Structure of Matter (25%)
Atomic Structure
Important scientists

Dalton's atomic theory
o unique, indestructible atoms for each element
o chemical reactions rearrange atoms
o element mass proportion is constant in compound

subatomic structure
o J. J. Thomson: measured electron charge-to-mass
o Millikan: measured electron charge
o Rutherford: characterized dense, positive nucleus
Components of the atom
Particle
Location
Charge
Mass
Symbol
1 p or 1 H
Proton
nucleus
+1
1.0
1
1
1 n
Neutron
nucleus
0
1.0
0
o e
Electron
outside
-1
.00055
-1
Nuclear symbol AZX

A = #p + #n

Z = #p

isotopes have same Z, but different A
Average atomic mass (100mav = %1m1 + %2m2 + ...).
Forms of matter

pure substance has unique formula and properties
o elements—one type of atom
(diatomic: H2, N2, O2, F2, Cl2, Br2, I2)
o compounds—two or more types of atoms
molecular—formula defines size
crystalline—formula shows ratio of atoms

mixture of pure substances variable composition
o uniform: homogenous mixture = solution
o non-uniform: heterogeneous
Three types of natural radioactivity
Name
Symbol
Mass
Charge Penetration
4He
alpha
low
4
+2

0e beta
middle
-1

0
gamma
high
0
0


Nuclear reactions

balance A (mass) and Z (charge) values

determine symbol by Z number

transmutations: induced nuclear reactions by impact
Radioactive decay (first order reactions)

rate = kNt

ln(N0/Nt) = kt

k = ln2/t½
Photon energy

c = f

Ephoton = hc/= 2.00 x 10-25/m (J)
Hydrogen electron energy

Eelectron = -2.18 x 10-18/n2 (J)

E = Ehigh – Elow = Ephoton
Quantum mechanical model

unpredictable orbitals (Heisenberg uncertainty principle)

orbital "address"
o principle energy levels (n)
o sublevels (l) = 0(s), 1(p), 2(d), 3(f), … (n -1)
o orbital (ml) = - l, …, -1, 0, +1, …, l (degenerate)
o spin (ms) = +½, -½ (Pauli exclusion principle)
Electron configurations, orbital diagrams and quantum numbers

the first three energy levels
n
1
2
3
l
0 0
1
0
1
2
ml 0 0 -1 0 1 0 -1 0 1 -2 -1 0 1
2
ms              

electron configuration (1s22s22p6)

orbital diagrams ()—maximize half filled (Hund’s rule)

Quantum numbers (n,l,ml,ms)
Periodic Table
Electron arrangements in monatomic ions

ions within 3 of a noble gas are isoelectric with noble gas

transition metal: lose s, then d except columns 6, 11
Periodic table organization
1s
1s
2s
2p
3s
3p
4s
3d
4p
5s
4d
5p
6s
4f
5d
6p
7s
5f
6d
7p

main group (1-8) families—similar properties
o same valence-electron configuration
o same ionic charge
o alkali metals (1), alkaline earth metals (2), halogens
(7 or 17), noble gases (8 or 18)
Periodic nature of some properties.

atomic size (volume/radius)
o increase down a group—larger n
o decrease to the right—increase core charge
(nucleus – core electrons) on valence electron
increases attraction (shielding effect = Zeff)

ionization energy: X(g)  X+(g) + 1eo +H: increases as radius decreases (harder to
remove closer electron—more attraction to core)
o successive ionization energies gradual increase
until all valence electrons are removed

electron affinity: X(g) + 1e-  X-(g)
o ±H: more negative as radius decreases (lower
energy state as electron approaches core)
o –H = stable anion

electronegativity: attraction for covalent bond electrons
o smaller atoms have greater electronegativity (closer
to nucleus = stronger attraction)
o electronegativity difference between bonding atoms
is proportional to bond polarity

anomalies (period 2)
Group
1
2
3
4
5
6
7
element
Li
Be
B
C
N
O
F
valence electrons s1
s2
s 2 p 1 s 2p 2 s 2p 3 s 2p 4 s 2p 5
radius
1.34 0.90 0.82 0.77 0.75 0.73 0.71
electronegativity 1.0
1.5
2.0
2.5
3.0
3.5
4.0
ionization
520 899 801 1086 1402 1314 1681
affinity
-60
>0
-27 -122 >0 -141 -328

sp: group 3 loses p electron  lower ionization
group 2 adds p electron  + electron affinity

