CHEM 14A FINAl
configuration diagram
- gives the order of filling for elements 1-20 (H-Ca) - only provides the overall configuration for remaining elements
quantum theories of bonding
- implements the idea that electrons have wave-like properties and are characterized by their entire distributions (wavefunctions/orbitals) with no determinant simultaneous position and momentum - if waves combine in a destructive/constructive manner, that's how electrons bond (bonding vs. anti-bonding) & you can't have one w/o the other (both occur at the same time) *wavefunction (probability amplitude) is not observable; wavefunction^2 (probability density) is *wavefunction^2 = identified with bonding/antibonding respectively TWO FOUNDATIONAL THEORIES: - molecular orbital theory (MO theory) - valence bond theory
examples of ions with resonance structures
- nitrate ion (NO3-) - sulphate ion (SO4 2-) - phosphate ion (PO4 3-)
problems with VSEPR
- no simple way to predict which shape is the most stable - *for these reasons, quantum mechanical approach to chemical bonding = more general and more reliable theory of chemical bonding, but it does not always give simple predictions on shapes of molecules
Schrodinger vs. Bohr model of the atom
- shell in Schrodinger atom = orbit in Bohr atom - Bohr model of the atom does not have subshells or orbitals
strength of acids and bases
- strength =/= concentration - a strong acid loses protons easily and has high Ka's; easily ionized - a weak acid does not lose protons easily and has low Ka's; not easily ionized - a strong base gains protons easily and has high Kb's; easily ionized - a weak base does not gain protons easily and has high Ka's; not easily ionized
net dipole of XeF2
0 net dipole - an exception to the idea that AXn type molecules are the only type that give 0 net dipoles
Drawing Lewis structures
0. Determine arrangements of atoms (C, N, P, S often occur @ center; H's always terminal; O can be both terminal and central) 1. Determine V, or total number of valence e's (for + ions subtract e's; for - ions add e's) 2. Determine NG, or total # of e's needed if each atom had its own noble gas configuration (H = 2; others = 8) 3. Subtract NG from V to get B, the number of shared e's (NG - V = B) 4. Assign 2 bonding e's (one pair) to each bond 5. If bonding e's remain, make double or triple bonds (in some cases, there is more than one way to do this) 6. Remaining e's (V - B) form lone pairs on terminal atoms to give octets (except H) 7. CHECK VIABILITY OF LEWIS STRUCTURE/obtain more stable structure: determine formal charge on each atom; total FCs should give correct charge on atom/molecule *if not possible to place LPs on terminal atoms, place on central atom (ex. for H2O) *in pink = if octet rule is exceeded
m sub l
magnetic quantum number - 1 of the 3 quantum numbers that characterize each orbital - any value from -l to +l - representative of an orbital's orientation in space
[Ar] 3d^1 4s^2
noble gas electron configuration of Sc
Arrhenius acids and bases
*assumed that water is the solvent (aqueous solution) acid = forms H+ ions in an aqueous solution - ex. HCl (in H2O) -> H+ + Cl- base = forms OH- ions in an aqueous solution - ex. NaOH (in H2O) -> Na+ + OH-
VSEPR shapes and bond angles of AXn type molecules
*no lone pairs on central atom AX = linear (trivial): 180 deg AX2 = linear: 180 deg AX3 = trigonal planar: 120 deg AX4 = tetrahedral: 109.5 deg AX5 = trigonal bipyramidal (hexahedral): 90 and 120 deg AX6 = octahedral: 90 deg AX7 = pentagonal bipyramidal: 72 and 90 deg
3 definitions of acids and bases
- Arrhenius acids and bases - Bronsted-Lowry acids and bases - Lewis acids and bases
Einstein vs De Broglie
- Einstein: suggested that waves have particular nature - De Broglie: suggested that particles also might have wave-like nature *De Broglie proved that the wave-particle duality works both ways!
bonding orbitals
- causes a build-up of electron density b/w nuclei - can't have this without anti-bonding
anti-bonding orbitals
- causes a removal of electron density b/w nuclei - can't have this without bonding
how to tell if octet rule is exceeded
1. Determine V, or total number of valence e's (for + ions subtract e's; for - ions add e's) 2. Determine NG, or total # of e's needed if each atom had its own noble gas configuration (H = 2; others = 8) 3. Subtract NG from V to get B, the number of shared e's (NG - V = B). *if number is not enough to form required bonds as shown in the formula, then octet rule is exceeded. 4. Assign 2 bonding e's (one pair) to each bond even if this uses more e's than should be available. 5. Remaining e's (V - B) form lone pairs on terminal atoms to give octets (except H); if any remain, assign them to the central atom lone pairs 6. CHECK VIABILITY OF LEWIS STRUCTURE/obtain more stable structure: determine formal charge on each atom; total FCs should give correct charge on atom/molecule
bond order equation
1/2 (B-A) - B = # of e's in bonding molecular orbitals - A = # of e's in anti-bonding molecular orbitals
geometric isomerism
2+ coordination complexes contain the same # and types of atoms and bonds (the connections between bonds = the same) but have different SPATIAL ARRANGEMENT of atoms - 1 of the forms of coordination complex isomerism ex. square planar MA2B2 or MA2BC
Rydberg's constant
2.18 x 10^-18 J - used in Bohr's theory equation - repped by R
forces acting in an H2 molecule (quantum theories of bonding)
