Cheat Sheet
CHEM 142
Printable Cheat Sheets
Professor Li allows students to bring one cheat sheet, printed or handwritten, to exams. Attached are the cheat sheets I created and used (successfully) for my exams. Feel free to modify and print.
Quantum Mechnics and Atomic Theory
Key Equations
| Wavelength and Frequency Relationship | \(\lambda\nu = c\) |
| Quantization of Energy | \(\Delta E = nh\nu\) |
| Energy of a Photon | \(E_\text{photon} = h\nu = \frac{hc}{\lambda}\) |
| Photoelectric Effect | \(h\nu_\text{photon} - \phi = \frac{1}{2}m_e\nu^2\) |
| Mass and Energy Relationship | \(E = mc^2\) |
| de Broglie’s Equation | \(\lambda = \frac{h}{mv}\) |
| Momentum Equation | \(p = mv\) |
| Energy Levels for One-Electron Atoms | \(E = -2.178 \times 10^{-18} J \left(\frac{Z^2}{n^2}\right)\) |
| Change in Energy of Electron State | \(\Delta E = E_\text{final} - E_\text{initial}\) |
| Schrodinger’s Equation | \(\hat{H}\psi = E\psi\) |
| Heisenberg Uncertainty Principle | \(\Delta x \times \Delta p \ge \frac{h}{4\pi}\) |
| Balmer-Rydberg Formula | \(\frac{1}{\lambda} = -R_H\left(\frac{1}{n^2_\text{initial}}\right) + \left(\frac{R_H}{n^2_\text{final}}\right)\) |
Variables:
- \(\lambda\) - wavelength.
- \(\nu\) - frequency (in units of \(s^{-1}\)/inverse seconds/Hertz).
- \(\phi\) - work function in the photoelectric effect equation, defined as \(h\nu_0\).
- \(E\) - energy (in units of Joules).
- \(Z\) - atomic number.
- \(n\) - an arbitrary (usually positive) integer.
- \(v\) - velocity.
- \(p\) - momentum.
- \(c\) - the speed of light (\(\frac{m}{s}\))
- \(h\) - the Planck constant (\(J\cdot s = \frac{kg^2 \times m^2}{s^2}\)).
- \(\Delta x\) - uncertainty in particle position for HUP.
- \(\Delta p\) - uncertainty in particle momentum for HUP.
Key Principles and Concepts
| Name | Description |
|---|---|
| Energy | Energy is the capacity to do work or produce heat. Energy can be converted from one form to another, but cannot be created or destroyed. Two types: potential and kinetic energy. |
| Exothermic and Endothermic Reactions | Exothermic - reaction flows out of the system. Endothermic - heat flows into a system. |
| Energy as Waves | Electromagnetic radiation - one way energy travels trhough space. Waves are characterized by wavelength \(\lambda\), frequency \(\nu\), and speed \(c\). \(\lambda\nu = c\). |
| Wave Particle Duality | All matter exhibits the properties both of waves and particles. This is most evident in ‘intermediate-sized pieces’ of matter, like photons. |
| Quantization of Energy | Energy is quantized and can only be gained or lost in integer multiples of \(h\nu\): \(\Delta E = nh\nu\). Thus, energy possess particulate properties. |
| Photoelectric Effect | Electrons are emitted from the surface of metal when light strikes it, converting wave to chemical energy: \(h\nu_\text{photon} - \phi = \frac{1}{2}m_e\nu^2\). |
| Quantization of Electron Energy Levels | Continuous spectrum: contains all lengths of visible light. Line spectrum: only a few wavelengths are visible (show up as a few lines when passed through a prism. Only certain energies are allowed for an electron in the hydrogen atom; thus, it is *quantized. |
| Bohr Model | Bohr found that an atomic model based on classical physics was untenable. In Bohr’s model, a hydrogen electron could exist only in stationary, non-radiating orbits. As the electron is brought closer to the nucleus, energy is released from the system (higher energy to lower energy state). |
| Quantum Numbers | An orbital is characerized by three quantum numbers: the principal quantum number \(n\), the angular momentum quantum number \(l\), the magnetic quantum number \(m_l\). To account for the details of the emission spectra of atoms, the electron spin quantum number \(m_s\) is introduced. |
| Pauli Exclusion Principle | In a given atom, no two electrons can have the same set of four quantum numbers. |
| Aufbau Principle | As protons are added one by one ot the nucleus to build up elements, electrons are similarly added to the atomic orbitals. |
| Hund’s Rule | The lowest-energy configuration for an atom is the one having the maximum number of unpaired electrons allowed but the Pauli principle in a particular set of degenerate orbitals. |
| Koopman’s Theorem | The ionization energy of an electron is equal to the energy of the orbital from which it came. |
| Ionization Energy Periodic Trend | Ionization energy increases left to right across a period and up to down across a group. |
| Atomic Radius Periodic Trend | Atomic radius decreases in going from left to right across a period and increases up to down across a group. |
