chem exam 3

oxidation-reduction

• reactions involving the transfer of electrons from one reactant to the other

• aka redox reactions (may involve reaction of a substance with O₂)

• usually single replacement

• for a free element to form an ion, the atom must lose or gain electrons

  • atoms that lose electrons are oxidized

  • atoms that gain electrons are reduced

oxidation state rules

• imaginary charges assigned based on a set of rules

• NOT ionic charges (ionic charges are real, measurable charges)

rules (if two rules conflict, follow the rule that is higher on the list)

1. oxidation state of an atom in a free element or compound = 0

2. oxidation state of a monoatomic ion = charge of ion

3. sum of oxidation states of all atoms in:

   1. a compound = 0

   2. a polyatomic ion = charge of the ion

4. in a compound, metals have positive oxidation states

   1. group 1A metals = +1

   2. group 2A metals = +2

5. in compounds, non-mentals have negative oxidation state (table)

redox (OILRIG)

• oxidation occurs when an element’s oxidation state increases on the product side (losing electrons, becoming more positive)

• reduction occurs when an element’s oxidation state decreases on the product side (gaining electrons, becoming more negative)

  • oxidation and reduction must occur simultaneously (one atom loses an electron, another must accept the electron)

• reactant that reduces an element in the other reactant is the reducing agent (oxidized)

• reactant that oxidizes an element in the other reactant is the oxidizing agent (reduced)

waves

• light can be described as a combination of oscillating electric and magnetic field that propagate through space as a wave

• wavelength = the length of the smallest repeating unit of a wave (ex: node to node, peak to peak, trough or trough)

  • symbol is λ (lambda)

• frequency = a measure of how many cycles of the wave pass by a specific point in a single second

  • units are cycles per second (s^-1, 1/s or Hz)

  • symbol is f or v (nu)

  • c = 3.00 × 10⁸ m/s = λv

light

• both a wave nature and a particle nature (photon)

• Max Plank discovered that photons have an energy

  • quanta of energy

  • E = hv

  • h (Plank’s constant) = 6.626 × 10^-34 J x s

• higher the frequency (lower wavelength), the more energy the photon has

  • ex: red visible light has a lower frequency compared to violet light

Bohr’s model

• electrons can have only specific amounts of energy

  • fixed amounts - quantized

• electrons travel in orbits that are a fixed distance from the nucleus (stationary states)

• energy of the electron is proportional to the distance between the orbital and the nucleus

  • longer distance from nucleus = more potential energy

  • as electrons move farther from the nucleus, the electrostatic attraction weakens, and they occupy higher energy levels, making them less tightly bound to the atom

• electrons emit energy energy when “jump” from an orbital of higher energy to an orbital of lower energy

• distance between orbitals determines energy of emitted light

determinacy vs indeterminacy

• classical physics = particles move in a path determined by the particle’s velocity, position, and forces acting upon it

• determinacy = definite, predictable future

• electrons are indeterminant, indefinite (cannot know both position and velocity, cannot predict path it will follow)

wave functions

• calculations show that an orbital’s size, shape, and orientation in space are determined by three integer terms in the wave function (added to quantize the energy of e^-)

• integers are called quantum numbers

  • principle quantum number, n

  • angular momentum quantum number, l

  • magnetic quantum number, m_l

principle quantum number (n)

• n characterizes energy of an electron in a particular orbital

  • corresponds to Bohr’s energy level

• n can be any integer greater than 1

• energies are negative (an electron has E = 0 when it just escapes the atom)

• larger the value of n = large the orbital

• as n increases, distance between levels decreases

angular momentum quantum number (l)

• determines shape of an atomic orbital

• has integer value from 0 to (n-1)

• each value of l has a letter to designate orbital shape

  • s orbitals are spherical (l=0)

  • p orbitals are like two balloons tied at the knots (l=1)

  • d orbitals are mainly like 4 balloons tied at the knot (l=2)

  • f orbitals are mainly like 8 balloons tied at the knot (l=3)

s orbital

• each principal energy state has one’s orbital (l=0)

• lowest energy orbital in the principal energy state

• spherical in shape

• number of nodes = 0

p orbital

• each principal energy state above n=1 has three p orbitals

  • m_l = -1, 0, +1

• each p orbital points along a different axis

  • p_x, p_y, p_z

• second-lowest energy orbitals in an energy state

• two-lobed in shape

• number of lobe = (n)

  • node (gap) at the nucleus

d orbital

• each principal energy state above n=2 has five d orbitals

  • m_l = -2, -1, 0 +1, +2

• four d orbitals aligned in separate plans; 5th aligned with z-axis

  • d_xy, d_xz, d_yz, d_x2-y2, d_z2

• third-lowest energy orbitals in a principal energy state

• most are 8-lobed; some are two-lobed with a toroid (donut shape)

