Chem p2

Interaction potential

a mathematical function that describes how the potential energy of a system of particles (such as atoms, ions, or molecules) changes based on the distance and coordinates between them

Boundary conditions

the specific constraints or values applied at the edges of a physical, mathematical, or computational domain

Wave function

a mathematical function that describes the quantum state of a particle, such as an electron in an atom or molecule

Operator

a mathematical rule or instruction that transforms one function into another

Probability density

the likelihood of finding an electron at a specific point in space around an atom's nucleus

Nods

a specific point, surface, or plane within an atomic orbital where the probability of finding an electron is zero

Partial derivative

measure how one physical property changes when you alter a single variable while holding all other variables constant

Spherical polar coordinates

describe a point in three-dimensional space using a radial distance and two angular variables(r, theta, phee)

Principle quantum number

The principal quantum number (\(n\)) is a value that designates the main energy level or electron shell occupied by an electron in an atom

Orbital angular quantum number

Quantum number L that defines the shape of an atomic orbital and designates its subshell

Subshells

A subshell (or sublevel) is a subdivision of an electron shell in an atom, defined by the angular momentum quantum number (L)

Magnetic quantum number

The magnetic quantum number (symbolized as (ml) is the third quantum number in chemistry and physics that describes the spatial orientation of an atomic orbital around an atom's nucleus

Radial vs angular wavefunctions

Radial: Have to do with n, the principle quantum number, having to do with the distance of an electron from the nucleus

Angular: Angles phee and theta, Decides the 3d shape and orientation of orbital

Why do you square the wave function

To find the density of an electron in a specific area

Why are s orbitals spheres

because of the angular momentum quantum number (L=0), which means they have zero angular momentum.

Radial nodes

a 3D spherical region around the nucleus of an atom where the probability of finding an electron is zero

Radial distribution function

probability of finding an electron within a thin spherical shell at a distance r from the nucleus. Defined by 4 pi r2 [Rr]2.

Nodal plane

a flat, two-dimensional cross-section passing through the nucleus of an atom where the probability of finding an electron is zero

Angular nodes

a flat, two-dimensional plane or conical surface passing through the nucleus of an atom where the probability of finding an electron is zero

How to find radial and angular nodes

Radial nodes equals n - l - 1

Angular nodes equals l

Total Nodes

Total Nodes equals n-1 = (angular nodes) + (radial nodes)

Spin quantum number

a value that describes the intrinsic angular momentum (or "spin") of a subatomic particle, such as an electron

Defined by Ms

2 competing effects of orbital energy

1: The closer to the orbital energy of an interaction the greater the energy stabilization

2: Greater overlap between wavefunctions, the increased energy spliting

Amount of orbitals rules

1)Number of orbitals in a subshell is 2l + 1

2)Number of orbitals in a main energy is n2

3)Orientation of orbitals is defined by ml

4)Adjacent orbital spins must be opposite

Z(eff)

The effective nuclear charge is the net positive charge experienced by an electron in a multi-electron atom, taking into account the attractive pull of the nucleus and the repulsive shielding effect of inner-shell electrons. Equals Z - S(number of non-valence electrons)

Penetration

the ability of an electron in a specific orbital to get close to the positively charged nucleus

Pauli exclusion principle

no two electrons in an atom can share the exact same set of all four quantum numbers

Hund’s rule

electrons fill degenerate orbitals (orbitals with the same energy level, such as the (p), (d), or (f) subshells), they occupy each orbital singly with parallel spins before any pairing occurs

Nobel Gas Configuration

a short way to write the electron arrangement of an element. It uses the symbol of the nearest noble gas that comes before the element on the periodic table, written in brackets, followed by the remaining outer-shell electrons

Chromium Configuration

[Ar]3d5 4s1

Core vs valence electrons

Cores occupy the inner shell that shield the positive charge of of the nucleus from the valence electrons. Summarized using the previous Nobel gas.

Valence occupies the outermost shell, involved in chemical bonding and feel the pull of the nucleus. Written our explicitly after the Nobel gas core.