4 attractions - H proton to electron around it and electron from other H (x 2: 2 H atoms) 2 repulsions - electrons from both H atoms repulse each other; protons from both H atoms repulse each other *in an H atom there is just 1 force: proton-electron attraction
various representations of wavefunction
5 different ways of repping the solution of the wavefunction 1. wavefunction x r (distance from nucleus) 2. wavefunction^2 x r (distance from nucleus) 3. 4pi r^2 wavefunction^2 x r (distance from nucleus 4. 90% surfaces for wavefunction 5. 90% surfaces for wavefunction^2
Planck's constant
6.626 x 10^-34 Js or kg m^2 s^-1 - used in De Broglie wavelength equation - repped by h
Louis De Broglie (1924)
A chemist who suggested that just as waves have particular nature (Einstein), particles also might have wave-like nature. - λ = h/mv where h is Planck's constant (Js or kg m^2 s^-1), m is the mass of the particle (in kg), v is the velocity of the particle (in m/s), and λ is in m - also suggested that if particles have a wave-like nature, they should show diffraction and interference effects - observed and confirmed a few years later by Davisson and Germer - Schrodinger wrote a wave equation later, treating e-'s as matter waves
ambidentate ligand
A ligand which can coordinate through more than 1 donor atom
polydentate ligand
A ligand with many lone pairs ("poly" = many, "dent" = teeth)
3 principles of many-electronic configurations
Aufbau Principle Pauli Exclusion Principle Hund's Rule *used to fill orbitals with e's *all 3 principles = based on experiments and not derived from theory *due to the electron-electron repulsion terms that occur in many-electron systems
En = -R (Z^2/n^2)
Bohr's theory equation ex. Calculate the orbit energy of an Li2+ ion at n = 6. ex. Calculate the energy involved in a transition from n = 6 to n = 4 in a Li2+ ion
benzene and resonance
C6H6 - has 2 resonance structures - quantum view of benzene involves delocalization of e's
Bohr's Theory equation
En = -R (Z^2/n^2) - Z = atomic number - n = orbit number - R = Rydberg's constant (2.18 x 10^-18 J or 3.29 x 10^15 s^-1 or Hz) - En in Joules *USED TO CALCULATE THE ORBIT ENERGIES/TRANSITION ENERGIES FOR ANY 1 ELECTRON SYSTEM (EX. H, He+, Li2+, Be3+... U91+, etc) ex. Calculate the energy involved in a transition from n = 6 to n = 4 in a transition from n = 6 to n = 4 in a Li2+ ion Li2+ ion
wavelength = h/mv
De Broglie wavelength equation (type out formula) ex. Calculate the De Broglie wavelength of an electron moving at 1000 m/s
K
EQUILIBRIUM THEORY - the equilibrium constant - equal to [C]^c [D]^d / [A]^a [B]^b, where [ ] = concentrations of reactants or products - higher K = higher concentration of products
violation of octet rule (valence bond theory/hybridization)
EX) why does N only form NCl3, while P can form PCl3 and also PCl5? why can P break the octet rule? P ground state config: 1s^2 2s^2 2p^6 3s^2 3p^3 electron promotion occurs: 1s^2 2s^2 2p^6 3s^1 3p^3 3d^1. the 3 level electrons now rearrange (hybridize) themselves to give 5 hybrid orbitals, all of equal energy, called sp^3d hybrids (sp^3d hybridization) *** another ex = Xe forming XeF2, XeF4, XeF6, XeF*, etc
formal charge
FC = GN - LP e's - 1/2 B e's (or # of bonds) - GN = group # - LP e's = lone pair e's - B e's = bonding e's - the charge assigned to an atom in a molecule or polyatomic ion, assuming that electrons in all chemical bonds are shared equally between atoms, regardless of relative electronegativity *the lower the individual values of the formal charges, the more stable the structure (THE LOWER THE SUM OF THE ABSOLUTE VALUES OF FC'S) - ex. PO4 3- ion has lower formal charges with inclusion of a double bond vs. ion having just 4 single bonds
Coulomb's Law
Force ∝ 1/d^2 (Force = proportional to 1/d^2) - Force = force of attraction between nucleus and valence electrons - d = distance b/w nucleus and valence electrons *explains why ionization energy decreases down any group *as d increases, the force of attraction decreases, so the ionization energy (energy required for an atom to lose an electron) is decreased too
3+
Given [Fe(CN)5Cl]^3-, what is the charge on Fe? Hint: Make Fe the unknown by adding all the charges together to be equal to -3 (total charge of compound) and then solving for it
ionization of H2O
H2O (l) <-> H+ aq + OH- aq *H+ = hydrated and forms H3O+ *the full version is therefore (autoionization): H2O (l; a1) + H2O (l; b2) <-> H3O (a2) + OH- aq (b1) *since these are eq reactions, we can write a Kc: Kc = [H+][OH-]/[H2O] OR Kc = [H3O+][OH-]/[H2O]^2
sp3
H2O molecule hybridization O ground state: 1s^2 2s^2 2p^4 does not involve promotion of electrons
concentration of water at 25 deg c
Kw = [H+][OH-] = 10^-14
concentration of water
Kw = [H+][OH-] where Kw is a modified eq' constant - at 25 deg C, Kw = [H+][OH-] = 10^-14 *the extent of ionization of H2O at any particular temperature has a specific value *typically [H+] will have values ~ 10^-5 mol/L or 1.6 x 10^-3 mol/L or smtg like that
order of
Lewis -> VSEPR -> net dipole? - 2d bonding -> 3d shape -> net dipole or not
advantage of QM approach vs. Lewis structures
MO theory predicts paramagnetism of O2; Lewis structure does not. *Periodic Table of Homonuclear Diatomic Molecules (paramagnetic molecules shown in bold red)
sp1
N2 molecule hybridization N ground state: 1s^2 2s^2 2p^3 does not involve promotion of electrons ...