: group 6 loses electron  lower ionization
group 5 adds electron  + electron affinity

metals, nonmetals—separated by stair step
ion formed
ion radius
most reactive
metal
cation
smaller than atom
alkali metals
nonmetal
anion
larger than atom
halogens

paramagnetism (unpaired electrons) and diamagetism
(all paired electrons—when sublevel is full)
Hybrid orbitals
system
atomic orbitals
bonding hybrids
2
s+1p
sp
3
s+2p
sp2
4
s+3p
sp3
5
s+3p+d
sp3d
6
s+3p+2d
sp3d2

single bond electrons (sigma bond—) and lone pairs
are hybridized

second and third bonding electron pairs (pi bonds—)
remain in p orbitals
Polar and/or multiple bonds are shorter and stronger
Molecular Structure
Octet rule

lone + bonding pairs equals 8—octet rule

exceptions:
o H (2), Be (4), B (6)—2 x valence #
o odd number of available valence electrons
Lewis structures for molecules and ions

count the total number of valence electrons

draw a skeleton structure

place electrons around each atom

count Lewis structure electrons
o if Lewis electrons > valence electrons: add multiple
bonds
o if Lewis electrons < valence electrons: add 2 or 4
electrons to central atom (expanded octet)

resonance forms when placement of double bond is
arbitrary

bond order = # bonds to outer atoms  # outer atoms

best Lewis structure has minimum formal charge
o assigned electrons (unshared + ½ bonding
electrons) – valence electrons = formal charge
o any negative charge goes to most electronegative
atom
Hybridization, bond angle and geometry from its Lewis structure
# atoms + lone electron pairs around central atom
#
2-sp
3-sp2
4-sp3
5-sp3d
6-sp3d2
o
o
o
o
o
120
109.5
90 + 120
90o
 180
2 linear bent
bent
linear
3
T-shaped
 planar  pyramid
4
tetrahedron
Seesaw
 planar
5
 pyramid
 bipyramid
6
octahedron
Polarity of a simple molecule

two possibilities
o asymmetrical shape (lone pair of electrons around
the central atom, except sp3d-linear and sp3d2square planar
o symmetrical, but different outside atoms

properties of polar molecules
o soluble in water (polar solvent)
o strong intermolecular attraction  high melting and
boiling temp., low evaporation rate—low volatility)
Naming simple hydrocarbons

prefix based on number of main chain carbons
1
2
3
4
5
6
meth…
eth…
prop…
but…
pent…
hex…

suffix based on bonding between carbons
single
1-double
2-double
3-double
triple
…ane
…ene
…diene
…triene
…yne

carbon branches number based on lowest number of
main branch carbon and end in "yl"
Effect of functional groups on a hydrocarbon

halogen replaces H increases polarity

oxygen containing groups
o increases polarity (C–OH > C=O > C–O–C)
o alcohols—OH (ending: …ane  …anol)
o acids—COOH (ending: …ane  …anoic acid)

amines
o replace H in ammonia with hydrocarbon groups
(CH3NH2 = methylamine, (CH3)2NH = dimethylamine)
o weak bases
Structural and geometric isomers

structural isomer—same formula but different structure
and name

geometric isomer—same formula, structure and name,
but different orientation around double bond:
(cis X>C=C<X, trans X>C=C<X)
States of Matter (25%)
Gas and Liquid State
Kinetic theory for gases (ideal gas)

Kinetic energy: K = 3/2RTK (R = 8.31)

velocity, u = (3RT/MM)½ [u1/u2 = (MM2/MM1)½]

energy/temperature/velocity distribution curve
energy/temperature/velocity

molecular volume  zero

collisions produce pressure

molecules don't interact
Gas laws

gas pressure is affected by:
o n  P: more gas molecules exert pressure
o T  P: more and harder collisions
o V  1/P: spread out = less collisions/area

ideal gas law: PV = nRT
o R = 0.0821 (P in atm) or 8.31 (P in kPa)
o TK = ToC + 273
o Patm = Ptorr/760 = PkPa/101

rate of effusion or diffusion: RateA/RateB = (MMB/MMA)½

partial pressure: Ptot = PA + PB, where PA = XAPtot
Real gas deviation for ideal gas law

low temperature: clumping = fewer molecules collide 
less pressure than ideal

high pressure: crowding = gas molecules take up
measureable space  greater volume than ideal
Phase diagram

critical temperature and pressure (C)

triple point (A)



