T = 8(N) + 4(2)(H) = 16\,e^-$

  • $S = 16 - 8 = 8\,e^- \rightarrow BP = 4$

  • $U = 8 - 8 = 0\,e^- \rightarrow LP = 0$

• Resonance Structures: Occur when multiple equivalent Lewis structures can be drawn for a single molecule. Electrons forming double bonds are delocalized across the structure, producing equivalent intermediate bond lengths (e.g., $SO_2$ exhibits bond lengths corresponding to an effective bond order of $1.5$).

• Expanded Valence Shells: Occur when central atoms from Period 3 or below accommodate more than 8 valence electrons using accessible $d$ orbitals. When calculated bonding requirements are insufficient to connect all atoms, add lone pairs directly to outer atoms until satisfied, placing extra remaining electron pairs on the central atom.

  • Example: Phosphorus Pentachloride ($PCl_5$)

    • $V = 5(P) + 5(7)(Cl) = 40\,e^-$

    • Five single bonds are formed around Phosphorus, placing 10 electrons around the central atom.

  • Lewis Diagram Worksheet Assignment

• Draw Lewis structures for: $\text{1. } AsH_3, \quad \text{2. } BrO^-, \quad \text{3. } ClNO, \quad \text{4. } CO_3^{2-}, \quad \text{5. } NO^+,$ $\text{6. } ClO_3^-, \quad \text{7. } NO_2^-, \quad \text{8. } SF_6, \quad \text{9. } XeBr_4, \quad \text{10. } ICl_3$

Molecular Geometry (VSEPR Theory) and Polarity

• Valence Shell Electron Pair Repulsion (VSEPR) Theory

  • Electron pairs surrounding a central atom orient themselves in three-dimensional space to minimize electrostatic repulsion by maximizing angular separation.

  • Electron Group: Any concentrated electron zone surrounding a central atom. Single, double, or triple covalent bonds and lone pairs each count as one electron group.

• Fundamental VSEPR Geometries (Electron Arrangements)

  • 2 Electron Groups: Linear geometry; fundamental bond angle = $180^\circ$.

  • 3 Electron Groups: Trigonal Planar geometry; fundamental bond angle = $120^\circ$.

  • 4 Electron Groups: Tetrahedral geometry; fundamental bond angle = $109.5^\circ$.

  • 5 Electron Groups: Trigonal Bipyramidal geometry; bond angles = $90^\circ$ (axial-equatorial), $120^\circ$ (equatorial-equatorial), $180^\circ$ (axial-axial).

  • 6 Electron Groups: Octahedral geometry; bond angles = $90^\circ$, $180^\circ$.

• Determining Molecular Shape vs. Electron Arrangement

  • Electron Arrangement: The geometric layout of all electron groups (both bonding pairs and lone pairs).

  • Molecular Shape: The spatial arrangement of constituent nuclei only. Unshared lone pairs exert greater repulsive forces than bonding pairs, compressing adjacent bond angles. Lone pairs occupy equatorial positions in trigonal bipyramidal arrangements to maximize angular space.

• Molecular Polarity and Symmetry

  • Dipole Moment: Vector sum of individual bond dipoles within a 3D geometry.

  • Symmetry Test for Polarity:

  • Non-Polar Molecule: Possesses a highly symmetrical VSEPR molecular geometry AND identical terminal atoms attached to every position (bond dipole vectors cancel out completely).

  • Polar Molecule (Permanent Dipole): Possesses an asymmetrical VSEPR molecular geometry (containing lone pairs on the central atom) OR differing terminal atoms with distinct electronegativities (bond dipoles fail to cancel).

• Molecular Shape & Polarity Practice Problems

  1. VSEPR Analysis:

  • a) $HCN \rightarrow 2\text{ groups} \rightarrow \text{Linear arrangement, Linear shape } (180^\circ) \rightarrow Non\text{-}Polar$

  • b) $SO_3 \rightarrow 3\text{ groups} \rightarrow \text{Trigonal Planar arrangement, Trigonal Planar shape } (120^\circ) \rightarrow Non\text{-}Polar$

  • c) $AsCl_5 \rightarrow 5\text{ groups} \rightarrow \text{Trigonal Bipyramidal arrangement and shape } (90^\circ/120^\circ) \rightarrow Non\text{-}Polar$

  • d) $NH_3 \rightarrow 4\text{ groups} \rightarrow \text{Tetrahedral arrangement, Trigonal Pyramidal shape } (<109.5^\circ) \rightarrow Polar$

