General Chemistry

Avogadro’s Number

N_A = 6.02 × 10²³

Planck Relation (E = ?)

E = hf

h = Planck’s Constant

Angular Momentum (L = ?)

L = nh/2π

(of an electron orbiting a hydrogen nucleus)

Energy of the Electron (E = )

E = -R_H/n²

R_H = 2.18 × 10^-18 J/electron (Rydberg unit of energy)

Electromagnetic Energy of Photons (E = ?)

E = hc/γ

E = hf

Calculating Electron Orbital Transitions (Bohr’s and Planck’s Calculations) (E = ?)

E = hc/γ = R_H [(1/n_i²) - (1/n_f²)]

The energy of the emitted photon corresponds to the difference in energy between the higher-energy initial state and the lower-energy final state

Heisenberg Uncertainty Principle

It is impossible to simultaneously determine, with perfect accuracy, the momentum and the position of an electron

Pauli Exclusion Principle

States that no two electrons in a given atom can possess the same set of four quantum numbers

Principal Quantum Number (n)

Maximum number of electrons within a shell = 2n²

Azimuthal (Angular Momentum) Quantum Number (l)

Refers to the shape and number of subshells within a given principal energy level

For any given value of n, the range of possible values for l is 0 to (n-1); Thus, n value also tells you the number of possible subshells (If n = 1, then l = 0 and there is one possible subshell)

• l = 0 → Subshell is called s

• l = 1 → Subshell is called p

• l = 2 → Subshell is called d

• l = 3 → Subshell is called f

Maximum number of electrons within a shell = 4l + 2

Magnetic Quantum Number (m_l)

Specifies the particular orbital within a subshell where an electron is most likely to be found at a given moment in time. Each orbital can hold a maximum of two electrons.

The possible values for m_l are the integers between -l and +l, including 0 (l = 1 → m_l values are -1, 0, 1)

Spin Quantum Number (m_s)

Two values: +1/2 and -1/2

Whenever two electrons are in the same orbital, they must have opposite spins (paired electrons)

Parallel Spins

When electrons in different orbitals have the same m_s values

Aufbau Principle

Electrons fill from lower- to higher-energy subshells

n + l rule

The lower the sums of the values of the first and second quantum numbers, n + l, the lower the energy of the subshell. The subshell with the lower energy will fill first.

Hund’s Rule

Within a given subshell, orbitals are filled such that there are a maximum number of half-filled orbitals with parallel spins

Paramagnetic

Materials composed of atoms with unpaired electrons; These materials will orient their spins in alignment with a magnetic field, and the material will thus be weakly attracted to the magnetic field

Diamagnetic

Materials consisting of atoms that have only paired electrons and will be slightly repelled by a magnetic field

Metals

Shiny (lustrous), conduct electricity well, malleable, ductile; Have valence electrons that can move freely

Effective Nuclear Charge (Z_eff)

The net positive charge experienced by electrons in the valence shell and forms the foundation for all periodic trends; Increases from left to right across a period, very little change in value from top to bottom in a group; Calculated by subtracting the number of non-valence electrons from the number of protons

• # Protons - # non-valence electrons

Ionization Energy

The amount of energy necessary to remove an electron from the valence shell of a gaseous species; Increases from left to right across a period and decreases from top to bottom in a group

Second _______ always larger than first _______

Alkali Metals

1st period; Typically take on an oxidation state of +1 and prefer to lose an electron to achieve a noble gas-like configuration; 1st and 2nd period are the most reactive of all metals

Alkaline Earth Metals

2nd period; Take on an oxidation state of +2 and can lose two electrons to achieve noble gas-like configurations

Chalcogens

Take on an oxidation state of -2 or +6 (depending on whether they are nonmetals or metals, respectively) in order to achieve noble gas configuration

Complex Ion

An ion that contains one or more ligands that are attached to a central metal cation through a dative covalent bond