2 Modes of electron configuration

Full electron configuration written subsequentially by energy shells and subshells. Shortens replaces the core electrons with most recent Nobel gas.

Groups and periods in electron configuration

Elements of the same group have the same number and arrangement of valence electrons and moving down a group increases the principle quantum number. Valence electrons increase as you go down a period. Groups 1-2 s subshell, Groups 13-18 p subshell, Transition metals d subshell, bottom periods are f subshell

S, F, D, P block element properties

S: Relative metals with electrons determined by period

P: All kinds with electrons increasing as you move from left to right. Given by ns2 np1-6

D:Transition metals with electrons increasing as you move left to right, in middle of s and p, Given by (n-1)d1-10 ns1-2

F: Bottom 2 rows increasing from left to right, Given by n-2f1-14 n-1d0-1 ns2

Atomic radius

a measure of the size of an atom, typically defined as the distance from the center of the nucleus to the boundary of the surrounding electron cloud

Atomic radius trend

Increases as you move down and descreases from left to right on the periodic table

Ionic radius

the measure of the size of a monatomic ion in a crystal lattice

Size rules in atoms

Increases as you move down groups and decreases left to right on periods

Isoelectric

the specific pH value at which a molecule or solid surface carries zero net electrical charge

Ionization energy

the minimum energy required to remove the most loosely bound electron from an isolated gaseous atom, ion, or molecule

First ionization energy

the minimum energy required to remove the outermost electron from one mole of neutral atoms in the gas phase

Ionization trend

Increases from left to right on a period and decreases going down a group

Electron affinity (Eea)

the energy change that occurs when an electron is added to a neutral gaseous atom to form a gaseous anion

Positive and negative electron affinity

Negative:Energy is released when the atom gains an electron. The resulting anion is at a lower energy state and is relatively stable

Positive: required (absorbed) to force an electron onto the atom. The resulting anion is higher in energy and unstable or temporary

Breaks in the electron affinity trend

Beryllium (Be), Magnesium (Mg), Calcium (Ca), Nitrogen (N), Phosphorus (P). When electrons move to the next subshell

Chemical bonds

the attractive forces that hold atoms and ions together to form molecules, crystals, and chemical compounds

Duplet and Octet

Duplet: An atom is stable when it has a pair (2) of electrons in its outermost shell

Octet: An atom is stable when it has eight (8) electrons in its outermost shell

Lattice energy

the energy released when gaseous ions combine to form one mole of a solid ionic crystalline compound

Lattice energy dependents

Ionic size - Distances increases and lattice energy drops

Ionic charges - larger charges means larger lattice energy

Lewis symbol procedure

o   Find the elements chemical symbol

o   Count the number of valence electrons(given by group on periodic table) and arrange it around the four sides(place of dots doesn’t matter)

o   Place one electron on each of the four sides of the atomic symbol before paring electron

o   Once each side has an electron, additional electrons are added as pairs

Lewis symbols of ions

Cations are represented by removing the dots from the symbol for the metal atoms

Anions are represented by transferring those dots to Lewis structures for nonmetals to complete valence electrons

Indicate charge with brackets with subscripts

Lewis symbols for covalent compounds

1)Identify the total number of electrons between the elements

2)Apply the octet rule and denote shared electrons with lines

3)Recount the number of electrons to ensure correctness

Electronegativity

the tendency of an atom to attract shared electrons (or electron density) toward itself when forming a chemical bond

Delta EN

Represents the difference in electron negativity between two bonded atoms

Dipole moment equation

Dipole moment(mew) = Q x d = Magnitude of the partial electron charge x distance of separation between the charges

Octet rule

a chemical principle stating that main-group elements tend to bond so that each atom has eight valence electrons in its outer shell

Lone vs bonding pairs

Lone pairs are the non-bonding pairs of electrons and the bonding pairs are the ones sharing electrons

Lewis structures for polyatomatic ions

1)Identify the number of electrons and add or subtract electrons based on the charge

