CHMA10 Fall 2024 Notes PDF

CHMA10 FALL SEMESTER 2024 INSTRUCTOR: DR. BERNIE KRAATZ AND DR. XIAO-AN ZHANG ✫✫✫ keywords will be highlighted. Anything from the textbook will be highlighted. Any formulas will be in colour. Anything prof said outside notes is also in colour. Lecture 2 - The Quantum-Mechanical Model of the Atom V...

CHMA10 FALL SEMESTER 2024 INSTRUCTOR: DR. BERNIE KRAATZ AND DR. XIAO-AN ZHANG ✫✫✫ keywords will be highlighted. Anything from the textbook will be highlighted. Any formulas will be in colour. Anything prof said outside notes is also in colour. Lecture 2 - The Quantum-Mechanical Model of the Atom Views of Matter → 400s BCE: Democrius believed tiny indivisible particles called atoms made up all matter. Metals such as gold, silver, tin, and lead. → 1600s: In the age of alchemy, the main goal was to try to change lead to gold. → 1800s: John Dalton created the atomic theory which is that all matter is created by atoms. He also believed that atoms are hard indivisible spheres. → 1909: J.J. Thompson discovered electrons. He also believed that electrons are distributed inside a positive mass. → 1911: Ernest Rutherford discovered the proton and the nucleus of an atom. He also believed that most of an atom is empty space The Nature of Light → Maxwell (1873) proposed that visible light consists of electromagnetic waves. ⤷ Electromagnetic waves are composed of both an oscillating magnetic and electric field. ⤷ Waves are described using amplitude, wavelength (λ) and frequency (ν) using the 8 equation: 𝑣 = 𝑐/λ (𝑐 = 3𝑥10 𝑚/𝑠) → speed of light Electromagnetic Radiation Spectrum → Electromagnetic radiation is defined as energy that is emitted and transmitted in the form of electromagnetic waves. Properties of Waves: Interference → When two waves are in phase, they → When two waves are out of phase, they interfere with each other to give interfere with each other to give constructive interference. destructive interference. Properties of Waves: Diffraction → Diffraction is the bending of waves → A beam of particles does not diffract around obstacles and openings when passed through a small opening. → If light passes through a small opening, it diffracts, classifying as a wave. Nature of Light: Wave Evidence → Comes from diffraction patterns when a double slit is used. → Double slit experiment used to show how waves interact by producing light and dark spots due to constructive and destructive interference, proving it's a wave. Blackbody Radiation → A blackbody is a theoretical object that absorbs all radiation that falls on it and re-emits it with a broad range of frequencies. ⤷ Intensity of radiation escaping a blackbody varies with frequency of the radiation ⤷ Frequency shifts to higher values as the temperature increases. ⤷ Majority falls in the visible range. Blackbody Radiation and the UV Catastrophe → The inconsistency between observations and predictions based on classical physics is called the Ultraviolet Catastrophe. The Birth of Quantum Mechanics → In 1900, Max Planck decided to solve the Ultraviolet Catastrophe. → His idea was to postulate that the energy that is emitted or absorbed (in the form of light aka electromagnetic radiation) exists ONLY in discrete energy bundles called quanta. ⤷ Energy is not continuous but quantized The Planck Constant and Energy Quanta → Planck created an equation that predicts the energy of blackbody radiation ⤷ E = hv −34 −1 ⤷ h = Planck’s constant = 6. 626 × 10 𝐽 · 𝑠 and v is the frequency in Hertz, 𝑠 → Example: Nature of Light: The Photoelectric Effect  → Photoelectric effect → When light shines on some metal surfaces, then electrons are emitted from the metal that can be detected. → The kinetic energy of these electrons can be measured in various conditions. ⤷ High vs. low frequency light ⤷ High vs. low amplitude (intensity) light Quantum Mechanics: Einstein’s Noble Prize → He showed that light exists as discrete packets called photons by combining the description of light as a wave with Planck’s equation ⤷ 𝐸𝑝ℎ𝑜𝑡𝑜𝑛 = ℎ𝑣 = ℎ𝑐 ÷ λ = ∆𝐸 𝑎𝑡𝑜𝑚 −34 ⤷ h = Plank’s constant 6. 626 × 10 𝐽 ·𝑠 ⤷ λ in m 8 ⤷ c = speed of light 3. 00 × 10 𝑚/𝑠 Atomic Spectra: → An emission spectrum is formed by an electric current passing through a gas in a vacuum tube (at very low pressure) which causes the gas to emit light. ⤷ All called a bright line spectrum → An absorption spectrum is formed by shining a beam of white light through a sample of gas ⤷ Absorption spectra indicate the wavelengths of light that have been absorbed. → Every element has a unique spectrum. → We can use spectra to identify elements → Lecture 3: quantum mechanics has no explanation for multiple split lines until, it was suggested that electrons have spin (spin up or down. Fourth quantum number ms, spin of the electron that take values of ½ or -½ to represent two spin states of the electron) → Lecture 3: atomic emission spectra appear as single lines, but not always ⤷ Using high resolution instruments reveals the lines can be made of multiple “split lines” of the same wavelength Applying Quantum Mechanics: The Bohr Atomic Model → Niels Bohr took Plank’s idea of quantization and applied it to atomic spectra. ⤷ Molecules and atoms have very specific atomic spectra (colours) ⤷ Bohr aimed to link spectral data (colours it displayed) to the underlying structure of a particular compound or atom by applying quantization to electrons ⤷ Electrons release or emit light while moving between shells ⤷ En = - RH (1/n2) n = 1,2,3…. and - RH = 2.18 x 10-18 J Bohr Atomic Model  → Atoms have definite and discrete energy levels (orbital) in which an electron may exist without emitting or absorbing electromagnetic radiation → electron moves in a circular orbit about the nucleus and its motion is governed by ordinary laws of mechanics and electrostatics ⤷ RESTRICTION: The angular momentum of the electron is quantized i.e. it can only have certain discrete values → As the orbital radius increases, so does the energy i.e. the larger the orbital, the higher the energy level → electron may move from one discrete energy level (orbit) to another, with the energy difference given by: → 𝛥𝐸 = −𝑅𝐻 (1/𝑛𝑓2 - 1𝑛𝑖2) → monochromatic radiation is emitted or absorbed when an electron moves energy levels and the energy of the light photons is given by: → ΔE = ℎ𝜈 ⤷ ΔE > 0 when light is absorbed ⤷ ΔE < 0 when light is emitted Ground State vs. Excited State → Atoms that have not absorbed any energy are said to be in the ground state ⤷ The ground state is the electron configuration such that all electrons are the most stable ⤷ Lowest possible energy state ⤷ Has not absorbed any excess energy → When electrons are excited to higher energy states, they release the energy absorbed to get back to the ground state ⤷ Energy released in the form of light ⤷ Has absorbed energy Bohr Atomic Model → Example: LECTURE 2 SUMMARY → The history of the discovery of atoms. → The nature of light: light consists of electromagnetic waves → Properties of Waves: interference and diffraction → Black Body Radiation & UV CATASTROPHE → Max Planck’s experiment and constant → The Photoelectric Effect → Atomic spectra → Keywords: atoms, matter, atomic theory, proton, electron, neutron, nucleus, electromagnetic, waves, radiation, interference, diffraction, black body, UV catastrophe, quanta, photoelectric, photons, emission spectrum, atomic spectra, absorption spectrum, ground state → Key formulas: calculating frequency (𝑣 = 𝑐/λ), calculating energy using Planck’s constant (E = hv), En = - RH (1/n2), change in energy using 𝛥𝐸 = −𝑅𝐻 (1/𝑛𝑓2 - 1𝑛𝑖2) Lecture 3 - The Quantum-Mechanical Model of the Atom Cont’d Quantum Mechanics: Waves or Particles? → Bohr’s model reproduced the line spectra for 1 electron system perfectly, but it relied on electrons being particles → Louis de Broglie wondered if light energy has particle-like properties, does matter have wave-like properties?  ⤷ His suggestion was based on Einstein’s proof that light existed as discrete particles and he derived a relationship between momentum (the product of speed and mass) and wavelength for electrons ⤷ λ = ℎ/𝑚𝑣 → de Broglie’s ideas were “ad hoc”, meaning purely theoretical → Experimental evidence showed that electrons diffract and produce an interference pattern in a double slit experiment just like light…electrons act like waves ⤷ Redone experiment with laser detector: no more diffraction, wave nature gone /// laser removes wavelength…particle beam How did de Broglie get there? → de Broglie hypothesized particles and wave have the same traits, and thus the two energies are equal: → E = mc2 = hν → substitute v for c – think real particles that travel at lower speeds!!!! → E = mv2 = hν → Through the equation λ, de Broglie substituted v/λ for ν and arrived at the final expression that relates wavelength and particles with speed. → mv2 = hv/λ → λ = hv/mv2 = h/mv Quantum Mechanics: Uncertainty → Werner Heisenberg wanted to explain how wave-particle duality works and why electrons seemed to change their nature depending on the experiment. → Evidence of the dual particle/wave nature of the electron led Heisenberg to the Heisenberg Uncertainty Principle ⤷ The act of measurement changes the properties of the electron ⤷ Impossible to determine simultaneously both the position and velocity of an electron ⤷ Can’t precisely specify where an electron of known energy is at any moment in time. The Heisenberg Uncertainty Principle → Werner Heisenberg used probabilities to describe where the electron was: ⤷ ∆𝑥 · 𝑚 · ∆𝑣 ≥ ℎ/4Π = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 ⤷ Here ∆𝑥 and ∆𝑣 are the uncertainties in the position and velocity respectively Schrodinger Wave Equation → Describes both the particle and wave nature of the electron in a hydrogen atom.  → Solutions give energy states and their corresponding wave functions → Wave function ѱ (“psi”)- a mathematical representation of an atom Quantum Mechanics: Born and Probability → Max Born realized that the wave function is not suited to visualize the atom but based on his work with Heisenberg, he noticed that one can calculate a probability density for an electron. Radial Distribution Functions → Radial probability = probability/unit volume × volume of shell → We divide up the space around the nucleus into shells…sort of like an anion → Radial probability is defined as the probability of finding an electron in a given shell → Shell volume is defined as zero at the nucleus, probability of finding the electron is also zero. Atomic Orbitals and Quantum Numbers → Atomic Orbital - a three-dimensional description of the probability density for a given wave function. ⤷ Note: Orbital does not equal orbit ⤷ Characterized by a set of quantum numbers which determine orbital size, energy, shape and orientation. → The four quantum numbers for each wave function, ѱ = (n, l, ml , ms) are: ⤷ n = principal quantum number ⤷ L = 1 → angular quantum number ⤷ ml = magnetic quantum number ⤷ ms = spin quantum number The Principal Quantum Number, n → ѱ = (n, l, ml , ms) → Describes average size of the orbital and indicates the energy level → n can take on values of 1, 2, 3, 4, 5…. (only be positive integers) → The numbers of n also corresponds to letters where ⤷ 1=k ⤷ 2=L ⤷ 3=M ⤷ 4=N → In a hydrogen atom, the energy of an electron with principal quantum number n is : En = -2.18 x 10-18 J (1/n2) → ѱ2 gives probability of finding an electron in a given location (90% of the electron density is found for the 1s orbital) → “N” determines the size of this 90% boundary The Angular Momentum Quantum Number, L → ѱ = (n, l, ml , ms) → The angular momentum quantum number, L determines the shape of the boundary described by n. ⤷ L = 0, 1, 2, 3,....n-1 ⤷ Note that n limits L : that is, principal quantum number sets a limit on the angular momentum quantum number ⤷ E.g. when n = 1, L can only be equal to 0. → The value of L also corresponds to a letter ⤷ L = 0 → s - corresponds to an s orbital ⤷ L = 1 → p - corresponds to a p orbital ⤷ L = 2 → d - corresponds to a d orbital ⤷ L = 3 → f - corresponds to an f orbital → S, p, d, and f are the designations that come from the characteristics of spectral emission lines produced by electrons occupying those atomic orbitals → S = sharp; p = principal; d = diffuse; f = fundamental ⤷ If n = 1, L = 0 → s - 1 sublevel s ⤷ If n = 2, L = 0, 1 → p - 2 sublevels s, p ⤷ If n = 3, L = 0, 1, 2 → d - 3 sublevels s, p, d ⤷ If n = 4, L = 0, 1, 2, 3 → f - 4 sublevels s, p, d, f L - shapes of orbitals S orbitals → A s-type orbital has a round or spherical shape with its center at the nucleus. P orbitals → A p-type orbital has a barbell-shaped electron cloud and is centred at the nucleus. D orbitals → A d-type orbital has a multi-lobed shape and can have several lobes in a plane centred at the nucleus ml - The Magnetic Quantum Number → ѱ = (n, l, ml , ms) → The magnetic quantum number, ml, defines the spatial orientation of a single atomic orbital in 3D space around the nucleus. → ml takes all integral values from -l through 0 up to and including +l ⤷ ml = (-L….0,....+L) ⤷ Note that L limits ml : that is, the angular momentum quantum number puts a limit on the magnetic quantum number ⤷ E.g. when L = 1, that designates the p sublevel and there are only 3 allowable values of ml : -1, 0 and + 1 LECTURE 3 SUMMARY → Waves and Particles → Heisenberg’s Uncertainty Principle → Schrödinger’s wave theories → Atomic orbitals → Quantum numbers → Keywords: waves, diffraction, particles, speed, momentum, Heisenberg uncertainty principle, Schrödinger, atomic orbital, quantum numbers, principal quantum number, angular momentum quantum number, shape of orbitals (L), the magnetic quantum number (ml) → Key formulas: calculating wavelength (λ = ℎ/𝑚𝑣), calculating energy for lower speeds by substituting c for v (E = mv2 = hν) Lecture 4 - The Quantum-Mechanical Model of the Atom Cont’d Quantum Mechanics: Pauli and Exclusion → Pauli proposed that for a multi-electron system (atoms other than hydrogen) there must be restrictions on the electrons in the orbitals → The Pauli Exclusion Principle states that no two electrons in a poly-electron atom can be described by the same 4 quantum numbers. ms - The Spin Quantum Number → Every electron in an atom needs 4 quantum numbers to fully describe it ⤷ 4th quantum number is the spin number, ms → Each orbital (s, p, d, f) can contain a maximum of 2 electrons → Value of ms is +½ or -½ Orbital Nodes → A node - region in space with zero probability of finding an electron, ⤷ Results of destructive interference → Type 1: Angular (planar or conical) ⤷ Never occur in s orbitals → Type 2: Radial (spherical) ⤷ Seen in radial distribution diagram ⤷ Number of radial nodes = n - L - 1 → Total number of nodes in for any given orbital equals n - 1 Orbital Phases  → Wave functions (and therefore orbitals) have a phase: → Orbitals change phase when they cross a node ⤷ Represent with a colour or sign change Quantum Field Theory: Paul Dirac → Paul proposed the idea of wave mechanics and matrix mechanics in one unified formulation now known as Quantum Field Theory ⤷ Allowed light or electrons to be treated as a wave or a particle Orbital Energies in a Hydrogen Atom → Energy depends only on the principal quantum number ⤷ Only one electron Multi-Electron Systems → Schroginer’s equation can only be solved exactly for one-electron system → Multi-electron systems are complicated by electron-electron repulsion. → Orbital energies depend on n and L Coulomb’s Law → Coulomb’s law explains why orbitals lose degeneracy: 𝐸𝑝𝑜𝑡 = 1/4Πξ𝑜 𝑞1𝑞2/𝑟 → Attraction and repulsion of two charged particles influenced by; ⤷ Charge on particles: ⤷ Energy is positive for the same charge leading to repulsion ⤷ Energy is negative for opposite charges leading to attraction → Attraction and repulsion of two charged particles influenced by; ⤷ The distance between the particles: ⤷ The closer together, the greater the energy. Electron Shielding → Atoms are composed of protons and electrons → With more than one electron present, have both attractive (electron-proton) and repulsive (electron-electron) interactions → Electrons screen or shield each other from the full force of the nuclear charge (where the protons live) → Electrons closer to the nucleus (in lower energy levels) are more effective at shielding than electrons farther from the nucleus. → This leads to some orbitals being more stable than others Electron Penetration → From the radial distribution function, we see that the s and p functions overlap → What does this overlap mean? ⤷ Compare the 1s and 2s functions...we see there is a local maximum from the 2s within the 1s function ⤷ This indicates that there is a high probability of finding the 2s electron close to the nucleus i.e. the 2s electrons penetrate the 1s orbital ⤷ 2p orbital does not have a local maximum and hence 2p electrons do not penetrate to the nucleus as effectively as 2s electrons Electron Configuration → Electron configuration is the distribution of an atom’s electrons among its atomic orbitals Aufbau Principle - The Energy of Orbitals → The Aufbau principle tells the order to fill in electrons. → Electrons will occupy the lowest energy orbitals first Hund’s Rule; Energy Levels of Orbitals → Not all orbitals have the same energy.  → If there are degenerate orbitals, the electron configuration of the lowest energy has the maximum number of unpaired electrons with parallel spins. → When two electrons occupy separate orbitals of equal energy, the repulsive interaction between them is lower. LECTURE 4 SUMMARY → The Pauli Exclusion Principle → ms - The Spin Quantum Number → Orbital nodes → Orbital phases → Quantum field theory → Coulomb’s law → Electron shielding → Electron configuration → Aufbau principle → Hund’s Rule → Keywords: electrons, spin quantum number, nodes, phases → Key formulas: Coulomb’s law (𝐸𝑝𝑜𝑡 = 1/4Πξ𝑜 𝑞1𝑞2/𝑟) Lecture 5 - The Quantum-Mechanical Model of the Atom Cont’d SLIDE NOTES MAIN TOPIC → ORBITAL FILLING BASED ON TRENDS AND PERIODIC TABLE Magnetic Properties and Electron Configurations → Since electrons are moving electric charges, they create a magnetic field. → If there are unpaired electrons, then a net magnetic field is generated and the species is attracted to an external magnetic field ⤷ Known as paramagnetic → If there are no unpaired electrons, all the magnetic fields cancel out, there is no net magnetic field generated and the species is slightly repelled by an external magnetic field ⤷ Known as diamagnetic SLIDE NOTES SUMMARY → Electrons occupy orbitals so as to minimize the energy of the atom, therefore, lower energy orbitals fill before higher energy orbitals (Aufbau Principle). → Orbitals fill in the following order: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6f  → Orbitals can hold no more than two electrons each. When two electrons occupy the same orbital their spins are opposite. This is another way of expressing the Pauli exclusion principle (no two electrons in one atom can have the same four quantum numbers). → When orbitals of identical energy are available, electrons first occupy these orbitals singly with parallel spins rather than in pairs. Once the orbitals of equal energy are half-full, the electrons start to pair (Hund’s rule). OVERALL SUMMARY Lecture 2: The Basics of Atoms and Light 1. History of the Atom: → scientists thought everything was made of tiny, unbreakable particles called atoms. Over time, they discovered the parts of atoms: protons, neutrons, and electrons. 2. Light and Waves: → Light acts like a wave, with peaks and valleys. These waves can interact with each other (called interference) or bend around objects (called diffraction). 3. Black Body Radiation & UV Catastrophe: → A black body is something that absorbs and emits light perfectly. Scientists couldn’t explain why it didn’t emit unlimited high-energy light (UV catastrophe). 4. Planck’s Experiment: → Max Planck figured out light energy comes in tiny packets called quanta. He gave us Planck’s constant,. 5. The Photoelectric Effect: → Einstein showed light is not just a wave but also a particle (photon). Shining light on metal can knock electrons loose, but only if the light has enough energy. 6. Atomic Spectra: → Atoms emit light in specific colors when their electrons move between energy levels. These colors are like fingerprints for each element. → Key Formulas to Remember: → Frequency = speed of light / wavelength → Energy of light = Planck’s constant × frequency Lecture 3: Waves, Particles, and Quantum Mechanics 1. Wave-Particle Duality: → Tiny particles (like electrons) sometimes act like waves. This means they don’t just exist in one spot—they’re spread out. 2. Heisenberg’s Uncertainty Principle: → You can’t know exactly where an electron is and how fast it’s moving at the same time. 3. Schrödinger’s Wave Theory:  → Schrödinger used math to describe electrons as waves. This led to the idea of atomic orbitals—clouds where electrons are likely to be found. 4. Quantum Numbers: → Quantum numbers are like an electron’s address, describing its energy, shape, and position: n: Energy level l: Shape (s, p, d, f orbitals) m : Direction of the orbital mₛ: Spin (up or down) → Key Formula: → Wavelength = Planck’s constant / (mass × speed) Lecture 4: Rules for Electrons 1. Pauli Exclusion Principle: → No two electrons in an atom can have the same quantum numbers. Each orbital can hold at most two electrons with opposite spins. 