sp3
NH3 molecule hybridization N ground state: 1s^2 2s^2 2p^3 does not involve promotion of electrons
sp2
O2 molecule hybridization O ground state: 1s^2 2s^2 2p^4 does not involve promotion of electrons
sp^3d
PCl5 hybridization
6.626 x 10^-34 Js or kg m^2 s^-1
Planck's constant (write the value + units) - used in De Broglie wavelength equation - repped by h
molecular orbital theory
QUANTUM THEORY OF BONDING - a theory that accounts for the allowed states for electrons in molecules - good for stability and magnetic behavior (vs. VB theory which is good for rationalizing structure)
unstable bond
QUANTUM THEORY OF BONDING - if the # of bonding e's < or = # of anti-bonding e's
stable bond
QUANTUM THEORY OF BONDING - if the # of bonding e's > # of anti-bonding e's
quantum theory: molecular geometry
QUANTUM THEORY OF BONDING - the theory that molecules adopt the particular shape they do in order to minimize energy - done via VSEPR in Lewis' classical theory, but we can go beyond that with MOs with another approach
valence bond theory
QUANTUM THEORY OF BONDING - treatment of valence bonds involves hybridization - vs. MO where electrons fed into a set of common molecular orbitals - in VB: retains some classical aspects (ex. some e's still "belong" to their parent atoms); good for rationalizing structure (not "predicting"; vs. MO which is good for stability and magnetic behavior) *emphasis on directionality of orbitals
hybridization
QUANTUM THEORY OF BONDING: VALENCE BOND THEORY - atomic orbitals that are similar in energy but not equivalent are combined mathematically to produce sets of equivalent orbitals properly oriented to form bonds ex. BeCl2 - groundV state configuration of Be = 1s^2 2s^2 2p^0 - to achieve di-valency, assume 1 e- is "promoted" to a 2p orbital to give 2 unpaired electrons: 1s^2 2s^2 2p^1 - these 2 orbitals, 2s and 2p, are now assumed to "hybridize" to form 2 sp hybrid orbitals, which are equivalent and adopt directions of 180 deg apart
hybridization of BCl3
QUANTUM THEORY OF BONDING: VALENCE BOND THEORY (example) B ground state of atom: 1s^2 2s^2 2p^1 - ground state configuration does not allow for the appropriate valency of 3 in this case - assume electron promotion occurs: 1s^2 2s^1 2p^2 (3 unpaired electrons) - 1 s orbital and the 2 p orbitals now assumed to hybridize to form 3 sp^2 hybrid orbitals, which are equivalent and adopt a trigonal planar geometry with 120 deg angles
sp^2 hybridization in carbon
QUANTUM THEORY OF BONDING: VALENCE BOND THEORY (example) C ground state of atom: 1s^2 2s^2 2p^2 (only 2 unpaired electrons) electron promotion occurs: 1s^2 2s^1 2p^3, which hybridizes into 3 equivalent sp^2 hybrid orbitals (forming trigonal planar geometry) with one unhybridized px orbital* *unhybridized px orbitals on adjacent C atoms can overlap and produce a pi bond
sp^3 hybridization in carbon
QUANTUM THEORY OF BONDING: VALENCE BOND THEORY (example) C ground state of atom: 1s^2 2s^2 2p^2 (only 2 unpaired electrons), suggesting a valency of 2 (which rarely occurs in C; valency is commonly 4). in CH4 and other singly bonded C compounds, the hybridization = sp^3; electron promotion occurs: 1s^2 2s^1 2p^3, which hybridizes into 4 sp^3 hybrid orbitals and forms a tetrahedral shape
sp^1 hybridization in carbon
QUANTUM THEORY OF BONDING: VALENCE BOND THEORY (example) simplest case = C2H2 (ethyne or acetylene) C ground state of atom: 1s^2 2s^2 2p^2 (only 2 unpaired electrons) electron promotion occurs: 1s^2 2s^1 2p^3, which hybridizes into 2 equivalent sp hybrids and 2 unhybridized px and py orbitals, producing pi bonds w adjacent C atoms' unhybridized px and py orbitals
Molecular Aufbau Principle
Quantum mechanics equivalent of Lewis' shared pair of electrons - as in the case of atoms... 1. follow order of increasing energy 2. Pauli's principle 3. Hund's principle
2.18 x 10^-18 J
Rydberg's constant (write the value + units) - used in Bohr's theory equation - repped by R
180 deg
VSEPR bond angle(s) of AX
180 deg
VSEPR bond angle(s) of AX2
120 deg
VSEPR bond angle(s) of AX3
109.5 deg
VSEPR bond angle(s) of AX4
90 and 120 deg
VSEPR bond angle(s) of AX5
90 deg
VSEPR bond angle(s) of AX6
72 and 90 deg
VSEPR bond angle(s) of AX7
linear (trivial)
VSEPR shape of AX
linear
VSEPR shape of AX2
trigonal planar
VSEPR shape of AX3
tetrahedral
VSEPR shape of AX4
trigonal bipyramidal (hexahedral)
VSEPR shape of AX5
octahedral
VSEPR shape of AX6
pentagonal bipyramidal
VSEPR shape of AX7
VSEPR
Valence Shell Electron Pair Repulsion theory - pairs of bonded electrons around the central atom arrange themselves to minimize repulsion, which dictates the shape of the molecule - vs. Lewis structure, which gives 2D shape - shape determination b/w AXn type molecules vs. AXnEm type molecules vs. AXnYm type molecules
l
azimuthal or angular momentum number - 1 of the 3 quantum numbers that characterize each orbital - any integer between 0 and n-1 - representative of an orbital's shape s orbital: l = 0 p orbital: l = 1 d orbital: l = 2 f orbital: l = 3, and so on...