  • e) $SeF_2 \rightarrow 4\text{ groups} \rightarrow \text{Tetrahedral arrangement, Bent shape } (<109.5^\circ) \rightarrow Polar$

  • f) $SeCl_4 \rightarrow 5\text{ groups} \rightarrow \text{Trigonal Bipyramidal arrangement, Seesaw shape} \rightarrow Polar$

  • g) $NO_2^- \rightarrow 3\text{ groups} \rightarrow \text{Trigonal Planar arrangement, Bent shape } (<120^\circ) \rightarrow Polar$

  • h) $XeI_2 \rightarrow 5\text{ groups} \rightarrow \text{Trigonal Bipyramidal arrangement, Linear shape } (180^\circ) \rightarrow Non\text{-}Polar$

  • i) $PF_6^- \rightarrow 6\text{ groups} \rightarrow \text{Octahedral arrangement and shape } (90^\circ) \rightarrow Non\text{-}Polar$

  • j) $BrCl_5 \rightarrow 6\text{ groups} \rightarrow \text{Octahedral arrangement, Square Pyramidal shape} \rightarrow Polar$

  • k) $IBr_3 \rightarrow 5\text{ groups} \rightarrow \text{Trigonal Bipyramidal arrangement, T-shaped} \rightarrow Polar$

  • l) $IF_4^- \rightarrow 6\text{ groups} \rightarrow \text{Octahedral arrangement, Square Planar shape } (90^\circ) \rightarrow Non\text{-}Polar$

  1. Central Atom Identification:

  • a) $XF_3^+$ (Trigonal Pyramidal) $\rightarrow$ Group 16 element (e.g., $S, Se, Te$)

  • b) $XF_4^+$ (Tetrahedral) $\rightarrow$ Group 15 element (e.g., $P, As, Sb$)

  • c) $XF_3$ (T-shaped) $\rightarrow$ Group 17 element (e.g., $Cl, Br, I$)

  1. Polarity Comparison:

  • a) $TeCl_4$ is more polar than $ICl_4^-$ because $TeCl_4$ has an asymmetrical seesaw shape, whereas $ICl_4^-$ adopts a symmetrical square planar shape where dipoles cancel.

  • b) $NF_3$ is more polar than $NCl_3$ because the $\Delta EN$ of $N-F$ ($3.98 - 3.04 = 0.94$) exceeds that of $N-Cl$ ($3.16 - 3.04 = 0.12$).

  1. Shapes for Polar $XY_3$: Trigonal Pyramidal or T-shaped.

Intermolecular Forces (IMFs)

• Definition and Nature of Intermolecular Forces (Johannes van der Waals, 1873)

  • Electrostatic attractive forces operating between separate particles (molecules, atoms, or ions).

  • Weaker than intramolecular chemical bonds (ionic, covalent, metallic), but primary determinants of physical properties such as melting point, boiling point, volatility, viscosity, and solubility.

• The 6 Categories of Intermolecular Attractions (Ordered by Relative Strength)

  1. Ion-Dipole Forces: Electrostatic attraction between a full ionic charge and an oppositely charged pole of a polar molecule. Energy release = $40 - 600\,kJ/mol$.

  2. Hydrogen Bonding: Exceptionally strong dipole force occurring when a Hydrogen atom covalently bound to a highly electronegative atom ($N, O, F$) interacts with an unshared lone pair on an $N, O, F$ atom of an adjacent molecule. Energy release = $10 - 40\,kJ/mol$.

  3. Dipole-Dipole Forces: Attraction between opposite partial charges of permanent molecular dipoles. Energy release = $5 - 25\,kJ/mol$.

  4. Ion-Induced Dipole Forces: A full charge from an ion distorts the electron cloud of a nearby non-polar particle, inducing a temporary dipole (e.g., $Fe^{2+}$ interacting with $O_2$). Energy release = $3 - 15\,kJ/mol$.

  5. Dipole-Induced Dipole Forces: A permanent dipole distorts the electron cloud of an adjacent non-polar particle (e.g., $H_2O$ interacting with $O_2$). Energy release = $2 - 10\,kJ/mol$.

  6. London Dispersion Forces: Universal weak attractions resulting from instantaneous fluctuations in electron density that create temporary transient dipoles, which induce synchronized dipoles in neighboring particles. Magnitude scales directly with total electron count, molecular size, and accessible contact surface area. Energy release = $0.05 - 40\,kJ/mol$.