2. Hund’s Rule: → Electrons fill orbitals of the same energy one at a time before pairing up, like sitting alone on a bus before sitting next to someone. 3. Electron Shielding: → Inner electrons block the pull of the nucleus on outer electrons, making outer ones easier to remove. 4. Electron Configuration: → Electrons fill orbitals in a specific order based on energy (1s, 2s, 2p, etc.). → Key Formula: → Coulomb’s law explains the energy between two charges: Lecture 5: Magnetic Properties & Orbital Filling 1. Magnetic Properties: → Atoms with unpaired electrons are attracted to magnets (paramagnetic). → Atoms with paired electrons are slightly repelled (diamagnetic). 2. Orbital Filling Trends: → Electrons fill lower-energy orbitals first (Aufbau principle). → The periodic table helps predict the order: 1s → 2s → 2p → 3s… CHMA10 FALL SEMESTER 2024 INSTRUCTOR: DR. BERNIE KRAATZ AND DR. XIAO-AN ZHANG ✫✫✫ keywords will be highlighted. Anything from the textbook will be highlighted. Any formulas will be in colour. Anything prof said outside notes is also in colour. Lecture 6 - Periodic Properties of the Elements Developments of the Periodic Table → 1865: John Newlands arranged elements in order of atomic mass → 1870: Dmitri Mendeleev arranged elements by atomic mass but also made adjustments in order to group elements with similar properties. Periodic Trends: Within a Group → Elements in the same group (column) have similar chemical or physical properties, or properties that vary systematically. → Alkali metals have similar properties: ⤷ Soft metals ⤷ Relatively low-melting ⤷ Reactive with water → Their reactivity increases as you move down the group → Reaction with oxygen: alkali metal + oxygen → alkali metal oxide Multi-Electron Systems → Orbital energies depends on n and l Origin of Trends: Electron Configuration → Periodic trends explained by electron configuration of valence electrons. ⤷ Valence Electrons - outermost electrons which are involved in bonding; Those with the highest value of n (plus outermost d electrons for transition metals) ⤷ Core (inner) Electrons - those electrons corresponding to the previous noble gases. → Same valence electron configuration leads to similar properties Metals, Non-Metals and Semi-metals → Electrons can also be classified as metals, non-metals, or semi-metals based on their chemical and physical properties Metallic Character → Metallic character is how closely an element’s properties match the ideal properties of a metal → Metallic character decreases left-to-right across a period → Metallic character increases down the column → Metals tend to lose electrons → Non-metals tend to gain electrons → Transition metals lose electrons from the orbital with the highest principal quantum number. SUMMARY: → The periodic table is organized based on increasing atomic number → Other general organizational trends that are reflected in the table are it can be divided into blocks based on the valence orbital electrons → It can also be broken into categories based on the character of the element ⤷ Metal  ⤷ Semi metal ⤷ Non metal Explaining Periodic Trends: Shielding → In a multi-electron system, electrons are simultaneously attracted to the nucleus and repelled by each other. → Outer electrons are shielded from nucleus by the core electrons ⤷ screening or shielding effect ⤷ Outer electrons do not effectively screen each other from the nucleus charge → The shielding causes the outer electrons to not experience the full strength of the nuclear charge. Effective Nuclear Charge → The effective nuclear charge, 𝑍eff is the net positive charge that is attracting a particular electron in the valence cell. → Where Z is the nuclear charge, S is the number of electrons in lower energy levels. ⤷ 𝑍eff = Z - S Shielding Effect Between Subshells → Within a shell, partial shielding occurs (much less than between shells) via penetration → 2s is more penetrating than 2p → 2p is partially shielded by 2s Slater’s Rules → 𝑍eff = Z - 𝜎 → Z = atomic number, 𝜎 = screening, Slater or shielding constant → To determine 𝜎: ⤷ Write the electron configuration of the element and group the subshells as follows: (1s), (2s, 2p), (3s, 3p), (3d), (4s, 4p), (4d), (4f), (5s, 5p),... ⤷ Electrons in the groups on the right from the designated electron contribute nothing to the shielding constant → 4s is filled before 3d LECTURE 6 SUMMARY → → Keywords: → Key formulas: Lecture 7 - Cont’d Periodic Properties of the Elements Trend #1: Atomic Radius - Main Group → There are several methods for measuring the radius of an atom, and they give slightly different numbers. ⤷ Van der waals radius = nonbonding ⤷ Covalent bonding = bonding radius ⤷ Atomic radius is the average radius of an atom based on measuring large numbers of elements and compounds → Atomic Radius increases down a group ⤷ Valence shell farther from nucleus and principal quantum number increasing ⤷ Effective nuclear charge fairly close → Atomic Radius decreases across a period (left to right) ⤷ Adding electrons to same valence shell ⤷ Effective nuclear charge increases ⤷ Valence shell held closer Trend in Atomic Radius - Transition Metals → Atoms in the same group increase in size down the column → Atomic radii of transition metals roughly the same size across the d block ⤷ Valence shell ns2, not the (n-1)d electrons and once the 4s orbital is filled, it is higher in energy than 3d orbitals ⤷ 4s electrons determine size ⤷ Inner 3d electrons screen increasing nuclear charge Trend #2: Ionic Radius → Ionic radius - radius of a cation or anion → Ion size increases down the column ⤷ Higher valence shell therefore large ion → Ions in same group have same charge → Cations are smaller than neutral atoms → Anions are larger than neutral atoms → Cations smaller than anions → For isoelectronic species: ⤷ Larger positive charge = smaller cation ⤷ Larger negative charge = larger anion Explaining Trends in Cationic Radius → When atoms form cations, the valence electrons are removed  ⤷ Results in cation being smaller than atom → “New valence electrons” get larger effective nuclear charge than “old valence electrons”, shrinking the ion. → Down a group, increases (n-1) level, causing cations to get larger → To the right across a period, increases effective nuclear charge for isoelectronic cations, causing cations to get smaller. Explaining Trends in Anionic Radius → When atoms form anions, electrons are added to the valence shell ⤷ Results in anion being larger than atom → “New valence electrons” get smaller effective nuclear charge than “old valence electrons”, increasing the size. → Down a group, increases n level, causing anions to get larger → To the right across a period, increases effective nuclear charge for isoelectronic anions, causing anions to get smaller. Trend #3: Ionization Energies, IE → Ionization energy - amount of energy required to remove a ground state electron from a gaseous atom. → Minimum energy needed to remove an electron from an atom or ion ⤷ Defined for atoms or ions in the gas state ⤷ Endothermic process (requires energy input…doesn’t happen spontaneously) ⤷ The lowest ionization energy value corresponds to removal of a valence electron (easiest electron to remove) ⤷ E.g. Mg(g) → Mg+(g) + e- ∆𝐸1 = 𝐼𝐸1 = 738 𝑘𝐽 // remove e- from neutral atom ⤷ E.g. Mg+(g) → Mg2+(g) + e- ∆𝐸2 = 𝐼𝐸2 = 1451 𝑘𝐽 // energy to remove from 1+ ion → I is always positive → I1 < I2 < I3 → I1 increases with Zeff → IE = RH Z2eff/n2 LECTURE 7 SUMMARY → → Keywords: → Key formulas: Lecture 8 - Cont’d Periodic Properties of the Elements Irregularities in the General Trend of IE → The trend is not followed when the added valence electron in the next element ⤷ Enters a new sublevel (higher energy sublevel) ⤷ Is the first electron pair in one orbital of the sublevel (electron repulsions lower energy) First Ionization Energies Trends ⤷ Across period: Increasing ⤷ Down column: decreasing Trend #4: Electron Affinity → Electron affinity - the amount of energy released when an atom gains an electron in the gas state ⤷ Measure of extent to which an atom can accept an extra electron ⤷ Unlike ionization energies, either positive or negative depending on the element ⤷ If EA < 0, energy is released when adding an electron (exothermic) ⤷ If EA > 0, energy must be added to produce an anion (endothermic) ⤷ EA can be zero i.e. no net change in energy ⤷ Mg(g) + e- → Mg-(g) ∆𝐸1 = 𝐸𝐴1 → The trends in EA are similar for IE: ⤷ Within a group, there is not much change ⤷ Within a period, there is a general increase…might be related to Zeff. → Across a period: Increasing → Down a column = decreasing Exceptions in Electron Affinity Trends → Three notable exceptions in EA trends (Group 2A (2), 5A (15), 8A (18)) → Highest EA values in any period occur for the halogens First and Second Electron Affinity Values → EA1 can be greater than or equal to zero or negative → Second electron affinity is always positive ⤷ Electron-electron repulsion in a dianion ⤷ Attractive forces of the nucleus are not great enough to overcome the extra repulsion force due to the second added electron Reactive Chemical → Atoms that have incomplete valence shell are reactive atoms  → Chemical bond making: losing or gaining electrons from other atoms or sharing electrons with other atoms. Types of Chemical Bonds → Two types: → Ionic bonds are formed between ions; there is no electron sharing → Covalent bonds are formed between elements via electron sharing Electronegativity and the Periodic Table → Move left to right in periodic table = electronegativity increases → Move down a group = electronegativity decreases → One of the reasons why metals and nonmetals form ionic bonds ⤷ Large difference in electronegativity, then the bond will be ionic (elements separated by 4 or more other elements on the periodic table) Ionic Bonds → Ionic bonds occur between atoms when there is a large difference (2.0 or more) in electronegativity between the two atoms → In general, when you mix a metal and a nonmetal: ⤷ metal will lose electrons or become oxidized (smaller electronegativity) ⤷ non-metal will gain lose electrons or become reduced (larger electronegativity) → both elements will obtain a complete valence shell and become more stable through this process Covalent Bonds → Covalent bonds occur between atoms with a small difference (or even no difference) in electronegativity ⤷ The elements are generally not very far apart on the periodic table (usually less than 4 atomic numbers apart) → If the difference in electronegativity is between 0.4 and 2.0, then the bond is considered polar covalent ⤷ The electrons are not shared perfectly evenly → If the difference in electronegativity is less than 0.4, then the bond is considered