Electron Affinity

The amount of energy released when a gaseous species gains an electron in its valence shell; it increases from left to right across a period and decreases from top to bottom in a group; Greater for Cl than for F because electrons too crowded in F

Lithium Valence Electrons

2 Valence Electrons

Beryllium Valence Electrons

4 Valence electrons

Boron Valence Electrons

6 valence electrons

Expanded Octet

Any element in period 3 and greater can hold more than 8 electrons, including P (10), S (12), Cl (14), and many others

Odd Numbers of Electrons

Any molecule with an odd number of valence electrons cannot distribute those electrons to give eight to each atom; for example, NO has 11 valence electrons

Ionic Bonding

1+ electrons from an atom with low ionization energy, typically a metal, are transferred to an atom with a high electron affinity, typically a nonmetal; Ex. NaCl; Ions held together by electrostatic attraction; Very high melting and boiling points; Crystalline lattice

Covalent Bonding

An electron pair is shared between two atoms, typically non-metals, that have relatively similar values of electronegativity; Polarity of bond determines sharing of electrons

Nonpolar: Electron pair is shared equally (Dif in electronegativities <0.5)

Polar: Electron pair is shared unequally (Dif in electronegativities 0.5-1.7)

Coordinate Covalent Bonds

If both of the shared electrons in a covalent bond are contributed by only one of the two atoms

Bond Order

The number of shared electron pairs between two atoms (Single bond has ____ of 1, and so on)

Dipole Moment (p = ?)

p = qd

q = Magnitude of the charge

d = Displacement vector separating the two partial charges

Units: coulomb-meters

Formal Charge

The charge assigned to an atom in a molecule

FC = V - N - B/2

V = # valence electrons

N = # non-bonding valence electrons

B = # electrons shared in bonds with other atoms in the molecule

Electronic Geometry

Describes the spatial arrangement of all pairs of electrons around the central atom, including both the bonding and lone pairs; Determines ideal bond angle

Ex. CH₄, NH₃, and H₂O all have four pairs of electrons surrounding the central atom = tetrahedral ________

Molecular Geometry

Describes the spatial arrangement of only the bonding pairs of electrons

Coordinate Number

The number of atoms that surround and are bonded to a central atom; Important for molecular geometry

Strengths of Intermolecular Forces

Dispersion (London) Forces < Dipole-Dipole Interactions < Hydrogen Bond (still much weaker than a covalent bond)

London Dispersion Forces

The weakest intermolecular forces that occur when electrons in adjacent atoms form temporary dipoles; The reason why noble gases liquefy

Dipole-Dipole Interactions

Between two polar molecules oriented such that their oppositely-charged sides are closest to each other; Present in the solid and liquid phases but become negligible in the gas phase (distance)

Hydrogen Bonds

A special type of dipole-dipole attraction between molecules, not a covalent bond to a hydrogen atom. It results from the attractive force between a hydrogen atom covalently bonded to a very electronegative atom such as a N, O, or F atom and another very electronegative atom.

Not actually bonds, basically just adding a proton; Results in high bp for molecules with this type of bond

Law of Constant Composition

States that any pure sample of a given compound will contain the same elements in an identical mass ratio

Combination Reaction

Has 2+ reactants forming one product

Neutralization Reactions

Type of double-displacement reaction in which an acid reacts with a base to produce a salt (and usually water)

Electrolytes

Solutes that enable solutions to carry currents; Electrical conductivity of aqueous solution governed by the presence and concentration of ions in the solution; Solution is a strong ___ if it dissociates completely into its constituent ions

Arrhenius Equation (k = ?)