Vapor



melting/freezing (A-B)
o higher pressure favors more dense phase
o Q = nHfus
sublimation/deposition (A-D): skip the liquid state (dry
ice—CO2) when below triple point pressure
boiling/liquefaction (A-C)
o temperature depends on atmospheric pressure
(boiling point decreases as altitude increases)
o Q = nHvap
vapor: gaseous phase below boiling point
evaporation (+Hvap)—opposite is condensation
equilibrium vapor pressure
o condensation = evaporation
o independent of container size
o vapor pressure increases with temperature
Solid and Solution State
Crystalline solid structure

structural unit in geometric pattern + bond

structural unit: molecule, atom or ion

bond holding units together
o covalent—strong bond

C (diamond) and SiO2 (quartz) have strong 3-d
crystal structure

C (graphite) has 2-d structure, with dispersion
forces holding sheets together
o ionic—strong bond (strength depends on ionic
charge, Q, and ion radius, d: E = kQ1Q2/(d1 + d2)
o metallic—variable bond strength
o molecular—weak bond (from strongest to weakest)

H-bond: N, O, F bond to H

dipole force: polar molecules

dispersion force: temporary polarization
o all molecules
o more electrons = stronger
o stronger than dipole force for large mass

ranking from weakest bond/lowest melting point to
strongest/highest: molecular < metallic < ionic < covalent

conductors: metals and liquid/aqueous ionic

water solubility: ionic and polar molecular

malleable: metal and molecular
Concentration units

mass percent: % = g solute/total g x 100

mole fraction: X = mole solute/total moles

molality: m = mole solute/kg solvent

molarity: M = mole solute/ L solution
Convert from one concentration unit to another
Unit
Solute
Solvent
%
gsolute = %
gsolvent = 100 – %
X
nsolute = X
nsolvent = 1 – X
M
nsolute = M
gsolvent = 1000d – (nsolute)MM
m
nsolute = m
msolvent = 1000 g

convert numerator and/or denominator
o mass  volume: m = (d)(V)
o mass  moles: m = (n)(MM)
Principles of solubility

solute-solvent interactions
o breaking solute-solute bonds and solvent-solvent
interactions absorbs energy (endothermic)
o forming solute-solvent bonds releases energy
(exothermic)

effect of temperature upon solubility
o dissolving most solids is endothermic  higher
temperature increases solubility
o dissolving most gases is exothermic  lower
temperature increases solubility

gas solubility proportional to pressure: Mg = kPg
Colligative properties of solutions

colligative properties
o effect depends on concentration only
o nonelectrolyte vs. electrolyte

electrolyte forms ions in solution: conducts
electricity

number of ions  i (van't Hoff factor)

vapor pressure lowering
o solute particles lower vapor pressure (VP)
o VP = X1P1o (X1 and P1 are solvent values)

osmotic pressure
o solute increase osmotic pressure ()
o  = MRTi (R = 0.0821)

boiling point elevation and freezing point depression
o solute extends the liquid phase of solvent
o Tb = kbmi, Tf = kfmi
Reactions (50%)
Chemical Formulas and Equations
Molar mass MM from a formula: add atomic masses
Convert mass or volume of solution into moles, n
_m x n/MM = n
_V x n/V = n
Preparing a solution

moles needed: nstandard = MstandardVstandard
o mass of stock powder, m = (nstandard)MM
o volume of stock solution, V = (nstandard)/(Mstock)