pure covalent ⤷ The electrons are shared evenly Bonding and Electronegativity Overview → Two types of Covalent Bonds: Pure covalent bond and polar covalent bond → Pure Covalent Bond: ⤷ < 0.4 ΔEN with electrons that are shared evenly → Polar Covalent Bond:  ⤷ < 0.4 ΔEN < 2.0 with electrons that are not shared equally and element with larger electronegativity pulls electrons closer LECTURE 8 SUMMARY → → Keywords: → Key formulas: OVERALL SUMMARY CHMA10 FALL SEMESTER 2024 INSTRUCTOR: DR. BERNIE KRAATZ AND DR. XIAO-AN ZHANG ✫✫✫ keywords will be highlighted. Anything from the textbook will be highlighted. Any formulas will be in colour. Anything prof said outside notes is also in colour. Lecture 9 - Bonding Ⅰ: Lewis Theory Chemical Bonding → Chemical Bonding Theory: describes interactions between atoms. → From elements to molecules Why Do Atoms Form Bonds? → Chemical bonds form because they lower the potential energy between the charged particles that compose atoms → A chemical bond forms when the potential energy of the bonded atoms is less than the potential energy. → To calculate potential energy, we need the following interactions: ⤷ Nucleus-to-nucleus repulsions ⤷ Electron-to-Electron repulsions ⤷ Nucleus-to-electron repulsions Types of Bonds → Type of Atoms = Type of Bond = Characteristic of Bond ⤷ Metal and nonmetal = ionic = electrons transferred ⤷ Non Metal and nonmetal = covalent = electrons shared ⤷ Metal and metal = metallic = electrons pooled Lewis Bonding Theory → Lewis’ theory emphasizes valence electrons to explain bonding → Atoms bond together by either transferring or sharing electrons → Usually results in all atoms obtaining an outer shell with eight electrons (Octet Rule) The Octet Rule → When atoms bond, they tend to gain, lose, or share electrons to result in eight valence electrons → ns2np6 → EXCEPTIONS: ⤷ H, Li, Be, B attain an electron configuration like He: ⤷ He = two valence electrons, a duet ⤷ Li loses its one valence electron ⤷ H shares or gains one electron (though it commonly loses its on electron to become H+ with zero electron ⤷ Be loses two electrons to become Be2+ (though it commonly shares its two electrons in covalent bonds, resulting in four valence electrons) ⤷ B may lose three electrons to become B3+ (though it commonly shares its three electrons in covalent bonds, resulting in six valence electrons) ⤷ Expanded octets for elements in Period 3 or below ⤷ d orbitals Valence Electrons & Bonding → Valence electrons are held most loosely → Chemical bonding involves the transfer or sharing of electrons between two or more atoms → Valence electrons are most important in bonding Lewis Structures of Atoms → Represent the valence electrons of main-group elements as dots surrounding the symbol of the element → IONS (MAIN GROUP) ⤷ Cations metals usually have lewis symbols without valence electrons ⤷ Anions have lewis symbols with eight valence electrons Stable Electron Arrangements & Ion Charge → Metals form cations by losing enough electrons to get the same electron configuration as the previous noble gas → Nonmetals form anions by gaining enough electrons to get the same electron configuration as the next noble gas → The noble gas configuration is very stable. Ionic Bonding and Electron Transfer → Lewis symbols can be used to represent the transfer of electrons from metal atom to nonmetal atom, resulting in ions that are attracted to each other and therefore bond Energy of Ionic Bond Formation → The ionization energy of the metal is endothermic → The electron affinity of the nonmetal is exothermic → Ionization energy of metal > electron affinity of nonmetal Ionic Bonding & Crystal lattice → The extra energy that is released from the formation of a structure in which every cation is surrounded by anions. (crystal lattice) → Held together by the electrostatic attraction of the cations for all surrounding anions → Maximizes attraction between cations and anions, leading to the most stable arrangement → Electrostatic attraction is non directional → Chemical formula is an empirical formula, giving ratio of ions Lattice Energy → The extra stability that accompanies the formation of the crystal lattice is measured as the lattice energy → The lattice energy is the energy released when the solid crystal forms from separate ions in the gas state (always exothermic // hard to measure) → Lattice energy depends directly on size of charges and inversely on distance between ions Enthalpy: Chapter 6.6-6.8) → The value of ΔrH for a chemical reaction is the amount of heat absorbed or evolved in the reaction under conditions of constant pressure. → An endothermic reaction absorbs heat from the surroundings and has a positive ΔrH. An endothermic reaction feels cold to the touch. → An exothermic reaction gives off heat to the surroundings and has a negative ΔrH. AN exothermic reaction feels warm to the touch. → Chemical Potential Energy: source of heat given off in an exothermic chemical reaction ⤷ In an endothermic chemical reaction, the heat absorbed is stored as chemical potential energy ⤷ Potential energy interconverts with thermal energy ⤷ Bonds break ⤷ Bonds form ⤷ Nuclei & electrons reorganize → Hess’s Law: the heat of any reaction ΔH°f for a specific reaction is equal to the sum of the heats of reaction for any set of reactions which in sum are equivalent to the overall reaction LECTURE 9 SUMMARY → → Keywords: → Key formulas: Lecture 10 - Cont’d Bonding Ⅰ: Lewis Theory Determining Lattice Energy: The Born-Haber Cycle → The Born–Haber Cycle is a hypothetical series of reactions that represents the formation of an ionic compound from its constituent elements → The reactions are chosen so that the change in enthalpy of each reaction is known except for the last one, which is the lattice energy → Use Hess’s Law to add up enthalpy changes of other reactions to determine the lattice energy. → H°f(salt) = H°f(metal atoms, g) + H°f(nonmetal atoms, g) + H°f(cations, g) + H°f(anions, g) + H°(crystal lattice) → H°(crystal lattice) = Lattice Energy → for metal atom(g) → cation(g), H°f = 1st ionization energy → don’t forget to add together all the ionization energies to get to the desired cation → M2+ = 1st IE + 2nd IE → for nonmetal atoms (g) → anions (g), H°f = electron affinity Trends in Lattice Energy: Ion SIze → The force of attraction between charged particles decreases with increase of the distance between them → Larger ions mean the center of positive charge (nucleus of the cation) is farther away from the negative charge (electrons of the anion) → larger ion = weaker attraction → weaker attraction = smaller lattice energy → COULOMB’S LAW : 𝐸 = 1/4ΠΣ0 𝑞1𝑞2/𝑟 Trends in Lattice Energy: Ion Charge → The force of attraction between oppositely charged particles is directly proportional to the product of the charges → Larger charge means the ions are more strongly attracted → larger charge = stronger attraction → stronger attraction = larger lattice energy → Of the two factors, ion charge is generally more important Ionic Bonding: Model vs. Reality → Lewis theory predicts ionic compounds should have high melting points and boiling points because breaking down many strong ionic attractions in crystal should require a lot of energy → the larger the lattice energy, the higher the melting point → Ionic compounds have high m.p. and b.p. → Lewis theory implies that if the ions are displaced from their position in the crystal lattice, that repulsive forces should occur → This predicts the crystal will become unstable and break apart. Lewis theory predicts ionic solids will be brittle. → Ionic solids are brittle. When struck they shatter. → To conduct electricity, a material must have charged particles that are able to flow through the material → Lewis theory implies that, in the ionic solid, the ions are locked in position and cannot move around → Lewis theory predicts that ionic solids should not conduct electricity → Ionic solids do not conduct electricity → Lewis theory implies that, in the liquid state or when dissolved in water, the ions will have the ability to move around → Lewis theory predicts that both a liquid ionic compound and an ionic compound dissolved in water should conduct electricity → Ionic compounds conduct electricity in the liquid state or when dissolved in water Lewis Theory of Covalent Bonding → Lewis theory implies that another way atoms can achieve an octet of valence electrons is to share their valence electrons with other atoms → The shared electrons would then count toward each atom’s octet → The sharing of valence electrons is called covalent bonding Covalent Bonds → Nonmetal atoms have relatively high ionization energies, so it is difficult to remove electrons from them → When nonmetals bond together, it is better in terms of potential energy for the atoms to share valence electrons → potential energy lowest when the electrons are between the nuclei → Shared electrons hold the atoms together by attracting nuclei of both atoms Covalent Bonding: Bonding and Lone Pair Electrons → Electrons that are shared by atoms are called bonding pairs → Electrons that are not shared by atoms but belong to a particular atom are called lone pairs Single Covalent Bonds → When two atoms share one pair of electrons it is called a single covalent bond → One atom may use more than one single bond to fulfill its octet Double Covalent Bonds → When two atoms share two pairs of electrons the result is called a double covalent bond Triple Covalent Bonds → When two atoms share three pairs of electrons the result is called a triple covalent bond LECTURE 10 SUMMARY → → Keywords: → Key formulas: Lecture 11 - Cont’d Bonding Ⅰ: Lewis Theory Covalent Bonding: Model vs. Reality → Lewis theory implies that some combinations should be stable, whereas others should not (because the stable combinations result in “octets”) → Using these ideas of Lewis theory allows us to predict the formulae of molecules of covalently bonded substances → Hydrogen (H2) and the halogens (X2) are all diatomic molecular elements, as predicted by Lewis theory → Oxygen generally forms either two single bonds or a double bond in its molecular compounds, as predicted by Lewis theory → Lewis theory of covalent bonding implies that the attractions between atoms are directional → the shared electrons are most stable between the bonding atoms → Therefore Lewis theory predicts covalently bonded compounds will be found as individual molecules → rather than an array like ionic compounds → Compounds of nonmetals are often made of individual molecule units → Lewis theory predicts the melting and boiling points of molecular compounds should be relatively low  ⤷ involves breaking the attractions between the molecules, but