Kinetic Product

Formed at lower temperatures with smaller heat transfer; Higher energy product

Thermodynamic Product

Formed at higher temperatures with larger heat transfer; Lower energy product

Sublimation

When a solid goes directly into the gas phase

Deposition

When a gas goes directly into the solid phase

Zeroth Law of Thermodynamics

Objects are in thermal equilibrium only when their temperatures are equal; Heat (Q) is therefore a process function

Enthalpy (Delta H)

Equivalent to heat (Q) under constant pressure

Heat Capacity

Mass times specific heat (mc)

Hess’s Law

Enthalpy changes of reactions are additive

Second Law of Thermodynamics

States that energy spontaneously disperses from being localized to becoming spread out if it is not hindered from doing so.

Change in Entropy

Standard Free Energy

Free Energy of a Reaction in Progress

Q < Keq = Reaction is spontaneous in forward direction

Q > Keq = Reaction is spontaneous in reverse direction

Deviations from Ideal Gas Behavior

Gases deviate from ideal behavior at higher pressures and lower volumes and temperatures, all of which force molecules closer together. The closer they are, the more they can participate in intermolecular forces, which violates the definition of an ideal gas. At low temperatures, the kinetic energy of the particles is reduced, so collisions with other particles or the walls of the container are more likely to result in significant changes in kinetic energy.

1 Mole Gas Volume at STP

1 mole of gas occupies 22.4 L at STP

Calculate Pressure of Gas with Vapor Pressure

The pressure of the gas is calculated by subtracting the vapor pressure of water from the measured pressure during the experiment

Ideal Gas Law with Density

T = PM/dR

M = Molar Mass

d = Density

Pressure Conversions

1 atm = 760 mmHg = 760 torr = 101.325 kPa

Kinetic Molecular Theory

1) Gases are made up of particles with volumes that are negligible compared to the container volume

2) Gas atoms or molecules exhibit no intermolecular attractions or repulsions

3) Gas particles are in continuous, random motion, undergoing collisions with other particles and the container walls

4) Collisions between any two gas particles are elastic (conservation of momentum and KE)

5) The average KE of gas particles is proportional to the absolute temperature of the gas, and it is the same for all gases at a given temperature

KE of Gas Equation

KE = (1/2)mv² = (3/2)k_BT

k_B = Boltzmann Constant = 1.38 × 10^-23 J/K

Root-Mean-Square Speed of a Gas (u_rms)

u_rms = sqrt(3RT/M)

M = Molar Mass

Maxwell-Boltzmann Distribution Curve

The bell-shaped curve flattens and shifts to the right as the temperature increases, indicating that at higher temperatures, more molecules are moving at higher speeds.

Graham’s Law

The rates at which two gases diffuse are inversely proportional to the square roots of their molar masses

Solvation

The electrostatic interaction between solute and solvent molecules

When the new interactions are stronger than the original ones, _____ is exothermic, and the process is favored at low temperatures. The dissolution of gases into liquids is an exothermic process because the only significant interactions that must be broken are those between water molecules. This is the reason that lowering the temperature of a liquid favors solubility of a gas in the liquid.

When the new interactions are weaker than the original ones, _____ is endothermic and the process is favored at high temperatures (most dissolutions).

Ideal Solution

Solutions in which the enthalpy of dissolution is equal to zero

Solubility

Solutes are considered soluble if they have a molar solubility above 0.1 M in solution

Sparingly Soluble Salts

Those solutes that dissolve minimally in the solvent (molar solubility under 0.1 M)

General Solubility Rules

1) All salts containing ammonium (NH₄⁺) and Group 1 cations are water-soluble.

2) All salts containing nitrate (NO₃^-) and acetate (CH₃COO^-) anions are water-soluble.

3) Halides, excluding fluorides, are water-soluble, with the exceptions of those formed with Ag+, Pb2+, and Hg₂2+.

4) All salts of the sulfate ion (SO₄^2-) are water-soluble, with the exceptions of those formed with Ca2+, Sr2+, Ba2+, and Pb2+

5) All metal oxides are insoluble, with the exception of those formed with the alkali metals, ammonium, and CaO, SrO, and BaO, all of which hydrolyze the form solutions of the corresponding metal hydroxides.