• Influence of IMFs on Physical Properties

  • Melting and Boiling Points: Phase changes in molecular compounds involve disrupting intermolecular forces, not breaking intramolecular covalent bonds. Stronger IMFs require higher thermal energy inputs to disrupt, producing elevated transition temperatures.

• Solubility ("Like Dissolves Like"): Solutes dissolve in solvents capable of offering equivalent or stronger intermolecular attractive forces.

  • Intermolecular Forces Practice Problems

• Primary force between identical particles:

  • a) $Ne \rightarrow London\ Dispersion$

  • b) $Ca \rightarrow Metallic\ Bonding$

  • c) $NH_3 \rightarrow Hydrogen\ Bonding$

  • d) $CO_2 \rightarrow London\ Dispersion$

  • e) $MgCl_2 \rightarrow Ionic\ Bonding$

• $MgCl_2$ has a significantly higher melting point than $NH_3$ because ionic bonds ($400-4000\,kJ/mol$) are much stronger than hydrogen bonds ($10-40\,kJ/mol$).

• $CO_2$ has a higher boiling point than $Ne$ because $CO_2$ possesses a larger electron cloud, generating stronger London dispersion forces.

• $Ne$ is the softest substance among the choices due to extremely weak London dispersion forces ($0.05\,kJ/mol$).

• $MgCl_2$ is most soluble in water because it undergoes ion-dipole solvation, releasing substantial energy ($40-600\,kJ/mol$).

Classification and Properties of Crystalline Solids

• Crystalline Solids

  • Solids characterized by highly ordered, repeating three-dimensional structural arrangements of constituent particles.

• Electrical Conductivity Requirements

  • A substance conducts electricity if and only if it satisfies two conditions:

  1. It contains mobile charged particles (free electrons or mobile ions).

  2. These charged particles are capable of unhindered motion through the medium.

• The 6 Main Types of Crystalline Solids

  1. Atomic Solids:

  • Building Block: Individual noble gas atoms arranged in cubic close-packed lattices.

  • Interparticle Forces: Extremely weak London dispersion forces.

  • Properties: Extremely low melting points (e.g., $\approx -200^\circ C$), soft, non-conductive, insoluble in water.

  1. Non-Polar Molecular Solids:

  • Building Block: Non-polar covalent molecules (e.g., Candle wax, $P_4$).

  • Interparticle Forces: Weak London dispersion forces.

  • Properties: Low melting points, soft, non-conductive, insoluble in water.

3. Polar Molecular Solids:

   • Building Block: Polar covalent molecules (e.g., Sucrose/Candy, $CH_2Cl_2$).

   • Interparticle Forces: Dipole-dipole and/or Hydrogen bonding.

   • Properties: Intermediate-to-low melting points, soft-to-medium hardness, non-conductive as solids or liquids, soluble in polar solvents like water.

4. Metallic Solids:

   • Building Block: Metal cations organized in a crystal lattice surrounded by a delocalized sea of electrons (e.g., $Al, Os$).

   • Interparticle Forces: Metallic bonds.

   • Properties: Variable melting points (low to extremely high), highly malleable, ductile, highly conductive as solids and liquids, insoluble in water.

5. Ionic Solids:

   • Building Block: Alternating cations and anions forming 3D lattices (e.g., Face-centered cubic $NaCl$; Body-centered cubic $CsCl$).

   • Interparticle Forces: Strong 3D ionic bonds.

   • Properties: High melting points, hard and brittle, non-conductive in solid phase, highly conductive when dissolved in water or molten, generally water soluble.

6. Network Solids (Covalent Network Solids):

   • Building Block: Atoms connected by continuous 2D or 3D arrays of covalent bonds (e.g., Quartz/$SiO_2$; Carbon allotropes: Diamond, Graphite, Fullerenes, Carbon Nanotubes).

   • Interparticle Forces: Covalent bonds extending infinitely throughout the structure.

   • Properties: Extremely high melting points (e.g., $> 3500^\circ C$), extremely hard, non-conductive (except graphite), insoluble in all common solvents.

