# 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

NameDescription
EnergyEnergy 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 ReactionsExothermic - reaction flows out of the system. Endothermic - heat flows into a system.
Energy as WavesElectromagnetic radiation - one way energy travels trhough space. Waves are characterized by wavelength $$\lambda$$, frequency $$\nu$$, and speed $$c$$. $$\lambda\nu = c$$.
Wave Particle DualityAll matter exhibits the properties both of waves and particles. This is most evident in ‘intermediate-sized pieces’ of matter, like photons.
Quantization of EnergyEnergy 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 EffectElectrons 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 LevelsContinuous 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 ModelBohr 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 NumbersAn 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 PrincipleIn a given atom, no two electrons can have the same set of four quantum numbers.
Aufbau PrincipleAs protons are added one by one ot the nucleus to build up elements, electrons are similarly added to the atomic orbitals.
Hund’s RuleThe 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 TheoremThe ionization energy of an electron is equal to the energy of the orbital from which it came.
Ionization Energy Periodic TrendIonization energy increases left to right across a period and up to down across a group.
Atomic Radius Periodic TrendAtomic radius decreases in going from left to right across a period and increases up to down across a group.
Electron AffinityThe energy change associated with the addition of an electron to a gaseous atom: $$X(g) + e^- \to X^- (g)$$.
de Broglie WavelenghthThe de Broglie equation can be used to calculate the wavelength of particles with mass.
Schrodinger EquationSchrodinger 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 PatternsSchrodinger 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 ElectronElectrons 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 ShapesTo 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 $$r = n - l - 1$$.
DegeneracyWhen 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/GroupsIdeal Bond AngleArrangementPossible Classifications
2$$180^\circ$$LinearLinear ($$AX_2$$)
3$$120^\circ$$Trigonal PlanarTrigonal Planar ($$AX_3$$), Bent ($$AX_2E$$)
4$$109.5^\circ$$TetrahedralTetrahedral ($$AX_4$$), Trigonal Pyramidal ($$AX_3E$$), Bent ($$AX_2E_2$$)
5$$90^\circ$$ and $$120^\circ$$Trigonal BipyramidalTrigonal Bipyramidal ($$AX_5$$), Seesaw ($$AX_4E$$), T-shaped ($$AX_3E_2$$), Linear $$AX_2E_3$$)
6$$90^\circ$$OctahedralOctahedral ($$AX_6$$), Square Pyramidal ($$AX_5E$$), Square Planar ($$AX_4E_2$$), T-shaped ($$AX_3E_3$$), Linear ($$AX_2E_4$$)

#### Key Concepts

NameDescription
ElectronegativityThe ability of an atom in a molecule to attract shared electrons to itself.
Covalent-Ionic Bond SpectrumFew bonds are truly covalent or ionic. Rather, most are somewhere in between - polar covalent; ions are shared unequally across atoms.
Noble Gas Configurations for StabilityA 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 EnergyThe 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 StructureResonance 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 ChargeCalculated as the number of valence electrons minus the number of possessed electrons.
VSEPR ModelA 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 MomentAn asymmetry in charge caused by asymmtric arrangement of atoms in a molecule.
Structural IsomersLewis dot structures formed by moving atoms around.

### Stoichiometry

NameDescription
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.
MoleA 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 MassEquivalent to molar weight; this is grams-per-mole and allows us to convert between mole quantities and mass.
Empirical FormulaThe simplest whole-number ratio of various types of atoms in a compound.
Molecular FormulaA 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 ReactantA reactant that “runs out” first and therefore limits the products.
Theoretical YieldAmount of a given product formed when a limiting reactant is completely consumed.
Percent YieldSide 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

NameDescription
HydrationNegative ends are attracted to positively charged cations and positive ends are attracted to negatively charged anions.
AqueousIndicates that the ions are hydrated by unspecified numbers of water molecules.
SaltAn array of cations and anions that separate and become hydrated when the salt dissolves.
SolubilityMeasured 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.
AcidSubstance that produces $$H^+$$ ions (protons) when it is dissolved in water.
BaseSoluble compounds containing the hydroxide ion.
Weak ElectrolytesSubstances that produce few ions when dissolved in water are weak electrolytes - weak acids or bases.
Standard SolutionA solution whose concentration is accurately known.
Types of Chemical ReactionsReactions are divide dinto one of the following main groups: precipitation reactions, acid-base reactions, and oxidation-reduction reactions.
Ionic EquationAn 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 IonsIons that do not participate directly in a reaction in solution.
Net Ionic ReactionAn ionic equation without spectator ions.
Selective PrecipitationSeparate cations by precipitating them one at a time.
Qualitative AnalysisMixtures of ions are separated and identified.
Acid-Base ReactionA 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 ReactionsFormation of a solid (precipitate) that does not dissolve. Need to know solubility rules for salts in water.
Oxidation-Reduction ReactionMany 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 ReactionA metal and non-metal react to form a solid ionic compound.
Decomposition ReactionThe technical reverse of a combination reaction. One reactant forms two or more products.
Combustion ReactionCombustion of a carbohydrate in oxygen; the product must be carbon dioxide and water. All combustion reactions are redox reactions.
Displacement ReactionWhen 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 StatesA 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 AgentThe electron acceptor, or the species that undergoes reduction.
Reducing AgentThe electron donor, or the species that undergoes oxidation.
MolarityAlso represented using brackets, is measured as concentration in moles per volume.