not the bonds between the atoms ⤷ the covalent bonds are strong, but the attractions between the molecules are generally weak → Molecular compounds have low melting points and boiling points → Lewis theory predicts that the hardness and brittleness of molecular compounds should vary depending on the strength of intermolecular attractive forces → the kind and strength of the intermolecular attractions varies based on many factors → Some molecular solids are brittle and hard, but many are soft and waxy → Lewis theory predicts that neither molecular solids or liquids should conduct electricity → there are no charged particles around to allow the material to conduct → Molecular compounds generally do not conduct electricity in the solid or liquid state → Molecular acids conduct electricity when dissolved in water, but not in the solid or liquid state, due to them being ionized by the water → Lewis theory predicts that the more electrons two atoms share, the stronger the bond should be → Bond strength is measured by how much energy must be added into the bond to break it in half → In general, triple bonds are stronger than double bonds, and double bonds are stronger than single bonds → however, Lewis theory would predict double bonds are twice as strong as single bonds, but the reality is they are less than twice as strong → Lewis theory predicts that the more electrons two atoms share, the shorter the bond should be when comparing bonds to like atoms → Bond length is determined by measuring the distance between the nuclei of bonded atoms → In general, triple bonds are shorter than double bonds, and double bonds are shorter than single bonds Polar Covalent Bonding → Covalent bonding between unlike atoms results in unequal sharing of the electrons → one atom pulls the electrons in the bond closer to its side → one end of the bond has larger electron density than the other → The result is a polar covalent bond ⤷ bond polarity ⤷ the end with the larger electron density gets a partial negative charge ⤷ the end that is electron deficient gets a partial positive charge Bond Polarity → Most bonds have some degree of sharing and some degree of polarization to them → Bonds are classified as covalent if the amount of electron transfer is insufficient for the material to display the classic properties of ionic compounds  → If the sharing is unequal enough to produce a significant dipole in the bond, the bond is classified as polar covalent Electronegativity → The ability of an atom to attract bonding electrons to itself is called electronegativity → Increases across period (left to right) and → Decreases down group (top to bottom) ⤷ fluorine is the most electronegative element ⤷ francium is the least electronegative element ⤷ noble gas atoms are not assigned values ⤷ Generally opposite of atomic size trend → The larger the difference in electronegativity, the more polar the bond → negative end toward more electronegative atom Bond Dipole Moments → Dipole moment, µ, is a measure of bond polarity → a dipole is a material with a (+) and (−) end → it is directly proportional to the size of the partial charges and directly proportional to the distance between them → µ = (q)(r) → Generally, the more opposite partial charge on two atoms and the larger the atoms are, the larger the dipole moment Percent Ionic Character → The percent ionic character is the percentage of a bond’s measured dipole moment compared to what it would be if the electrons were completely transferred → The percent ionic character indicates the degree to which the electron is transferred → Percent ionic character = measured µ / µ for completed e-transfer × 100% Lewis Structures → Lewis Theory predicts that atoms will be most stable when they have their octet of valence electrons → It does not require that atoms have the same number of lone pair electrons they had before bonding ⤷ first use the octet rule → Some atoms commonly violate the octet rule ⤷ Be generally has two bonds and no lone pairs in its compounds ⤷ B generally has three bonds and no lone pairs in its compounds ⤷ many elements may end up with more than eight valence electrons in their structure if they can use their empty d orbitals for bonding ⤷ expanded octet  → Generally try to follow the common bonding patterns → C = 4 bonds & 0 lone pairs, N = 3 bonds & 1 lone pair, O= 2 bonds & 2 lone pairs, H and halogen = 1 bond, Be = 2 bonds & 0 lone pairs, B = 3 bonds & 0 lone pairs → often Lewis structures with line bonds have the lone pairs left off → their presence is assumed from common bonding patterns → Structures that result in bonding patterns different from the common may have formal charges Formal Charge → During bonding, atoms may end with more or fewer electrons than the valence electrons they brought in order to fulfill octets → This results in atoms having a formal charge → Sum of all the formal charges in a molecule = 0 WRITING LEWIS FORMULAS OF MOLECULES → 1. Write skeletal structure → 2. Count valence electrons → 3. Attach atom together with pairs of electrons, and subtract from the total → 4. Complete octets, outside-in → 5. If all octets complete, give extra electrons to the central atom → 6. If central atom does not have octet, bring in electrons from outside atoms to share → 7. Assign formal charges to the atoms LECTURE 11 SUMMARY → → Keywords: → Key formulas: Lecture 12 - Cont’d Bonding Ⅰ: Lewis Theory Exceptions to the Octet Rule → Odd number electron species e.g., NO (nitric oxide) ⤷ will have one unpaired electron ⤷ Free-radical ⤷ generally, very reactive → Incomplete Octets → ✓Boron: six electrons around B → Expanded octets  → ✓elements with empty d orbitals can have more than eight electrons (up to 12, occasionally 14, third row and beyond) Resonance → Lewis theory localizes the electrons between the atoms that are bonding together → Extensions of Lewis theory suggest that there is some degree of delocalization of the electrons – we call this concept resonance → Delocalization of charge helps to stabilize the molecule Resonance Structures → When there is more than one Lewis structures for a molecule that differ only in the position of the electrons, they are called resonance structures → The actual molecule is a combination of the resonance forms – a resonance hybrid → ✓the molecule does not resonate between the two forms, though we often draw it that way → Look for multiple bonds or lone pairs Rules of Resonance Structures → Resonance structures must have the same connectivity → ✓ only electron positions can change → Resonance structures must have the same number of electrons → Second row elements have a maximum of eight valence electrons → ✓ bonding and non-bonding → ✓ third row can have expanded octet → Formal charges must total molecular (ionic) charge DRAWING RESONANCE STRUCTURES → 1. Draw first Lewis structure that maximizes octets → 2. Assign formal charges → 3. Move electron pairs from atoms with (−) formal charge toward atoms with (+) formal charge → 4. If (+) fc atom is 2nd-row, only move in electrons if you can move out electron pairs from multiple bond → 5. If (+) fc atom 3rd row or below, keep bringing in electron pairs to reduce the formal charge, even if get expanded octet Bond Energies → Chemical reactions involve breaking bonds in reactant molecules and making new bonds to create the products → The ΔH° reaction can be estimated by comparing the cost of breaking old bonds to the income from making new bonds  → The amount of energy it takes to break one mole of a bond in a compound is called the bond energy → ✓ in the gas state → ✓ homolytically – each atom gets ½ bonding electrons General Trends in Bond Energies → In general, the more electrons two atoms share, the stronger the covalent bond → ✓must be comparing bonds between like atoms → ✓C≡C (837 kJ) > C=C (611 kJ) > C−C (347 kJ) → ✓C≡N (891 kJ) > C=N (615 kJ) > C−N (305 kJ) → In general, the shorter the covalent bond, the stronger the bond → ✓must be comparing similar types of bonds → ✓Br−F (237 kJ) > Br−Cl (218 kJ) > Br−Br (193 kJ) → ✓bonds get weaker down the column → ✓bonds get stronger across the period Using Bond Energies to Estimate ΔH° rxn → The actual bond energy depends on the surrounding atoms and other factors → We often use average bond energies to estimate the ΔHrxn → Bond breaking is endothermic, ΔH (breaking) = + → Bond making is exothermic, ΔH (making) = − → ΔHrxn = ∑ (ΔH(bonds broken)) + ∑ (ΔH(bonds formed)) Bond Lengths → The distance between the nuclei of bonded atoms is called the bond length → Because the actual bond length depends on the other atoms around the bond we often use the average bond length Trends in Bond Lengths → In general, the more electrons two atoms share, the shorter the covalent bond → ✓ must be comparing bonds between like atoms → Generally, bond length decreases from left to right across a period → Generally, bond length increases down the column → In general, as bonds get longer, they also get weaker BOND VIBRATIONS → Bond lengths are not static. Bonds vibrate. → Different vibrational motions: → 1. Symmetrical → 2. Scissoring → 3. Wagging  → 4. Anti-symmetrical stretching → 5. Rocking → 6. Twisting METALLIC BONDS → The low ionization energy of metals allows them to lose electrons easily → The simplest theory of metallic bonding involves the metal atoms releasing their valence electrons to be shared by all to atoms/ions in the metal → Bonding results from attraction of the cations for the delocalized electrons LECTURE 12 SUMMARY → → Keywords: → Key formulas: CHMA10 FALL SEMESTER 2024 INSTRUCTOR: DR. BERNIE KRAATZ AND DR. XIAO-AN ZHANG ✫✫✫ keywords will be highlighted. Anything from textbook will be highlighted. Lecture 13 - Chemical Bonding Ⅱ: Molecular Shape, Valence Bond Theory, & Molecular Orbital Theory Molecular Geometry → Molecules are 3-dimensional objects → We often describe the shape of a molecule with terms that relate to geometric figures → These geometric figures have characteristic “corners” that indicate the positions of the surrounding atoms around a central atom in the center of the geometric figure → The geometric figures also have characteristic angles that we call bond angles Effect of Lone Pairs → The bonding electrons are shared by two atoms, so some of the negative charge is removed from the central atom. → The nonbonding electrons are localized on the central atom, so area of negative charge takes more space Electron Groups → The Lewis structure predicts the number of valence electron pairs around the central atom(s) → Each lone pair of electrons constitutes one electron group on a central atom → Each bond constitutes one electron group on a central atom Electron Group Geometry → There are five basic arrangements