• planar nodes; higher principle energy levels also have spherical nodes

f orbitals

• each principal energy spate above n=3 has seven f orbitals

  • m_l = -3, -2, -1, 0, +1, +2, +3

• fourth-lowest energy orbitals in a principal energy state

• more lobes and nodes than d-orbitals

electron spin

• electrons spin on an axis and generate a magnetic field

• all electrons have the same amount of spin

• orientation of spin is quantized

  • only in one direction

  • spin up or spin down

spin quantum number

• describes how an electron spins on its axis

  • clockwise or counterclockwise

  • spin up or spin down

• for a given orbital, spins must cancel

  • paired

  • values of m_s are +1/2 or -1/2

Pauli exclusion principle

• electrons in an atom cannot have the same set of 4 quantum numbers

• no orbital may have more than 2 electrons

• electrons in an orbital must have opposite spins

electron configurations

• the ground state of the electron is the lowest energy orbital it can occupy

• distribution of an atom’s electrons into orbitals

• the number of designates the principal energy level (n)

• the letter designates the sublevel and type of orbital (l)

• the superscript designates the number of electrons in the sublevel

orbital diagrams

• sublevels in each principal energy shell of H have the same energy

• orbitals with the same energy are degenerate

• for multielectron atoms, energies of the sublevels are split

• caused by electron-electron repulsion

• lower values of the l quantum number, have lower energy

  • s < p < d < f

orbital diagrams cont.

• sublevels within an energy level are not degenerate cont.

• penetration of the fourth and higher energy levels, is so strong their their s sublevels are lower in energy than the d sublevels of the lower energy level

• energy difference between levels decreases for higher energy levels (and can cause anomalous electron configurations for certain elements)

orbital diagrams cont. 2

• energy shells fill from lowest to highest energy

• sublevels fill from lowest energy to highest

  • s → p → d → f

  • Aufbau principle

• orbitals that are in the same sublevel have the same energy

  • no more than two electrons in each orbital

  • Pauli exclusion principle

• when filling degenerate orbitals, place one electron in each before pairing

  • Hund’s rule

valence electrons

• the electrons in all the subshells with the highest principal energy shell

• electrons in lower energy shells are called core electrons

• one of the most important factors in the way an atom behaves, both chemically and physically, is the based on the number of VE

electron configuration, VE, periodic table

• for main group/representative elements:

  • group number (up and down) = number of valence electrons

  • number of columns in each “block” is the maximum number of electrons that sublevel can hold

  • period number corresponds to the principal energy level of the VE

electron configuration exceptions

• because of sublevel splitting, the 4s sublevel is lower in energy than the 3d, and therefore the 4s fills before the 3d

  • difference in energy is not large

• for some elements, the (n)s only partially fills before the (n-1)d or doesn’t fill at all

• therefore, their electron configurations must be found experimentally

• ex:

  • Cr = [Ar]4s²3d⁴ → [Ar]4s¹3d⁵

  • Cu = [Ar]4s²3d⁹ → [Ar] 4s¹3d¹⁰

  • Mo = [Kr]5s²4d⁴ → [Kr]5s¹4d⁵

  • Pd = [Kr]5s²4d⁸ → [Kr]5s⁰4d¹⁰

    • becod sublevel is one away from being half full (5 electrons) or full (10 electrons), electrons from the s sublevel will move to the d sublevel

becoming more noble-like

• alkali metals have one more electron than the previous noble gas

• alkali metals tend to lose their extra electron, resulting the same electron configuration as a noble gas

  • cation with a 1+ charge is formed

• halogens have one fewer electron than the next noble gas

  • halogens tend to gain one electron to attain the electron configuration of the next noble gas

  • anions with 1- charge is formed

atomic radius

• increases down a group

  • valence shells farther from nucleus (more n levels)

  • effective nuclear charge fairly similar

• decreases across period

  • adding electrons to same valence shell

  • effective nuclear charge increases

  • valence shell held closer

ionic radius (transitional metals)

for transition metals:

• atomic radius increases down the group

• radii nearly the same within a d-block

  • valence electrons are ns² NOT d electrons

  • effective nuclear charge on ns² electrons approx. the same

• cations form when atom loses VE

• for transition metals, d-block electrons may also be lost

  • Al atom → 1s²2s²2p⁶3s²3p¹

    • Al³⁺ ion → 1s²2s²2p⁶

  • Fe atom → 1s²2s²2p⁶3s²3p⁶4s²3d⁶

    • Fe²⁺ ion → [Ar]3d⁶

    • F2³⁺ ion → [Ar]3d⁵

ionic radius trends

• ions in a group have the same charge

• ion size increases moving down the group (higher valence shell = larger radius)

• cations are smaller than the neutral atom

• anions are larger than the neutral atom

• cations smaller than anions

  • except Rb⁺ and Cs⁺; comparable to or larger than F^- and O^2-

• for species with the same electron configuration: isoelectronic

  • larger positive charge = smaller cation

  • larger negative charge = larger anion

magnetic properties of transition metals

• electron configuration with unpaired electrons result in atoms/ions with a net magnetic field

  • paramagnetic (ex: Mn → [Ar] 4s²3d⁵)

  • atom/ion attracted to an external magnetic field

• electron configuration with all paired electrons result in atoms/ions with no magnetic field

  • diamagnetic (ex: Zn → [Ar]4s²3d¹⁰)

  • slightly repelled by an external magnetic field