| Electron Affinity | The energy change associated with the addition of an electron to a gaseous atom: \(X(g) + e^- \to X^- (g)\). |
| de Broglie Wavelenghth | The de Broglie equation can be used to calculate the wavelength of particles with mass. |
| Schrodinger Equation | Schrodinger inserted the de Broglie equation into classical wave equations; the result is the Schrodinger equation, which outputs a pair of solutions - energy \(E\) and the wave function \(\psi\). This means that energy and wave shape are correlated; energy is dependent on wave shape. Because wave shape is quantized, so is energy. |
| Electron Shape as Wave Patterns | Schrodinger and Louis de Broglie exploited wave-particle duality to describe matter and energy in terms of wave mechanics. It is the electron shape that changes, not the orbital distance. An electron can adopt only certain standing wave patterns of motion when subjecting to a constraining potential. |
| Probabilistic Wave Understanding of an Electron | Electrons can take on many different shapes; the probability amplitude of a wave function is an electron’s orbital. A picture of an orbital represents the surface containing 90% of the electron density. |
| Inferring Electron Orbital Shapes | To find \(n\) given a picture, count the number of nodes and add 1, (orbitals demonstrate \(n-1\) nodes for an orbital with principal quantum number \(n\)) taking into account \(l\). To find \(l\): \(s\) orbitals are spherical, \(p\) orbitals are lobed (‘dumbbell-like’), \(d\) orbitals are split into four ‘lobes’. The following relates the number of nodes \(r\), the principal quantum number \(n\), and the angular momentum number \(l\): \(r + 1 = n-l\), or \(r = n - l - 1\). |
| Degeneracy | When only one electron is involved, all orbitals with the same \(n\) are degenerate - they have the same energy (e.g. \(3s\), \(3d\), \(3p\)). When multiple electrons are involved, cross-electron relationships force differences in energy levels for orbitals with the same \(n\). |
General Concepts in Bonding
Electron Bonding and Molecular Structure Reference
| Number of Electron Pairs/Groups | Ideal Bond Angle | Arrangement | Possible Classifications |
|---|---|---|---|
| 2 | \(180^\circ\) | Linear | Linear (\(AX_2\)) |
| 3 | \(120^\circ\) | Trigonal Planar | Trigonal Planar (\(AX_3\)), Bent (\(AX_2E\)) |
| 4 | \(109.5^\circ\) | Tetrahedral | Tetrahedral (\(AX_4\)), Trigonal Pyramidal (\(AX_3E\)), Bent (\(AX_2E_2\)) |
| 5 | \(90^\circ\) and \(120^\circ\) | Trigonal Bipyramidal | Trigonal Bipyramidal (\(AX_5\)), Seesaw (\(AX_4E\)), T-shaped (\(AX_3E_2\)), Linear \(AX_2E_3\)) |
| 6 | \(90^\circ\) | Octahedral | Octahedral (\(AX_6\)), Square Pyramidal (\(AX_5E\)), Square Planar (\(AX_4E_2\)), T-shaped (\(AX_3E_3\)), Linear (\(AX_2E_4\)) |
Key Concepts
| Name | Description |
|---|---|
| Electronegativity | The ability of an atom in a molecule to attract shared electrons to itself. |
| Covalent-Ionic Bond Spectrum | Few bonds are truly covalent or ionic. Rather, most are somewhere in between - polar covalent; ions are shared unequally across atoms. |
| Noble Gas Configurations for Stability | A large number of stable compounds have noble gas arrangements of electrons. |
| Non-metallic electrons form covalent bonds with nonmetals or take electrons from metals to form ions. Two nonmetals in a covalent bond share electrons in a way that completes the valence electron configurations of both atoms (i.e. both obtain noble gas electron configurations). Nonmetal and representative group metal in a binary ionic compound form ions such that the valence electron configruation of the nonmetal is completed and the valence orbitals of the metal are emptied. | |
| Lattice Energy | The change in energy that takes place when separated gaseous ions are pakced together to form an ionic solid. Lots of energy is released when ions combine to form a solid. |
| Resonance Structure | Resonance structures for a molecule can be given by moving electrons around (lone pairs or single/double/triple bonds). The true resonance structure is an ‘average’ of all resonance structures. |
| Formal Charge | Calculated as the number of valence electrons minus the number of possessed electrons. |
| VSEPR Model | A model used to determine the molecular structure and electron geometry under the assumption that the structure around a given atom is determined principally by minimizing electron-pair repulsions. |
| Dipole Moment | An asymmetry in charge caused by asymmtric arrangement of atoms in a molecule. |