ionization energy
X(g) -> X+(g) + e- - one of the periodic trends - the energy required to remove an electron from its orbital around an atom to a point where it is no longer associated with the atom - across any period an overall increase occurs but with some anomalies at regular intervals (between groups 2 & 3, and between groups 15 & 16). - down any group a general decrease occurs *note: quite the opposite to the atomic radius trends examined above
Bronsted-Lowry acids and bases
acid = a substance that can donate or transfer protons to another polar substance base = a substance that can accept protons from another polar substance - ex. CH3COOH (base) + HCl (acid) <-> Cl- (base) + CH3COOH2+ (acid) - ex. HCl (g; acid) + NH3 (g; base) <-> Cl- (base) + NH4+ (acid) *solvent is no longer just H2O *includes cases not even involving any solvent *bases don't have to form OH-
unexpected electron configurations
Z = 19 to Z = 20: 4s orbital fills first transition metal elements fill 4s orbitals after 3d but lose 4s electrons first when losing electrons (becoming ions): "last in, first out" 4th, 5th, 6th rows: start with 3d from Group 1, not Group 3 ex. Cr (Z = 24): [Ar] 3d^5 4s^1 ex. Cu (Z = 29): [Ar] 3d^10 4s^1 Z = 57: start filling f orbitals *long form table says that Lu (Z = 71) and Lr (Z = 103) are the elements under Sc and Y, and preceding them are the lanthanide and actinide series respectively
effective nuclear charge
Zeff = Z - S (simple calculation of Zeff; can be more accurately calculated via quantum mechanics) - the net positive charge experienced by an electron in a multi-electron atom - Z = atomic number (# of protons) - S = number of inner shell e's (i.e. shielding e's or nonvalence e's) *increase in effective nuclear charge across a period = smaller atomic radius *does not explain any trend in atomic radius down any group alone
neutral solution
[H+] = [OH-] * [H+] can have any value in principle but still be neutral (ex. at 50 deg C, K2 = 5.47 x 10^-14; pH = 6.631 but still neutral)
1.0 x 10^-14
[H+][OH-] - relationship b/w [H+] and [OH-] of a solution at 25 deg C
weak base
a base that does not gain protons easily - has low K sub b's (Kb's) - conjugate acid = strong acid - not easily ionized ex. Cl- HCl (strong base) + H2O <-> Cl- (weak base) + H3O+
strong base
a base that gains protons easily - has high K sub b's (Kb's) - conjugate acid = weak acid - easily ionized ex. all hydroxides of group 1 (LiOH, NaOH, KOH, etc) and also Ca(OH)2, Ba(OH)2-- all highly ionized
covalent bonding
a bond formed when atoms share one or more pairs of electrons - the kind of bonding in organic chem, biochem, biology. - charge separation b/w atoms in this bond is less extreme - compounds are organic - can be drawn via Lewis structures
ionic bonding
a bond that results when electrons are transferred from one atom (made cation) to another (made anion) - electrostatic from attraction b/w positive and negative ions - arranged in crystals + often dissociate into ion in solution - compounds are inorganic - can be drawn via Lewis structures
dipole
a molecule that has two poles, or regions, with opposite charges - result of difference in electronegativity b/w regions
Bohr's Theory
a postulate surrounding allowed orbits and the quantization of energy. - En = -R (Z^2/n^2) where Z is the atomic number, n is the orbit number, and R is the Rydberg constant - this equation can be used to calculate the orbit energies and transition energies for any 1 electron system (H, He+, Li2+, Be3+... U91+, etc) - gives an explanation of the discrete nature of spectra and the fact that atoms and matter in general are stable (but these are ad hoc and not derived from principles; quantization is just assumed, not derived) - MORE SATISFACTORY EXPLANATION COMES LATER WITH THE REALIZATION THAT ELECTRONS BEHAVE AS WAVES
vector
a quantity that has magnitude and direction - used to calculate whether or not a molecule has a net dipole; taking this kind of sum of all the dipoles in a molecules
sigma bond
a single covalent bond that is formed when an electron pair is shared by the direct overlap of 2 s- orbitals - accompanied by an anti-bonding or sigma* orbital (node where the waves destructively interfere) - stable/unstable depending of # of bonding e's vs # of anti-bonding e's
many-electron systems
a species of elements and their ions that have 2+ electrons around the nucleus - vs. 1 electron systems: has electron-electron repulsion terms; has 4 analogous quantum numbers (n, l, m sub l, and m sub s); have certain periodic properties and conditions - 3 electronic configuration principles: Aufbau Principle, Pauli Exclusion Principle, Hund's Rule
hydrogenic systems
a species of elements and their ions that, like H, consist of a single electron around single nucleus - ex. H, He+, Li2+, etc. - vs. many-electron systems: does not have electron-electron repulsion - this is the only kind of system that the Schrodinger equation can be solved exactly for
coordination complexes (transition metal compounds)
a transition metal atom or ion bonded to several ligands-- atoms/ions/groups with lone pairs of electrons - general formula: MLn (M = transition metal atom/ion, L = ligand, n = # of ligands or coordination #) - 2 broad classes: simple inorganic examples + biologically important examples - most common coordination #s = 2, 4, 6 (#s of 3, 5, etc. occur but less commonly) - depending on charges on TM atom/ion and on ligands, the complex can be +, - or neutral -have distinctive properties like colors + magnetic properties
group
a vertical column of elements in the periodic table
Lewis structures
a way of representing molecular/ionic structures based on valence electrons (outer shells only shown), created by GN Lewis (who also created the notion of covalent bonds as shared pairs of e's) - seem to anticipate Hund's rule (see N or O) - vs. VSEPR model, which gives 3d shape *some need modification in light of experimental facts
Lewis acids and bases
acid = electron pair acceptor - ex. H+ (proton with no orbital can bond with the lone pair of another molecule); NH3 + H+ -> NH4+ (acid base complex) base = electron pair donor - ex. NH3 (ammonia, whose lone pair can bond with H+); NH3 + H+ -> NH4 (acid base complex) ex. BF3 (acid) + F- (base) -> BF4- (acid-base complex) *includes cases in which the H+ proton is not the particle being transferred *donor -> acceptor & proton -> electron(s)
weak acid
an acid that does not lose protons easily - has very low K sub a's (Ka's) - conjugate base = strong base - not easily ionized ex. HF (Ka = 6.8 x 10^-4) ex. HNO2 (Ka = 4.0 x 10^-4)
strong acid