(Mstock)(Vstock) = (Mstandard)(Vstandard)
% mass from a chemical formula

mass % = mpart/mwhole x 100
Empirical (simplest ratio) formula

convert m (or %)  n

divide each mole value by smallest

multiple by factor to make whole numbers = subscripts
Molecular formula

determine molar mass
o MM = mRT/PV = dRT/P (gas)
o MM = kf • msolute/Tf • msolvent (kg) (solute)

procedure
o MM/empirical formula mass = N
o empirical formula subscripts x N = molecular
formula
Formulas of ionic compounds

memorize ions
o columns ± 3 from noble gas (anions: ...ide)
o transition: 2+ except Ag+, Cr3+ or Roman numeral
o NH4+ (ammonium), OH- (hydroxide), CN- (cyanide)
o …ate: Cr2O72- (dichromate), C2H3O2- (acetate) and
123NO3-, ClO3CO32O3
PO43O4 per… ClO4-, MnO4- SO42-, CrO42o …ite: 1 fewer O than …ate

crisscross charges to become subscripts in formula
Balance a chemical equation

know formula, charge and state

balance numbers and kinds of atoms

reduce (coefficients don't have to be balanced)
Write net ionic equations

write aqueous species in ionic form

show reacting species only (remove spectator ions—
usually derived from strong acids and bases)
Determine mass/volume values from balanced equations
Given: A
Find: B
Grams of
Grams of
Substance A
Substance B
MM 
Moles of
Substance A
MM 
Coefficients from
balanced equation
Moles of
Substance B
M
M
Volume of
Volume of
Solution A
Solution B
Limiting reactant, theoretical yield

determine limiting reactant and theoretical yield

% yield = actual/theoretical x 100
Volumetric analysis (titration)

end point (color change)  equivalence (all reacted)

calculations
o balance equation to determine nX/nT ratio
o moles of titrant: nT = (MT)(VT)
o moles of unknown: nX = (nT)(nX/nT)
o molar mass of unknown: MMX = mX/nX
o molarity of unknown: MX = nX/VX
Thermodynamics and Kinetics
Enthalpy (H)

H = – Qcalorimeter = –mcT (c = 4.18 J/goC for H2O)

calculate H from bond energies
o for gaseous reactions only
o H =B.E broken –  B.E formed

calculate from standard heat of formation (Hfo)
o H (25oC, 1 M [ions] and 1 atm gases) for the
synthesis of compound from pure elements
o Ho = Hfo products –Hfo reactants

exothermic (-H), endothermic (+H)

Laws of Thermochemistry
o H is proportional to moles reacted
o H of reverse reaction has opposite sign
o Hess's Law: H = H1 + H2 + …
Entropy (S)

So = So products – So reactants

+S: more disorder: solids  liquids  gases, diffusion,
increase T, and production of additional gas molecules
Free energy (G)

spontaneous reactions (G < 0)
o decrease in energy (stronger bonds) (–H)
o increase in disorder (+S)

Go= Ho – TSo (T in Kelvin)
Temperatures for spontaneous reactions

H and S have opposite signs, T has no effect

+H and +S: spontaneous when T > Ho/So

–H and –S: spontaneous when T < Ho/So
Rate law

rate = k[Reactant A]m[Reactant B]n
o m, n = order (first, second, etc.),
o overall order = m+n

determine rate law from [ ]o and rate
o write rate law for each experiment
o divide rate laws to cancel out all but one reaction
order
o solve for unknown reaction order
o repeat for all orders
o solve for k (units are Mxt-1 (x = 1 – overall order))
Reactant concentration vs. time

first-order reactions (see radioactivity).
o ln(Xo/X) = kt
o t1/2 = ln2/k

linear plots (straight line graph for each order)
o zero order: [A] vs. t
o first order: ln[A] vs. t
o second order: 1/[A] vs. t
Collision theory and activation energy

collisions must be forceful and with correct orientation

activation energy (potential energy) diagrams
o Ea = Hactivated complex - Hreactants
o Ea' = Hactivated complex - Hproducts
o H = Hproducts – Hreactants = Ea – Ea'

reaction are faster (greater k) at higher T because more
reactants have Ea (see kinetic energy graph)

Catalyzed reactions have lower Ea
Reaction rate vs. temperature

ln(k1/k2) = (Ea/R)(1/T2 – 1/T1)