| Structural Isomers | Lewis dot structures formed by moving atoms around. |
Stoichiometry
| Name | Description |
|---|---|
| Atomic Mass Unit (amu) | Formally defined as one-twelfth the mass of carbon-12. The atomic mass of an element is the weighted average of all isotopes. |
| Mole | A sample of a natural element with a mass equal to the element’s atomic mass expressed in grams contains 1 mole of atoms. This is Avagadro’s number. |
| Molar Mass | Equivalent to molar weight; this is grams-per-mole and allows us to convert between mole quantities and mass. |
| Empirical Formula | The simplest whole-number ratio of various types of atoms in a compound. |
| Molecular Formula | A multiple of the empirical formula. Does not necessarily form simple repeating units of the empirical formula; molecular formuals can vary and become successively complex. |
| Limiting Reactant | A reactant that “runs out” first and therefore limits the products. |
| Theoretical Yield | Amount of a given product formed when a limiting reactant is completely consumed. |
| Percent Yield | Side reactions and other complications limit how much of the limiting reagant can be consumed, forming the actual yield. Percent yield is calcualted as actual yield divided by theoretical yield. |
Types of Chemical Reactions and Solution Stoichiometry
| Name | Description |
|---|---|
| Hydration | Negative ends are attracted to positively charged cations and positive ends are attracted to negatively charged anions. |
| Aqueous | Indicates that the ions are hydrated by unspecified numbers of water molecules. |
| Salt | An array of cations and anions that separate and become hydrated when the salt dissolves. |
| Solubility | Measured in terms of mass of solute that dissolves per given volume of solvent, or in terms of number of moles of solute that dissolve in a given volume of solution. |
| Acid | Substance that produces \(H^+\) ions (protons) when it is dissolved in water. |
| Base | Soluble compounds containing the hydroxide ion. |
| Weak Electrolytes | Substances that produce few ions when dissolved in water are weak electrolytes - weak acids or bases. |
| Standard Solution | A solution whose concentration is accurately known. |
| Types of Chemical Reactions | Reactions are divide dinto one of the following main groups: precipitation reactions, acid-base reactions, and oxidation-reduction reactions. |
| Ionic Equation | An equation written with the individual ions implied by the molecular equation. This better represents the actual forms of the reactants and products in the solution. |
| Spectator Ions | Ions that do not participate directly in a reaction in solution. |
| Net Ionic Reaction | An ionic equation without spectator ions. |
| Selective Precipitation | Separate cations by precipitating them one at a time. |
| Qualitative Analysis | Mixtures of ions are separated and identified. |
| Acid-Base Reaction | A neutralization reaction in which the hdyroxide ion reacts with the weak acid, producing water and another product. Formation of water from a hydroxide group and a proton. |
| Precipitation Reactions | Formation of a solid (precipitate) that does not dissolve. Need to know solubility rules for salts in water. |
| Oxidation-Reduction Reaction | Many subcategories, including combination, decomposition, combustion, and single-replacement. Driving force: electron transfer between species. When balancing reactions, we must keep in mind additional rules. Must think about charge conservation - cannot gain electrons from nowhere. |
| Combination Reaction | A metal and non-metal react to form a solid ionic compound. |
| Decomposition Reaction | The technical reverse of a combination reaction. One reactant forms two or more products. |
| Combustion Reaction | Combustion of a carbohydrate in oxygen; the product must be carbon dioxide and water. All combustion reactions are redox reactions. |
| Displacement Reaction | When an element of one reactant takes the place of another in the product. All displacement reactions are redox reactions. Use the activity series to determine the validity and form of a displacement reaction. |
| Oxidation States | A way to keep track of electrons in redox reactions, governed yb a set of rules describing how to divvy shared electrons in compounds containing covalent bonds. |
| Oxidizing Agent | The electron acceptor, or the species that undergoes reduction. |
| Reducing Agent | The electron donor, or the species that undergoes oxidation. |
| Molarity | Also represented using brackets, is measured as concentration in moles per volume. |