of electron groups around a central atom → Each of these five basic arrangements results in five different basic electron geometries → For molecules that exhibit resonance, the electron geometry of the central atom will be the same considering the resonance hybrid. VSEPR Theory → Valence-shell electron-pair repulsion (VSEPR) Theory predicts molecular geometry by arranging electron pairs (groups) so as to minimize electrostatic repulsions. FIVE BASIC SHAPES → Linear (hybridization = sp) → Trigonal-planar (hybridization = sp2) → Tetrahedral (hybridization = sp3) → Trigonal-bipyramidal (hybridization = sp3d) → Octahedral (hybridization = sp3d2) Electron Group vs. Molecular Geometry → Electron Group Geometry - geometrical distribution of electron groups. (Follows the five basic shapes) → Molecular Geometry - geometrical arrangements of atomic nuclei. Double and Triple Bonds → VSEPR theory treats all bonds equally (single, double…) AXmEn Designation with VSEPR → molecule or polyatomic ion is given an AXmEn designation ⤷ where A is the central atom ⤷ X is a bonded atom ⤷ E is a nonbonding valence electron group (usually a lone pair of electrons) ⤷ m and n are integers. → Each group around the central atom is designated as a bonding group (BG) or lone (nonbonding) pair (LP). Pyramidal Geometries: Derivatives of Tetrahedral Electron Geometry → When there are four electron groups around the central atom, and one is a lone pair, the result is called a pyramidal shape Bent Molecular Geometries: Derivatives of Tetrahedral Electron Geometry → When there are four electron groups around the central atom, and two are lone pairs, the result is called a tetrahedral—bent shape Lecture 14 & 15 - Cont’d Chemical Bonding Ⅱ: Molecular Shape, Valence Bond Theory, & Molecular Orbital Theory Derivatives of the Trigonal Bipyramidal Electron Geometry → When there are five electron groups around the central atom, and some are lone pairs, they will occupy the equatorial positions because there is more room → When there are five electron groups around the central atom, and one is a lone pair, the result is called the seesaw shape → When there are five electron groups around the central atom, and two are lone pairs, the result is called the T-shaped → When there are five electron groups around the central atom, and three are lone pairs, the result is a linear shape → The bond angles between equatorial positions are less than 120° → The bond angles between axial and equatorial positions are less than 90° Derivatives of the Octahedral Geometry → When there are six electron groups around the central atom, and some are lone pairs, each even number lone pair will take a position opposite the previous lone pair → When there are six electron groups around the central atom, and one is a lone pair, the result is called a square pyramid shape → When there are six electron groups around the central atom, and two are lone pairs, the result is called a square planar shape Predicting the Shapes Around Central Atoms → 1. Draw the Lewis structure → 2. Determine the number of electron groups around the central atom → 3. Classify each electron group as bonding or lone pair, and count each type → 4. determine the shape and bond angles Polarity of Molecules → 1. have polar bonds → electronegativity difference - theory → bond dipole moments - measured → 2. The sum of dipole moment of all bonds ≠ 0 → vector addition → Polarity affects the intermolecular forces of attraction → ✓ therefore boiling points and solubilities → like dissolves like  → Lone pairs affect molecular polarity, strong pull in its direction Predicting Polarity of Molecules → 1. Draw the Lewis structure and determine the molecular geometry → 2. Determine whether the bonds in the molecule are polar → a) if there is no polar bond, the molecule is nonpolar → 3. Determine whether the polar bonds add together to give a net dipole moment Intermolecular Forces → intermolecular forces hold molecules together in a liquid or solid → generally much weaker than covalent bonds → determine bulk properties such as melting point for solids and boiling point for liquids (less important for gases unless at high pressure) TYPES OF INTERMOLECULAR FORCES → 1. London Dispersion Forces (van der Waals forces) → 2. Dipole-Dipole Interactions → 3. Hydrogen Bonding → 4. Ion–Dipole Attraction Molecular Polarity Affects Solubility in Water → Polar molecules are attracted to other polar molecules → Because water is a polar molecule, other polar molecules dissolve well in water → ✓ and ionic compounds as well → Some molecules have both polar and nonpolar parts (amphiphile) Lecture 16 - Cont’d Chemical Bonding Ⅱ: Molecular Shape, Valence Bond Theory, & Molecular Orbital Theory Limitations of Lewis Theory → Lewis theory generally predicts trends in properties, but does not give good quantitative predictions → ✓ e.g. bond strength and bond length → Lewis theory gives good first approximations of the bond angles in molecules, but usually cannot be used to get the actual angle → Lewis theory cannot write one correct structure for many molecules where resonance is important → Lewis theory often does not predict the correct magnetic behavior of molecules Problems with VSEPR/Lewis Theory → Lewis structures treat all bonds as the sharing of an electron pair → ✓ Predicts that H-H and F-F should have the same properties (not true) → Valence bond theory – bonds are formed by sharing of e- from overlapping atomic orbitals. Valence Bond Theory → Valence Bond Theory: Bonds form when the potential energy of the system reaches a minimum. → Linus Pauling and others applied the principles of quantum mechanics to molecules → They reasoned that bonds between atoms would occur when the atomic orbitals on those atoms interact to make a bond → The kind of interaction depends on whether the orbitals align along the axis between the nuclei, or outside the axis HYBRIDIZATION → Hybridization – mixing of two or more non-equivalent atomic orbitals (e.g. s and p) to form a new set of hybrid orbitals → a) hybrid orbitals have different shapes and orientations than their parent atomic orbitals. → b) Number of hybrid orbitals = number of atomic orbitals. Bonding with Valence Bond Theory → According to valence bond theory, bonding takes place between atoms when their atomic or hybrid orbitals interact → ✓ “overlap” → To interact, the orbitals must either be aligned along the axis between the atoms, or → The orbitals must be parallel to each other and perpendicular to the interatomic axis Two Types of Bonds: 𝝈 (sigma) bond → A (sigma) bond results when the interacting atomic orbitals point along the axis connecting the two bonding nuclei → ✓ either standard atomic orbitals or hybrids Two Types of Bonds: π (pi) bond → A (pi) bond results when the bonding atomic orbitals are parallel to each other and perpendicular to the axis connecting the two bonding nuclei → ✓ between unhybridized parallel p orbitals TWO TYPES OF BONDS → The interaction between parallel orbitals is not as strong as between orbitals that point at each other; therefore 𝝈 bonds are stronger than π bonds → A p bond is one bond, not two. It has electron density above and below the axis connecting the two bonding nuclei. sp² → Atom with three electron groups around it → ✓ trigonal planar system → C = trigonal planar → central O = tetrahedral bent → terminal O = “linear” → ✓ 120° bond angles → ✓ flat → Atom uses hybrid orbitals for bonds and lone pairs, uses unhybridized p orbital for π bond Lecture 17 - Cont’d Chemical Bonding Ⅱ: Molecular Shape, Valence Bond Theory, & Molecular Orbital Theory Problems with Valence Bond Theory → VB Theory predicts molecular oxygen should be diamagnetic:  → Diamagnetic = all the electrons are paired! → Paramagnetic = there are unpaired electrons present in the molecule because it is attracted to a magnetic field Molecular Orbital Theory → Molecular orbital theory (MOT) is a more complete way of describing bonding → Doesn’t require tweaking to account for: ⤷ Geometry of molecule ⤷ Magnetic properties of the molecule i.e. the paramagnetism of the O2 molecule ⤷ Promotion and hybridization ⤷ Violations of the octet rule for elements beyond the 2nd period → Electrons in bonding MOs are stabilizing ⤷ lower energy than the atomic orbitals → Electrons in antibonding MOs are destabilizing ⤷ higher in energy than atomic orbitals ⤷ electron density located outside the internuclear axis ⤷ electrons in antibonding orbitals cancel stability gained by electrons in bonding orbitals Some Ground Rules Concerning MOs → 1. Number of MOs = Linear Combination of Atomic Orbitals combined → 2. Two AOs combine to give one bonding MO and one antibonding MO → No exceptions! → 3. Electrons fill the lowest energy MO first (Aufbau Principle) → 4. Pauli exclusion principle and Hund’s rule are followed → 5. The number of electrons in the MOs is equal to the sum of all the electrons in the bonding atoms → 6. A stable molecular species always will have more electrons in the bonding molecular orbitals than in the anti-bonding orbitals → Because the orbitals are wave functions, the waves can combine either constructively or destructively Molecular Orbitals → When the wave functions combine constructively, the resulting molecular orbital has lower energy than the original atomic orbitals – it is called a Bonding Molecular Orbital → most of the electron density between the nuclei → When the wave functions combine destructively, the resulting molecular orbital has higher energy than the original atomic orbitals – it is called an Antibonding Molecular Orbital → most of the electron density outside the nuclei → nodes between nuclei SUMMARY OF COVALENT BONDING MODELS → Lewis Bonding Theory ⤷ Covalent bonds result from the sharing of electrons between two atoms → VSEPR Theory (add-on to Lewis theory) ⤷ Molecular geometry is predicted by minimizing electron-electron repulsion between electron pairs…gives us shapes of molecules using AXmEn → Valence Bond Theory ⤷ Atomic orbitals of an atom mix to form new hybrid orbitals ⤷ Explains double and triple bonds more accurately and also relies on quantum model of the atom → Molecular Orbital Theory ⤷ Atomic orbitals of a molecule mix to form new molecular orbitals ⤷ Electrons in bonding and antibonding Mos determine stability of molecule so no need for resonance ⤷ Accurately predicts electronic structure of paramagnetic species as well as CHMA10 FALL SEMESTER 2024 INSTRUCTOR: DR. BERNIE KRAATZ AND DR. XIAO-AN ZHANG ✫✫✫ keywords will be highlighted. Anything from the textbook will be highlighted. Any formulas will be in colour. Anything prof said outside notes is also in colour. Liquids, Solids, and Intermolecular Forces Properties of the Three Phases of Matter → Definite (or Fixed) = keeps shape when placed in a container → Indefinite = takes the shape of the container Kinetic-Molecular Theory → What state a material is in depends largely on two major factors: ⤷ The amount of kinetic energy the particles possess ⤷ The strength of attraction between the particles → These two factors are in competition with each other. Types of Degrees of Freedom → Particles may have one or several types of freedom of motion and various degrees of each type. → Translational freedom is the ability to move from one position in space to another. → Rotational freedom is the ability to reorient the particle's direction in space. → Vibrational freedom is the ability to oscillate about a particular point in space. States and Degrees of Freedom → The molecules in a gas have complete freedom of motion. ⤷ Their kinetic energy overcomes the attractive forces between the molecules. → The molecules in a solid are locked in place; they cannot move around. ⤷ Though they do vibrate, they don’t have enough kinetic energy to overcome the attractive forces. → The molecules in a liquid have limited freedom; they can move around a little within the structure of the liquid.  ⤷ They have enough kinetic energy to overcome some of the attractive forces, but not enough to escape each other. Kinetic Energy → Increasing kinetic energy increases the motion energy of the particles. → The more motion energy the molecules have, the more freedom they can have. → The average kinetic energy of an ideal gas particle is directly proportional to the temperature (see C5.8). Phase Changes → Intermolecular attractive forces are fixed, thus changing the state requires changing of KE, or limiting the freedom. → Solids melt when heated; → Liquids boil when heated; → Gases can be condensed by decreasing the temperature and/or increasing the pressure. ⤷ Pressure can be increased by decreasing the gas volume. ⤷ Reducing the volume reduces the amount of translational freedom. → The stronger the attractive forces, the higher the mp & bp. ⤷ Other factors also influence the melting point. Why Are Molecules Attracted to Each Other? → Intermolecular attractions are due to attractive forces between opposite charges (electrostatic forces). ⤷ (+) ion to (−) ion ⤷ (+) end of polar molecule to (−) end of polar molecule ⤷ H-bonding especially strong ⤷ Even nonpolar molecules will have temporary charges → Larger charge = stronger attraction → Longer distance = weaker attraction → However, these attractive forces are generally small relative to the bonding forces between atoms. ⤷ Generally smaller charges ⤷ Generally over much larger distances Trends in the Strength of Intermolecular Attraction → The stronger the attractions between the atoms or molecules, the more energy it will take to separate them. → Boiling a liquid requires that we add enough energy to overcome all the attractions between the particles. ⤷ However, not breaking the covalent bonds  → The higher the normal boiling point of the liquid, the stronger the intermolecular attractive forces. Kinds of Attractive Forces → Temporary polarity in the molecules due to unequal electron distribution leads to attractions called dispersion forces. → Permanent polarity in the molecules due to their structure leads to attractive forces called dipole–dipole attractions. → An especially strong dipole–dipole attraction results when H is attached to an extremely electronegative atom. These are called hydrogen bonds. Dispersion Forces → Fluctuations in the electron distribution in atoms and molecules result in a temporary dipole. ⤷ Region with excess electron density has partial (–) charge ⤷ Region with depleted electron density has partial (+) charge → The attractive forces caused by these temporary dipoles are called dispersion forces. – Aka London Forces → All molecules and atoms will have them. → As a temporary dipole is established in one molecule, it induces a dipole in all the surrounding molecules. Size of the Induced Dipole → The magnitude of the induced dipole depends on several factors. → Polarizability of the electrons ⤷ Volume of the electron cloud ⤷ Larger molar mass = more electrons = larger electron cloud = increased polarizability = stronger attractions → Shape of the molecule ⤷ More surface-to-surface contact = larger induced dipole = stronger attraction Effect of Molecular Size on Size of Dispersion Force → The Noble gases are all nonpolar atomic elements. → As the molar mass increases, the number of electrons increases. Therefore, the strength of the dispersion forces increases. → The stronger the attractive forces between the molecules, the higher the boiling point will be. Effect of Molecular Shape on Size of Dispersion Force → Branched chains have lower BPs than straight chains. → The straight chain isomers have more surface-to-surface contact. Dipole-Dipole Attractions → Polar Molecules have a permanent dipole. ⤷ Bond polarity and shape (MG) ⤷ Dipole moment ⤷ The always present induced dipole → The permanent dipole adds to the attractive forces between the molecules, raising the boiling and melting points relative to nonpolar molecules of similar size and shape. → The positive end of a polar molecule is attracted to the negative end of its neighbor. Attractive Forces and Solubility → Solubility depends, in part, on the attractive forces of the solute and solvent molecules. ⤷ Like dissolves like ⤷ Miscible liquids will always dissolve in each other → Polar substances dissolve in polar solvents. ⤷ Hydrophilic groups = OH, CHO, C═O, COOH, NH2 → Nonpolar molecules dissolve in nonpolar solvents. ⤷ Hydrophobic groups = C—H, C—C → Many molecules have both hydrophilic and hydrophobic parts; solubility in water becomes a competition between the attraction of the polar groups for the water and the attraction of the nonpolar groups for their own kind. Immiscible Liquids → Pentane, C5H12 is a nonpolar molecule. → Water is a polar molecule. → The attractive forces between the water molecules is much stronger than their attractions for the pentane molecules. The result is that the liquids are immiscible. Hydrogen Bonding → When a very electronegative atom is bonded to hydrogen, it pulls the bonding electrons toward it. → O─H, N─H, or F─H → Because hydrogen has no other electrons, when its electron is pulled away, the nucleus becomes de-shielded, exposing the H proton. → The exposed proton acts as a center of positive charge, attracting the electron clouds from neighboring molecules. H-Bonds → Hydrogen bonds are strong intermolecular attractive forces. → Stronger than the most of dipole–dipole or dispersion forces  → Substances that can hydrogen bond will have higher boiling points and melting points than similar substances that cannot. → But hydrogen bonds are not nearly as strong as chemical bonds. Ion-Dipole Attraction → In a mixture, ions from an ionic compound are attracted to the dipole of polar molecules. → The strength of the ion–dipole attraction is one of the main factors that determines the solubility of ionic compounds in water. SUMMARY → Dispersion forces are the weakest of the intermolecular attractions. → Dispersion forces are present in all molecules and atoms. → The magnitude of the dispersion forces increases with molar mass. → Polar molecules also have dipole–dipole attractive forces. → Hydrogen bonds are generally the strongest of the intermolecular attractive forces a pure substance can have. → Hydrogen bonds will be present when a molecule has H directly bonded to either O, N, or F atoms. → The only example of H bonded to F is HF. → Ion–dipole attractions are present in mixtures of ionic compounds with polar molecules. → Ion–dipole attractions are the strongest intermolecular attraction. → Ion–dipole attractions are especially important in aqueous solutions of ionic compounds. Surface Tension → Surface tension is a property of liquids that results from the tendency of liquids to minimize their surface area. → To minimize their surface area, liquids form drops that are spherical, as long as there is no gravity → The layer of molecules on the surface behave differently than the interior, because the cohesive forces on the internal molecules make them resistant to come to the liquid surface. → The surface layer acts like an elastic skin, allowing you to “float” a paper clip even though steel is denser than water. → Because they have fewer neighbors to attract them, the surface molecules are less stable than those in the interior. → Have a higher potential energy → The surface tension of a liquid is the energy required to increase the surface area a given amount. → Surface tension of H2O = 72.8 mJ/m2 → At room temperature → Surface tension of C6H6 = 28 mJ/m2 Factors Affecting Surface Tension → The stronger the intermolecular attractive forces, the higher the surface tension will be. → Raising the temperature of a liquid reduces its surface tension. ⤷ Raising the temperature of the liquid increases the average kinetic energy of the molecules. ⤷ The increased molecular motion makes it easier to stretch the surface. Viscosity → Viscosity is the resistance of a liquid to flow. → 1 poise = 1 P = 1 g cm-1 ∙ s-1 (SI unit is Pa s) → Often given in centipoise, cP → H2O ~ 1 cP at room temperature → Larger intermolecular attractions = larger viscosity Factors Affecting Viscosity → The stronger the intermolecular attractive forces, the higher the liquid’s viscosity will be. → The more spherical the molecular shape, the lower the viscosity will be. → Molecules roll more easily. → Less surface-to-surface contact lowers attractions. → Raising the temperature of a liquid reduces its viscosity. ⤷ Raising the temperature of the liquid increases the average kinetic energy of the molecules. ⤷ The increased molecular motion makes it easier to overcome the intermolecular attractions and flow. Capillary Action → Capillary action is the ability of a liquid to flow up a thin tube against the influence of gravity. → The narrower the tube, the higher the liquid rises. → Capillary action is the result of two forces working in conjunction, the cohesive and adhesive forces. ⤷ Cohesive forces hold the liquid molecules together. ⤷ Adhesive forces attract the outer liquid molecules to the tube’s surface. → The adhesive forces pull the surface liquid up the side of the tube, and the cohesive forces pull the interior liquid with it. → The liquid rises up the tube until the force of gravity counteracts the capillary action forces. → The narrower the tube diameter, the higher the liquid will rise up the tube. Meniscus  → The curving of the liquid surface in a thin tube is due to the competition between adhesive and cohesive forces. → The