an acid that loses protons easily - has very large K sub a's (Ka's) - conjugate base = weak base - easily ionized ex. HCl, H2SO4, HNO3, HI, HBr, HClO4, HClO3 ex. HNO3 + H2O <-> H3O+ + NO3- (position of eq' lies to the right; almost all HNO3 is ionized, very close to 100%)
ligands
atoms/ions/groups with lone pairs of electrons that bind to transition metal atoms/ions to form coordination complexes/transition metal compounds
10^14
autoionization constant of water at 25 deg
pH
calculated by -log [H+] - hydrogen ion concentration - measurement of how acidic or basic an aqueous solution is - higher concentration = smaller exponent [H+] = lower pH = more acidic - water's = 7
pOH
calculated by -log [OH-] - OH- ion concentration
pKw
calculated by -logKw - at 25 deg C, pKw = 14 derived by: - [H+][OH-] = 10^-14 at 25 deg C - take -logs on both sides: -log([H+][OH-]) = -log(10^-14) - pH + pOH = -(-14) = 14
change in energy = final energy - initial energy
calculating transition energy equation - finding change in energy ex. Calculate the energy involved in a transition from n = 6 to n = 4 in a Li2+ ion
calculating transition energy
change in E = final energy - initial energy - plug final energy level n and initial energy level n into the equation and subtract the product of the latter from the product of the former - ex. level 4 to level 1 or vice versa, level 5 to 1 or vice versa
color of coordination complexes (transition metal complexes)
characteristic of coordination/transition metal complexes. depends on: - identity of metal - oxidation state metal - identity of ligand *arises from partly filled d orbitals in the metal ion (TMs fill 3d electrons first but lose 4s electrons first); d^1 to d^9 inclusive (should not apply to uncombined metals; Sc =/= colored even though it is d1) *also arises from an electronic transition in the range 400nm - 700nm (color = combo of the remaining colors after a frequency = absorbed for a transition) -> made possible bc ligands remove degeneracy of d-orbitals
2+
charge of whole ion: [Ni(H2O)sub6]^2+ - can form an ionic compound with another ion
d orbital
clover shaped orbital within the electron cloud - when l = 2 - at any given energy level (n=3 and above), there are 5 equivalent versions of these w 5 diff orientations (5 orbitals, 10 e-'s); 3 along the x-y, x-z, and y-z planes pointing between axes and 2 along the axes (the vertical one looks like a tube squeezed by a donut) - gets larger with increasing main energy level
wavefunction
created by Schrodinger - repped by ψ - mathematically describes electron's behavior as stationary waves that vary in energy level by number of full wavelengths - does not involve definite trajectories, solving the collapse problem; no orbits but ORBITALS, regions where electrons are 90% likely to be found (no planet-like paths) - incorporates De Broglie's equation of λ = h/mv (quantization rules) - this squared (ψ^2) is the probability that an electron can be found in a certain spot
GN Lewis (1875-1946)
creator of Lewis structures and the notion of covalent bonds as shared pairs of e's
transition metals
d- block elements - groups 3-12
f orbital
daisy/tube with 2 donuts shaped orbital within the electron cloud - when l = 2 - at any given energy level (n = 4 and above), there are 7 equivalent versions of these w 7 diff orientations (7 orbitals, 14 e-'s); 3 along the x-y, x-z, and y-z planes pointing between axes and 2 along the axes (the vertical one looks like a tube squeezed by a donut) - gets larger with increasing main energy level
atomic (molecular) geometry
description of the spatial arrangement of atoms (excluding lone pairs; determining molecular VSEPR shape)
electronic geometry
description of the spatial arrangement of electron groups (determining molecule VSEPR shape)
coordination number of a complex
determined by the type and number of ions or other species surrounding a central ion - most commonly 2, 4, and 6... 3, 5, etc are less common
electronic geometry for valence bond theory/hybridization
different shapes per # of hybrid orbitals (based on electronic geometry) - sp1 = linear - sp2 = trigonal planar - sp3 = tetrahedral - sp3d1 = trigonal bipyramidal
p orbital
dumbbell shaped orbital within the electron cloud that has the second lowest energy of all the other orbital shapes in each main energy level. - when l = 1 - at any given energy level (n = 2 and above) there are 3 equivalent versions of these w 3 diff orientations pointing at right angles from each other (3 orbitals, 6 e-'s) - gets larger with increasing main energy level
periodicity and electron configurations
each column (group) of the periodic table = explained through analogous electron configurations - ex. all group 1 atoms (Li, Na, K) have an s^1 outer shell configuration
electronic vs. atomic (molecular) geometry
electronic geometry: - shape of molecule dependent on spatial arrangement of electron groups atomic geometry - shape of molecule dependent on spatial arrangement of atoms (excluding lone pairs)
Zeff = Z - S
equation for effective nuclear charge - Z = atomic # (# of protons) - S = # of inner shell e's (i.e. shielding e's or nonvalence e's)
effect of chemical structure on strength of bases and acids
features of chemical structure that affect strength of bases and acids 1. bond polarity 2. bond strength 3. anion stability 4. electronegativity effects
equilibrium theory
for any reaction: aA + bB <-> cC + dD - the equilibrium constant K = [C]^c [D]^d / [A]^a [B]^b where [ ] = concentrations of reactants or products - the higher the value of K, the higher the concentration of products ex. for the dissociation of acids: - HCl <-> H+ + Cl- - Ka = [H+] [Cl-] / [HCl] *strong acids have fully ionized and therefore have very high values of Ka *weak acids have low Ka's
typical structures of coordinate compound
formula: MLn; structures depend on coordination number "n" - linear shape: n = 2 - square planar/tetrahedral: n = 4 - octahedral: n = 6
MLn
general formula for coordination complexes/transition metal compounds - M = transition metal atom/ion - L = ligand - n = # of ligands or coordination # - a transition metal atom/ion bonded to several ligands (atoms/ions/groups with lone pairs of e's) - can be +, -, or neutral
decrease
general trend in ionization energy down group - due to the decrease in the force of attraction due to the increasing distance of the outermost electron - Coulomb's law: force of attraction = proportional to 1/d^2 where d = distance
hybridization in CO2 molecule
given its linear geometry it should be described by sp1 hybridization on the central atom sp1 involves use of the pz orbital leaving px and py perpendicular to. bond axis these unhybridized orbitals px and py form pi bonds with orbitals on O atoms orbitals on O atoms shown as dashed lines are not used
old style group numbers