6) All hydroxides are insoluble, with the exception of those formed with the alkali metals, ammonium, and Ca2+, Sr2+, Ba2+.

7) All carbonates (CO₃^2-), phosphates (PO₄^3-), sulfides (S^2-), and sulfites (SO₃^2-) are insoluble, with the exception of those formed with the alkali metals and ammonium.

Chelation

A complex in which the central cation is bonded to the same ligand in multiple places; Generally requires large organic ligands that can double back to form a second bond with the central cation

Use to sequester toxic metals

Molality

m = (Moles of Solute)/(kg of Solvent)

Normality (N)

The number of equivalents of interest per liter of solution

An equivalent is a measure of the reactive capacity of a molecules, or a mole of the species of interest—-protons, hydroxide ions, electrons, or ions

Reaction dependent

Solubility Product Constant (Ksp)

Ksp = [Aⁿ⁺]^m[B^m-]ⁿ

Kf (Formation/Stability Constant)

Formation of the complex ion in solution

Ex:

Ag⁺ (aq) + 2NH₃ (aq) ←→ [Ag(NH₃)₂]⁺

Kf = [[Ag(NH₃)₂]⁺]/[Ag⁺][NH₃]²

Common Ion Effect

The solubility of a salt is considerably reduced when it is dissolved in a solution that already contains one of its constituent ions as compared to its solubility in a pure solvent

Colligative Properties

Physical properties of solutions that are dependent on the concentration of dissolved particles but not on the chemical identity of the dissolved particles (Ex. Vapor pressure depression, bp elevation, freezing point depression, and osmotic pressure)

Raoult’s Law

Accounts for vapor pressure depression caused by solutes in solution. As solute is added to a solvent, the vapor pressure of the solvent decreases proportionately.

P_A = X_AP_A°

P_A = Vapor pressure of solvent A when solutes are present

X_A = Mole fraction of the solvent A in the solution

P_A° = Vapor pressure of the solvent A in its pure state

Holds only when the attraction between the molecules of the different components of the mixture is equal to the attraction between the molecules of one component in its pure state. (Obeyed by ideal solutions)

Water at 100°C = Density ~ 1 g/mL = Vapor pressure of water is 1 atm (bp of water)

Boiling Point Elevation

When a nonvolatile solute is dissolved into a solvent to create a solution, the bp of the solution will be greater than that of the pure solvent.

Van’t Hoff Factor (i)

The number of particles into which a compound dissociates in solution; Ex: i = 2 for NaCl

Freezing Point Depression

The presence of solute particles in a solution interferes with the formation of the lattice arrangement of solvent molecules associated with the solid state. Thus, a greater amount of energy must be removed from the solution (AKA lower temp) in order for the solution to solidify.

Osmotic Pressure

A “sucking” pressure generated by solutions in which water is drawn into a solution

Arrhenius Acid

Will dissociate to form an excess of H+ in solution

Arrhenius Base

Will dissociate to form an excess of OH- in solution

Lewis Acid

An electron pair acceptor (electrophile)

Lewis Base

An electron pair donor (nucleophile)

Acid-Base Nomenclature

Acids formed from anions with names that end in -ide have the prefix hydro- and the ending -ic (Ex. HF is hydrofluoric acid)

If the anion ends in -ite (less oxygen), then the acid will end with -ous acid

If the anion ends in -ate (more oxygen), then the acid will end with -ic acid (Ex. ClO₃^- is chlorate and HClO₃ is chloric acid)

Amphoteric

Describes a species that reacts as an acid when in the presence of a base and reacts as a base when in the presence of a base (Ex. water)

Water Dissociation Constant (Kw)

Kw = [H3O+][OH-] = 10^-14 at 25°C (298 K)

pH =

pH = -log[H+]

If [H+] = 10^-3 then pH = 3

pOH =

pOH = -log[OH-]

pKa

pKb

Convert log to p value

Given -log (n x 10^-m), p value = ~m - 0.n