meniscus of water is concave in a glass tube because its adhesion to the glass is stronger than its cohesion for itself. → The meniscus of mercury is convex in a glass tube because its cohesion for itself is stronger than its adhesion for the glass. → Metallic bonds are stronger than intermolecular attractions. The Molecular Dance → Molecules in the liquid are constantly in motion. ⤷ Vibrational, and limited rotational and translational → The average kinetic energy is proportional to the temperature. → Some molecules have more kinetic energy than the average, and others have less. Vaporization → If these high energy molecules are at the surface, they may have enough energy to overcome the attractive forces. ⤷ Therefore, the larger the surface area, the faster the rate of evaporation. → This will allow them to escape the liquid and become a vapor. Distribution of Thermal Energy → Only a small fraction of the molecules in a liquid have enough energy to escape. → But, as the temperature increases, the fraction of the molecules with “escape energy” increases. → The higher the temperature, the faster the rate of evaporation. Condensation → Some molecules of the vapor will lose energy through molecular collisions. → The result will be that some of the molecules will get captured back into the liquid when they collide with it. → Also some may stick and gather together to form droplets of liquid, particularly on surrounding surfaces. → We call this process condensation. Evaporation vs. Condensation → Vaporization and condensation are opposite processes. → In an open container, the vapor molecules generally spread out faster than they can condense. → The net result is that the rate of vaporization is greater than the rate of condensation, and there is a net loss of liquid. → However, in a closed container, the vapor is not allowed to spread out indefinitely.  → The net result in a closed container is that at some time the rates of vaporization and condensation will be equal. Effects of Intermolecular Attraction on Evaporation and Condensation → The weaker the attractive forces between molecules, the less energy they will need to vaporize. → Also, weaker attractive forces means that more energy will need to be removed from the vapor molecules before they can condense. → The net result will be more molecules in the vapor phase, and a liquid that evaporates faster; the weaker the attractive forces, the faster the rate of evaporation. → Liquids that evaporate easily are said to be volatile. (For example, gasoline, fingernail polish remover) → Liquids that do not evaporate easily are called nonvolatile. Energetics of Vaporization → When the high energy molecules are lost from the liquid, it lowers the average kinetic energy. → If energy is not drawn back into the liquid, its temperature will decrease; therefore, vaporization is an endothermic process. → Condensation is an exothermic process. → Vaporization requires input of energy to overcome the attractions between molecules. Heat of Vaporization → The amount of heat energy required to vaporize one mole of the liquid is called the heat of vaporization, ΔHvap. → Sometimes called the enthalpy of vaporization → It is always endothermic; therefore, ΔHvap is +. → It is somewhat temperature dependent. → ΔHcondensation = −ΔHvaporization Dynamic Equilibrium → In a closed container, once the rates of vaporization and condensation are equal, the total amount of vapor and liquid will not change. → Evaporation and condensation are still occurring, but because they are opposite processes, there is no net gain or loss of either vapor or liquid. → When two opposite processes reach the same rate so that there is no gain or loss of material, we call it a dynamic equilibrium. → This does not mean there are equal amounts of vapor and liquid; it means that they are changing by equal amounts. → A system in dynamic equilibrium can respond to changes in the conditions.  → When conditions change, the system shifts its position to relieve or reduce the effects of the change. Vapor Pressure → The pressure exerted by the vapor when it is in dynamic equilibrium with its liquid is called the vapor pressure. ⤷ More surface-to-surface contact = larger induced dipole = stronger attraction → The weaker the attractive forces between the molecules, the more molecules will be in the vapor. → Therefore, the weaker the attractive forces, the higher the vapor pressure. → The higher the vapor pressure, the more volatile the liquid. Vapor-Liquid Dynamic Equilibrium → If the volume of the chamber is increased, it will decrease the pressure of the vapor inside the chamber. ⤷ At that point, there are fewer vapor molecules in a given volume, causing the rate of condensation to slow. → Therefore, for a period of time, the rate of vaporization will be faster than the rate of condensation, and the amount of vapor will increase. → Eventually, enough vapor accumulates so that the rate of the condensation increases to the point where it is once again as fast as evaporation. → Equilibrium is reestablished. → At this point, the vapor pressure will be the same as it was before. Vapor Pressure vs. Temperature → Increasing the temperature increases the number of molecules able to escape the liquid. → The net result is that as the temperature increases, the vapor pressure increases. → Small changes in temperature can make big changes in vapor pressure. → The rate of growth depends on the strength of the intermolecular forces. Boiling Point → When the temperature of a liquid reaches a point where its vapor pressure is the same as the external pressure, vapor bubbles can form anywhere in the liquid, not just on the surface. → This phenomenon is what is called boiling and the temperature at which the vapor pressure equals external pressure is the boiling point. → The normal boiling point is the temperature at which the vapor pressure of the liquid = 1 atm. → The lower the external pressure, the lower the boiling point of the liquid. Heating Curve of a Liquid  → As you heat a liquid, its temperature increases linearly until it reaches the boiling point. q = mass × Cs × T → Once the temperature reaches the boiling point, all the added heat goes into boiling the liquid; the temperature stays constant. → Once all the liquid has been turned into gas, the temperature can again start to rise. Clausius-Clapeyron Equation −∆𝑣𝑎𝑝𝐻◦/𝑅𝑇 → 𝑃𝑣𝑎𝑝 = β 𝑒 → 𝐼𝑛(𝑃𝑣𝑎𝑝) = 𝐼𝑛β +− ∆𝑣𝑎𝑝𝐻 ◦ / 𝑅𝑇 → 𝐼𝑛(𝑃𝑣𝑎𝑝) =− ∆𝑣𝑎𝑝𝐻 ◦ /𝑅 (1/𝑇) + 𝐼𝑛β → The logarithm of the vapor pressure versus inverse absolute temperature is a linear function. → The equation below can be used with just two measurements of vapor pressure and temperature. It can also be used to predict the vapor pressure if you know the heat of vaporization and the normal boiling point. → Remember, the vapor pressure at the normal boiling point is 760 torr. → 𝐼𝑛 (𝑃2/𝑃1) = − ∆𝑣𝑎𝑝𝐻 ◦ /𝑅 (1/𝑇2 − 1/𝑇1) Supercritical Fluid → As a liquid is heated in a sealed container, more vapor collects, causing the pressure inside the container to rise, the density of the vapor to increase, and the density of the liquid to decrease. → At some temperature, the meniscus between the liquid and vapor disappears, and the states commingle to form a supercritical fluid. The Critical Point → The temperature required to produce a supercritical fluid is called the critical temperature. → The pressure at the critical temperature is called the critical pressure. → At the critical temperature or higher temperatures, the gas cannot be condensed to a liquid, no matter how high the pressure gets. Sublimation and Deposition → Molecules in the solid have thermal energy that allows them to vibrate. → Surface molecules with sufficient energy may break free from the surface and become a gas; this process is called sublimation. → The capturing of vapor molecules into a solid is called deposition. → The solid and vapor phases exist in dynamic equilibrium in a closed container at temperatures below the melting point. → Therefore, molecular solids have a vapor pressure. Melting = Fusion  → As a solid is heated, its temperature rises and the molecules vibrate more vigorously. → Once the temperature reaches the melting point, the molecules have sufficient energy to overcome some of the attractions that hold them in position and the solid melts (or fuses). → The opposite of melting is freezing. Heating Curve of a Solid → As you heat a solid, its temperature increases linearly until it reaches the melting point. ( q = mass × Cs × T ) → Once the temperature reaches the melting point, all the added heat goes into melting the solid. → The temperature stays constant. → Once all the solid has been turned into liquid, the temperature can again start to rise. → Ice/water will always have a temperature of 0 °C at 1 atm. Energetics of Melting → When the high energy molecules are lost from the solid, it lowers the average kinetic energy. → If energy is not drawn back into the solid its temperature will decrease; therefore, melting is an endothermic process, and freezing is an exothermic process. → Melting requires input of energy to overcome the attractions among molecules. Heat of Fusion → The amount of heat energy required to melt one mole of the solid is called the heat of fusion, ΔHfus. → Sometimes called the enthalpy of fusion → It is always endothermic; therefore, Hfus is +. → It is somewhat temperature dependent. → ΔHcrystallization = −ΔHfusion → Generally much less than ΔHvap → ΔHsublimation = ΔHfusion + ΔHvaporization Phase Diagrams → Phase diagrams describe the different states and state changes that occur at various temperature/pressure conditions. → Regions represent states. → Lines represent state changes. ⤷ The liquid/gas line is the vapor pressure curve. ⤷ Both states exist simultaneously. ⤷ The critical point is the farthest point on the vapor pressure curve. → Triple point is the temperature/pressure condition where all three states exist simultaneously.  → For most substances, the freezing point increases as pressure increases. PUT A DRAWING RIGHT HERE OF THE PHASE CHANGE GRAPH Crystal Lattice → When allowed to cool slowly, the particles in a liquid will arrange themselves to give the maximum attractive forces. → Therefore, minimize the energy. → The result will generally be a crystalline solid. → The arrangement of the particles in a crystalline solid is called the crystal lattice. → The smallest unit that shows the pattern of arrangement for all the particles is called the unit cell. → Unit cells are repeated over and over to give the macroscopic crystal structure of the solid. → Starting anywhere within the crystal results in the same unit cell. SEVEN UNIT CELLS Cubic Tetragonal Orthorhombic Monoclinic a=b=c a=c