group numbers that work best for Lewis structure determination - I to VIII or 1 to 8 *ignore transition metal groups
period
horizontal row of elements in the periodic table
molecular orbital diagram
in MO theory/quantum theory of bonding, an energy-level diagram showing the relative energies and electron occupancy of the molecular orbitals for a molecule - atomic orbitals on sides - molecular orbitals in the middle (sigma and sigma* bonds repping bonding and anti-bonding)
F
is strength of acids/bases the same as concentration? T/F
[Ar] 4s^1
noble gas electron configuration of K
standing wave behavior of an electron
like vibrating strings fixed at nodes (points with no vibration) - satisfy the condition: length = n (wavelength/2) - the ways in which a bound wave can vibrate = quantized bc only certain fixed vibrations can occur (certain ways of vibrating, called "modes") - different quantized modes/different number of half cycles (n) = different quantized energy levels or energy shells; n-1 nodes = points with 0 probability of finding electrons (no waves) *in this metaphor, a vibrating string = 1 dimensional object; 1 quantum number is needed to specify the quantization of a 1 dimensional object. a 2d vibrating object requires 2 quantum numbers (2 modes of vibration -> 2 dimensions). *AN ACTUAL ELECTRON WAVE IS A 3D VIBRATING OBJECT REQUIRING 3 QUANTUM NUMBERS. *ASSUMED by Bohr, DERIVED by Schrodinger
2
maximum # of electrons in 1 orbital
2n^2
maximum # of electrons that can occur in each shell
pH scale
measurement system used to indicate the concentration of hydrogen ions (H+) in aqueous solution; ranges from 0 to 14 (lower = acidic, higher = basic) - pH = -log[H+] (higher pH = smaller concentration of H+ and more basic bc more negative exponent = smaller #) - water has pH = 7, [H+] = 10^-7
homonuclear molecule
molecule containing atoms of only one element
3 quantum numbers of orbitals (hydrogenic systems)
n = principal quantum number l = azimuthal or angular momentum quantum number m sub l = magnetic quantum number - the relationship between these sets of numbers emerges from the details of the solution of the Schrodinger's equation. Can be derived. - only applies to hydrogenic systems
4 quantum numbers of orbitals (many-electron systems)
n = principal quantum number l = azimuthal or angular momentum quantum number m sub l = magnetic quantum number m sub s = electron's spin or intrinsic magnetism - only applies to many-electron systems; these 4 numbers describe each electron in a many-electron atom - no 2 electrons have the same 4 quantum numbers - n, l, and m sub l = 3 spatial quantum numbers - m sub s = spin
possible modifications to Lewis structures
necessary in light of experimental facts - resonance structures (sometimes 1 Lewis structure cannot explain the electronic bonding/electrons' delocalization of a molecule/polyatomic ion) - octet rule violation (sometimes molecules exceed or are deficient of octet)
[Ar] 4s^2
noble gas electron configuration of Ca
optical isomerism
non-superimposable mirror images are required (alternatively, if a molecule lacks a plane of symmetry) - can occur with polydentate ligands, but not essential - 1 of the forms of coordiantion complex isomerism ex. ethylene diamine bi dentate
Bronsted-Lowry base
one of the 3 definitions of a base - a substance that can accept protons from another polar substance - ex. CH3COOH (base) + HCl (acid) <-> Cl- (base) + CH3COOH2+ (acid) believed that... - acids and bases always occur together, like oxigants and reactants -acid-base conjugate pair differs by just 1 H+ ion (ex. HCl acid and Cl- base, NH4+ acid and NH3 base) - any acid-base reaction involves 2 such acid-base conjugate pairs in general (ex. HCl + NH3 <-> Cl- + NH4+; H2SO4 + H2O <-> H3O+ + HSO4-; etc) *solvent is no longer just H2O *includes cases not even involving any solvent *don't have to form OH-
Lewis base
one of the 3 definitions of a base - electron pair donor - ex. NH3 (ammonia, whose lone pair can bond with H+); NH3 + H+ -> NH4 (acid base complex) *includes cases in which the H+ proton is not the particle being transferred
Arrhenius base
one of the 3 definitions of a base - forms OH- ions in an aqueous solution (assumes water = the solvent) - ex. NaOH -> Na+ + OH- (in H2O)
Bronsted-Lowry acid
one of the 3 definitions of an acid - a substance that can donate or transfer protons to another polar substance - ex. CH3COOH (base) + HCl (acid) <-> Cl- (base) + CH3COOH2+ (acid) *solvent is no longer just H2O *includes cases not even involving any solvent
Lewis acid
one of the 3 definitions of an acid - electron pair acceptor - ex. H+ (proton with no orbital can bond with the lone pair of another molecule); NH3 + H+ -> NH4+ (acid base complex) *includes cases in which the H+ proton is not the particle being transferred
Arrhenius acid
one of the 3 definitions of an acid - forms H+ ions in an aqueous solution (assumes water = the solvent) - ex. HCl -> H+ + Cl- (in H2O)
Aufbau Principle
one of the conditions of many-electron systems - electrons fill lower-energy atomic orbitals before filling higher-energy ones (follow order of increasing energies)
Pauli Exclusion Principle
one of the conditions of many-electron systems - no 2 electrons in an atom can have the same 4 quantum numbers (can share 3, but not 4) - i.e. no 2 electrons can reside in exactly the same quantum state (the 2 "exclude" each other) - only 2 electrons can occupy the same orbital and they must have OPPOSITE SPINS - partially explains the lack of collapse of e's into the nucleus
Hund's Rule
one of the conditions of many-electron systems - when filling a set of orbitals with equal energies (n and l), as many different orbitals as possible are occupied with parallel spins (i.e. spin maximization occurs)
electronegativity effects
one of the features of chemical structure that affect strength of bases and acids
anion stability
one of the features of chemical structure that affect strength of bases and acids *the more resonance structures, the more delocalization
bond strength
one of the features of chemical structure that affect strength of bases and acids - increased bond strength of H-X (X is some atom) = decreased strength of acid (bond = stronger & more difficult to lose protons)
bond polarity
one of the features of chemical structure that affect strength of bases and acids - increased polarity of H-X (X is some atom) = increased strength of acid (bond = weaker & easier to lose protons)
octet rule violation
one possible modification to Lewis structures - sometimes molecules violate the octet rule (octet deficient or octet exceeded) ex. BF3: rules predict that there are 2 single bonds and one double bond between B and F's, but experimental evidence shows only single bonds. B violates octet rule; only 6 e's around B ex. PCl5: P has 10 electrons around it