• Master Property Comparison Matrix

  • Atomic: Attraction = London Dispersion | Melting Point = Extremely Low | Hardness = Very Soft | Solid Conductivity = No | Aqueous Conductivity = N/A | Water Solubility = Insoluble

  • Non-Polar Molecular: Attraction = London Dispersion | Melting Point = Low | Hardness = Soft | Solid Conductivity = No | Aqueous Conductivity = No | Water Solubility = Insoluble

  • Polar Molecular: Attraction = Dipole-Dipole / H-Bond | Melting Point = Low to Medium | Hardness = Soft to Medium | Solid Conductivity = No | Aqueous Conductivity = No | Water Solubility = Soluble

  • Metallic: Attraction = Metallic Bonding | Melting Point = Medium to High | Hardness = Variable / Malleable | Solid Conductivity = Yes | Aqueous Conductivity = N/A | Water Solubility = Insoluble

  • Ionic: Attraction = Ionic Bonding | Melting Point = High | Hardness = Hard & Brittle | Solid Conductivity = No | Aqueous Conductivity = Yes | Water Solubility = Soluble

  • Network: Attraction = Covalent Bonding | Melting Point = Extremely High | Hardness = Extremely Hard | Solid Conductivity = No (except graphite) | Aqueous Conductivity = N/A | Water Solubility = Insoluble

• Practice Problems: Solid Classification

  1. Solid identification from properties:

  • a) Conducts when dissolved $\rightarrow Ionic\ Solid$

  • b) Melting point $3500^\circ C$, non-conductive, insoluble $\rightarrow Network\ Solid$

  • c) Melting point $-243^\circ C$ $\rightarrow Atomic\ Solid$

  • d) Conducts in solid state $\rightarrow Metallic\ Solid$

  • e) Soft at room temperature, insoluble $\rightarrow Non\text{-}Polar\ Molecular\ Solid$

  • f) Melts at $50^\circ C$, non-conductive solid, water soluble $\rightarrow Polar\ Molecular\ Solid$

  1. Substance with $140^\circ C$ melting point, soluble in water:

  • a) Candidate types: Polar Molecular Solid or Ionic Solid.

  • b) Diagnostic test: Test electrical conductivity in aqueous solution. Conductivity indicates an ionic solid; non-conductivity indicates a polar molecular solid.

  1. Classification of specific substances:

  • a) $P_4 \rightarrow Non\text{-}Polar\ Molecular\ Solid$

  • b) $Na_3PO_4 \rightarrow Ionic\ Solid$

  • c) $Os \rightarrow Metallic\ Solid$

  • d) $SiO_2 \rightarrow Network\ Solid$

  • e) $Xe \rightarrow Atomic\ Solid$

  • f) $CH_2Cl_2 \rightarrow Polar\ Molecular\ Solid$

  1. Dissolution of $OI_2$: Non-polar bent molecular solid possessing weak IMFs; insoluble in water due to inability to form favorable interactions with polar water molecules.

  2. Boiling point difference between $H_2O_2\ (150^\circ C)$ and $H_2O\ (100^\circ C)$: $H_2O_2$ possesses two $-OH$ groups per molecule compared to one in water, forming twice as many hydrogen bonds per molecule.

  3. Melting point of $XeCl_2$: Low melting point because $XeCl_2$ is a linear, symmetrical non-polar molecular solid held together only by weak London dispersion forces.

Laboratory Activities and Analysis Questions

• Lab 1 Evaluation Checklist (PEDS Criteria)

  • P: Not fully engaged

  • E: Group of 4 or more

  • D: Not enough significant digits

  • S: Meniscus not measured properly

  • Missing/incorrect observations

  • Goggles not worn throughout experiment

  • Sitting down during active lab work

• Lab 1 Analysis Questions

  1. Distinguish Metallic vs. Network Solids: Metallic solids are electrical conductors in the solid phase and malleable; network solids are non-conductors and extremely brittle with higher melting points ($> 3000^\circ C$).

  2. Distinguish Ionic vs. Polar Molecular Solids: Ionic solids conduct electricity when dissolved in water and possess high melting points; polar molecular solids do not conduct electricity in solution and melt at lower temperatures.

  3. Soft Room Temperature Solids: Non-polar molecular solids.

  4. Ionic Solid Lattice Formation Rationale: Oppositely charged gaseous ions organize into a 3D repeating crystal lattice to minimize ion-ion repulsion and maximize electrostatic attraction. As ions lock into fixed positions, their kinetic motion decreases, releasing potential energy as lattice energy.

• Lab 2 Framework: Determining Solid Type and Explaining Properties

  • Procedure: Conduct systematic physical testing (hardness, solid conductivity, water solubility, solution conductivity, relative melting point) to identify Unknowns A, B, and C.

  • Analysis Requirements:

  1. State identified solid type.

  2. Describe structural building blocks, define attractive forces, and provide structural diagrams.

  3. Correlate identified structure and bonding forces directly to two observed physical properties.