2)Bond elements denoted by lines to satisfy the octet or duplet rule

3)Add or remove electrons based on charge

4) Recound total electrons to indicate correctness

5) Indicate charge outside brackets

Octet rule violations

1)Incomplete octet - Fewer than 8 valence electrons

2)Odd electron molecules - Total number of valence electrons is an odd number

3)Central atom accommodates more that 8 electrons

Dependents of melting point

Charge of elements and distance between elements

Electron configuration of cations

1)identify the charge of the ion

2)Write out original electron configuration

3)Remove the smaller subshell electrons first (s then p then d then f)

4) Rewrite equation for removed electrons

Normalized probability

Normalized probability is a measure of the probability of finding an electron in between a set of radii

What values are needed to determine the energy of an electron in a many-electron atom

n, l

How to find number of electrons in quantum numbers

1)Identify the n value and total amount of subshells

2)Identify the number of electrons for each subshell value

3)Add up total number of electrons

Shape of each subshell

S - 3 dimensional sphere

P - 2 ballon shaped ovals with the short parts adjacent to eachother

D - 4 ballon shaped ovals making a cross pattern

F - 2 ballon shaped ovals inside 2 short cones facing opposite dirrections

Electronic configuration procedure:

1) Identify total number of electrons and principle quantum number

2) Fill subsequent subshells with electrons

3) Add electrons to the next subshell once subshell is full

Ionic radius trend

The lower the ionic charge, the lower the Zeff, the higher the ionic radius and vice versa

Ionization energy trend

Decreases down a group and increases from left to right(exceptions to elements with a filled s or half-filled p subshell have higher energy)

Why does oxygen have a lower first ionization energy than flourine and Nitrogen

1)2p electron in fluorine experience a higher effective nuclear charge, and their for a higher ionization energy

2)Oxygen is relieved of electron-electron repulsion when ionized

When does Ionization have the biggest jump across a group

When the ionization level reaches the charge of the group

ex. Jumps most from 2-3 in group 2 because its a +2 charge

Electron affinity trend

More energy is released(electron affinity increases) than absorbed from left to right across a period and less energy is released(electron affinity decreases) down a group

VSEPR Model

a chemistry model used to predict the three-dimensional shape of individual molecules based on the electrostatic repulsion between electron pairs surrounding a central atom

VSEPR Model rules

1) Identify regions of high electron concentration repel one another (effective electron pairs)

2) Do not distinct single from multiple bonds

3)Only bonding regions form the 3D shape of the molecule

4)Strength of repultion in order

VSEPR steps

1) Identify total effective electron pairs

2) Divide 360 degrees by total to find separation

3)Place effective electron pair across the atom

Types of VSEPR electron arrangements

Number of pairs: Linear (2), Triagonal Planer (3), Tetrahedral (4), Trigonal Bipyramidal (5), Octahedral (6), Pentagonal Bipyramidal (7)

Electronegativity trend

Increases from left to right, decreases as you go down a period

Electronegativity equation

First ionization energy + electron affinity / 2

Resonance and hybrid resonance

Blending of Lewis structures

Merging electron structures

What is formal charge

Electron ownership of an element consisting of lone pair electrons and divided over bonding electrons

What happens to hydrogen energy when n increases

Hydrogen energy approaches 0

Spherical polar coordinate meaning

R, distance from nucleaus

Phee, angle from Z-axis

Theta - Angle about Z-axis

Coordinate covalent bond

Both electrons from one atom are shared

Equatorial vs axial position

Equatorial is the less crowded directed outward side of the molecule

Axial is the more crowded parallel to the axis of symmetry side of the molecule

1-3 lone pair for Triagonal bipyramidal

1)Lone pair goes in the equatorial position in a seesaw structure

2)Lone pair prefers equatorial positon

3)Lone pair prefers equatorial position, 120 degrees from the central atom and two enter the top and bottom

1-2 lone pairs for octahedral

1)Equatorial positon

2)Have them on opposite sides of one another

See-Saw structure

occurs when a central atom is bonded to four atoms and has one lone pair of electrons.

Polar covalent bond

two atoms share a pair of electrons unequally because they have different electronegativity, leading to the unequal sharing of electrons