resonance structures
one possible modification to Lewis structures -one of the two or more equally valid electron dot structures of a molecule or polyatomic ion that collectively describe the electronic bonding and that cannot be expressed by a single Lewis formula - same arrangement of atoms but different distribution of e's among the atoms - ex. NO3- ion (Lewis structure suggests that NO3- ion has 2 single bonds and 1 double bond but experiments show that all 3 bonds = of equal length), has 3 resonance structures to represent the situation (has a length somewhere b/w lengths of N-O and N=O)
exceeding octet rule
one possible modification to Lewis structures violating the octet rule made possible due to quantum concepts - only possible for elements in period 3 and on (not possible for periods 1 & 2; no available d orbitals) - electron promotion from 3s -> 3d results in 5 unpaired e's that can form 5 single bonds - ex. P in PCl5 - ex. As in AsCl5
2nd row diatomic molecules
order of MO energies changes as we cross ____________ (recall analogous 4s/3d case in atoms) - ex. Li2, B2, Be2, C2, N2, O2, F2, Ne2 - between N2 and O2 a small change occurs; 2 of the orbital energy levels cross over (occurs again in each subsequent period)
anomalies in ionization energy trend across period
overriding effects which more than compensate for the increasing Zeff cause these "____________ across period" (____________ does not increase) 1. B/W GROUPS 2 AND 3 - stability of outermost 2p e-'s in group 3 elements < 2s e-'s in group 2 elements (needs less ionization energy) 2. B/W GROUPS 15 & 16 - doubly paired outer electrons in group 16 elements' p orbitals = more easily removed than one of the outer electrons in group 15 elements (greater electron-electron repulsion)
14
pH + pOH - relationship b/w pH and pOH of a solution at 25 deg C
combination of p orbitals
px + py + pz - in each case, there is one lobe +, one lobe - (this represents phase, not change) *by convention the inter-nuclear axis is taken as z, and not x as usually done; this makes for simplifications in more advanced work *ex. in diagram = B2 molecule (B configuration: 1s^2 2s^2 2p^1)
relationship between atomic radius and Zeff
r = proportional to n^2 / Zeff - n = main quantum number for outer e - Zeff = effective nuclear charge - r = atomic radius *if you use the accurate Zeff (using quantum mechanics) for n^2/Zeff, and then you consider the accurate values for Na/Li and for K/Na, you'll see that there's ~1.22x increase in radius as you go down a group
n
principal quantum number - 1 of the 3 quantum numbers that characterize each orbital - any integer above 0 - representative of each shell's energy level and the number of subshells; each shell with principal quantum number n and energy level n has n subshells - also represents the avg distance of an electron from the nucleus of an atom/distinguishes each shell (equivalent to an orbit in the Bohr atom model) - n^2 = number of orbitals; 2n^2 = maximum number of electrons that can occur in each shell
periodic trends
property of the elements that can be predicted from the arrangement of the periodic table - atomic radius - ionization energy - electronegativity - electron affinity
Schrodinger
proposed the quantum mechanical model of the atom and treated electrons as matter waves - this equation can be solved to yield a series of wave function ψ, each of which is associated with an electron binding energy E. - square of the wave function ψ^2 represents the probability of finding an electron in a given region of the atom - atomic orbital = the region within an atom that encloses where the electron is likely to be 90% of the time *ψ's DO NOT INVOLVE DEFINITE TRAJECTORIES, which solves the collapse problem (no orbiting path)
disadvantage of pH scale
psychological disadvantage: the more acidic = lower pH
-log[H+]
relationship b/w pH and [H+]
log[OH-]
relationship b/w pOH and [OH-]
uncertainty in momentum
represented by Δp - used in the Heisenberg's Uncertainty Principle equation - Δp = m Δv (based on momentum equation; delta v = uncertainty in speed) - can be used to plug into the Uncertainty equation to find uncertainty in position (delta x)
linkage isomerism
requires an ambidentate ligand (ex. NO2-) - 1 of the forms of coordination complex isomerism ex. nitro vs. nitrito ion
sigma vs. pi notation
sigma or s = "symmetrical orbitals" (symmetrical about the internuclear/horizontal axis); single overlap pi = double overlap
atomic radius
size of an atom - one of the periodic trends - decreases from left to right across any period (due to an increase in effective nuclear charge; increase in protons pulls valence electrons closer to the nucleus) - increases from top to bottom down any group (increase in energy shell) - proportional to n^2/Zeff (where n = main quantum number for outer e- and Zeff = effective nuclear charge) *definition: simple Z sub eff = Z - # of inner shell e's
dative covalent (coordinate) bonding
special kind of covalent bonding between transition metal and ligands - features a shared pair of e's with both e's provided by 1 atom - transition metals = Lewis acids; accept lone pairs - ligands = Lewis bases; provide lone pairs
s orbital
spherical orbital within the electron cloud that has the lowest energy of all the other orbital shapes in each main energy level. - when l = 0 - has only one orientation (1 orbital, 2 e-'s) - gets larger with increasing main energy level
probability density
square of the wave function or ψ^2 - proportional to the probability of finding an electron in a particular volume of space within an atom - can be represented by plotting distance from the nucleus r x ψ^2 r^2 (ψ^2 = proportional to the probability) - probability of finding an electron farther from the nucleus increases with rising energy level of orbital - from Schrodinger's wave function / wave equation for e's
calculating net dipole
take the vector sum of all the dipoles in a molecule - all molecules of type AXn and no lone pairs = 0 net dipoles - most other cases give nonV zero dipoles, minus a few exceptions (ex. XeF2) STEPS - find the electronegativities of each atom on electronegativity table -
m sub s
the 4th quantum number (in many-electron systems) - "spin", or an electron's intrinsic magnetism (which generates spin angular momentum); a form of magnetism that occurs in electrons that is not related to its motion ("m" = magnetic; spin is a magnetic effect) - also quantized; can just take 2 values ("spin up" or "spin down") - the electron = structureless - nothing moves around anything else; it's not literally spin
electronegativity
