General Chemistry

Avogadro’s Number

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