the ability of an atom to attract both the e's in a bond - one of the periodic trends - ex. HCl: Cl pulls electrons closer to it than H, so Cl is the negatively charged end (negative partial charge) and H is the positively charged end (positive partial charge) *not to be confused with electron affinity which is the amount of energy liberated when a molecule or neutral atom acquires an e- from the other elements
Kw = [H+][OH-]
the autoionization constant of water equation
electron affinity
the energy change when a molecule/neutral atom acquires an e- from the other elements - one of the periodic trends - the amount of energy liberated (vs. electronegativity, which is the ability of an atom to attract e's)
quantization of energy
the idea that electrons exist in fixed energy levels surrounding the nucleus, behaving much like fixed waves with different "modes" of vibration (different by frequency) - increased frequency or increased "n" (the quantum number, or # of half cycles) = higher energy (higher energy shell) - there are n-1 nodes, points where there is 0 probability of finding an electron (where the waves are fixed) - emerges as a natural consequence of confinement or boundary conditions *this was ASSUMED by Bohr but DERIVED by Schrodinger
bond order
the number of electron pairs being shared by a given pair of atoms - in molecular orbital theory: BO = 1/2 (B-A); B = # of e's in bonding molecular orbitals; A = 3 of e's in anti-bonding molecular orbitals
blocks of periodic table
the periodic table is divided into 4 "blocks" based on the differentiating electron (not necessarily the outermost electron/the "final" electron to enter the atom)
Heisenberg's Uncertainty Principle
the principle that it is fundamentally impossible to precisely determine both the position and velocity of a particle at a given moment in time - Δx = uncertainty in position - Δp = uncertainty in momentum - h = Planck's constant (h/4pi = minimum value for the product of these 2 uncertainties) *the more certainty we have about either position or momentum (the smaller Δx or Δp is), the less certainty we have about the other (the bigger Δx or Δp is) *this is due to the fact that PARTICLES ALSO ACT AS WAVES, particles do not have a precise position and momentum at all times; no determinism (which is a characteristic of the quantum realm); indeterminacy rules vs. in classical mechanics, if x and p are known at t=0, x (or the position of a planet) can be predicted 300 years from t=0. *electron also no longer has a well-defined path or trajectory; no more orbits ex. a marble weighing 1.0 g with speed known to be within +/- 1.0 mm/sec. Calculate the uncertainty in position.
atomic orbital
the region within an atom that encloses where the electron is likely to be 90% of the time - the standing wave solutions of the Schrodinger equation with different energy levels - characterized by 3 quantum numbers (n, l, and m sub l) in hydrogenic systems, 4 in many-electron systems - no orbital in an atom shares the same energy except in the H atom (which only has 1 electron)
n + l rule
the rule that electrons fill the principal energy levels and subshells according to increasing energy level - always gives the correct overall configuration but not the order of filing (see electron. configuration from Z = 19 to Z = 21 on periodic table)
degeneracy
the similarity in energy between orbitals - only in the H atom are orbital energies that share the same n value degenerate - presence of electron-electron repulsion in many-electron atoms removes this quality
increase
trend in ionization energy across period - this is true overall, but there are 2 anomalies (between groups 2 & 3 and groups 15 & 16) due to overriding effects which more than compensate for increasing Zeff. ANOMALIES: - b/w groups 2 & 3: stability of outermost 2p e's in B is less than the 2s e's in Be - b/w groups 15 & 16: one of the opposite-spin electrons in O = more easily removed vs. one of the outer electrons in N due to electron-electron repulsion
electron configuration from Z = 19 to Z = 21
unusual order of filing electrons in orbitals in which 4s < 3d in energy (4s fills first) - begins with Z = 19 or the K atom (K atom configuration = [Ar] 4s^1, not [Ar] 3d^1) - continues with original ordering back to 3d < 4s from Z = 21 or the Sc atom
AXnEm type molecules
used to determine VSEPR shape - type of molecule WITH lone pairs on central atom - A = central atom - X = an atom bonded to A - n = number of atoms bonded to A (X) - E = a lone pair on A - m = # of lone pairs on A - most give nonV zero dipoles but there are some exceptions (ex. XeF2) *overall geometry still dictated by # of electron pairs but to name the shape of the molecule, consider only the bonded pairs *bond angles also change with lone pairs on the central atom *lone pairs occupy a larger volume vs. bond pairs
AXn type molecules
used to determine VSEPR shape - type of molecule with no lone pairs on central atom - A = central atom - X = an atom bonded to A - n = number of atoms bonded to A (X) - all have 0 net dipoles
AXnYm type molecules
used to determine VSEPR shape - type of molecule with other atoms on central atom - A = central atom - X = an atom bonded to A - n = number of atoms bonded to A (X) - Y = another atom bonded to A - m = # of the other atom bonded to A - most give nonV zero dipoles minus a few exceptions
isomerism
when 2+ coordination complexes have the same molecular formula but different structural formulas ("iso" = same; "mer" = parts) - comes in 3 main forms: 1. geometric 2. linkage 3. optical
Z = 19
where on the periodic table does the filing of electrons become unusual where 4s < 3d? - ex. K
Z = 21
where on the periodic table does the filing of electrons become usual again where 3d < 4s? - ex. Sc
periods 3 and on
which periods of elements can exceed the octet rule?
Heisenberg's Uncertainty Principle equation
Δx Δp > or = h/4pi - Δx = uncertainty in position - Δp = uncertainty in momentum - h = Planck's constant (h/4pi = minimum value for the product of these 2 uncertainties) *USED TO CALCULATE THE UNCERTAINTY OF A PARTICLE'S POSITION/MOMENTUM/SPEED ex. An electron moving within the diameter of a typical atom (200 pico meters) has a mass of 9.109 x 10^-31 kg. Find uncertainty in speed.
combination of 2 H atom orbitals
Ψmol = ΨA 1s + ΨB 1s - previously seen as the first representation *electron waves on each atom combine together either in phase or out of phase (constructive/destructive interference)
De Broglie wavelength equation
λ = h/mv - h = Planck's constant (6.626 x 10^-34 Js, or kg m^2 s^-1) - m = mass of object/particle in kg - v = velocity of object/particle in m/s - λ in m *PROVED THAT PARTICLES HAVE WAVE-LIKE PROPERTIES ex. Calculate the De Broglie wavelength of an electron moving at 1000 m/s