R = 8.31, Ea in J, T in K

reaction rate  k
Reaction mechanisms

reaction occurs in steps (lower Ea and fewer molecules
colliding), which add up to the overall reaction

slow step (rate determining step) determines rate law

intermediate formed early and consumed later

enzyme consumed in slow step and reform later
Electrochemistry
Redox reactions

assign oxidation numbers
o standards

always: group 1+1, group 2+2, F-1, Al+3

usually: O-2, H+1
o elements, compounds = 0, ions = charge

balancing redox equations
o assign oxidation numbers
o split into half reactions
o balance each half reaction

balance atoms except O,H

balance O, by adding H2O

balance H, by adding H+

balance charge, by adding eo equalize electrons
o add half reactions
o if basic, add OH- for each H+
Electrochemical terms

redox chemical reactions
o cathode: site of reduction
o anode: site of oxidation

electric energy
o 1 mole e– = 96,500 C (1 faraday-F)
o I, current in amps (A) I = Q/t (C/s)
Standard potentials

Eoox = -Eored (1 M ions and 1 atm gases)

oxidizing agent (attracts e–, more +Eored)

reducing agent (loses e–, more –Eored)

Eotot = Eored + Eoox
Eotot > 0: spontaneous (Eotot < 0: nonspontaneous)
Nonstandard potentials: E = Eo – (RT/nF)lnQ

R = 8.31, T = 298, F = 96,500 C/mol e
n = electrons transferred from redox

Q = equilibrium expression including (g) and (aq)
Voltaic Cells (+Etot)

anode (attracts anions from salt bridge): electrons pulled
from reducing agent (lower on Standard Potential Chart)

cathode (attracts cations from salt bridge): electrons
attracted to oxidizing agent (higher on Potential Chart)
Electrolytic cells (–Etot)

nonspontaneous redox reaction

storage battery provides energy

anode (+ pole) induces oxidation

cathode (– pole) induces reduction
Electrolysis in water

cathode (reduction)
o columns 1, 2, and Al3+: 2 H2O + 2 e-  H2 + 2 OHo acid: 2 H+ + 2 e-  H2
o others: Mx+ + X e-  M

anode (oxidation)
o halide except F-: 2 X-  X2 + 2 eo base: 4 OH-  O2 + 2 H2O + 4 eo others: 2 H2O  O2 + 4 H+ + 4 e-
Equilibrium
Equilibrium expression

example: N2(g) + 3 H2(g)  2 NH3(g) Kc = 50

expression: Kc = [NH3]2/[N2][H2]3

equilibrium constant K
o Kp = Kc x (RT)ng
Kp = 50 x (0.0821 x 373)-2 = 0.053
o for 2 NH3(g)  N2(g) + 3 H2(g):
Kc' = 1/Kc = 1/50 = 0.020
o for NH3(g)  1/2 N2(g) + 3/2 H2(g):
Kc'' = (kc')1/2 = (0.020)1/2 = 0.14
o adding chemical equations: K3 = K1 x K2
o large K = mostly product  reaction favored
K, Go and Eo (Go = -RTlnK = -nFEo ).
(R = 8.31, T = 298, F = 96,500, n = # e-)
Le Chatelier's principle

system reduces stress by shifting  or 
increase
decrease
Factor
Response
Reactant


Product


Temperature (exothermic)
 (K )
 (K )
Temperature (endothermic)
 (K )
 (K )
Volume (ng-reactant > ng-product)


Volume (ng-reactant < ng-product)



ng-reactant = ng-product: system doesn’t respond to V

adding inert gas or catalyst has no effect
Ionization of water

H2O(l)  H+(aq) + OH-(aq)

H+ (proton) is hydrated (H3O+) = hydronium ion

Kw = [H+][OH-] = 1 x 10-14

pure, "neutral" water: [H+] = [OH-] = 1 x 10-7 M

acidic: [H+] > [OH-], basic: [H+] < [OH-]

pH scale—pH = -log [H+], (pOH = -log[OH-])
o acidic < 7, neutral = 7, basic > 7
o pH + pOH = pKW = 14
Acids and bases

Acids: proton donor
o strong acids: HA  H+ + A(HCl, HBr, HI, HNO3, HClO3, HClO4, H2SO4)
o weak acids: HA  H+ + A
% ionization = [H+]/[HA]o x 100

HA (HF, H2S, organic acids—COOH)

HXOy (HClO, HBrO2, H2SO3, H3PO4)
o HClO > HBrO (Cl higher electronegativity)
o HClO2 > HClO (more oxygens)

nonmetal oxides: CO2(g) + H2O  H+ + HCO3
bases: proton acceptor
o strong bases (column 1, Sr2+, Ba2+)

soluble hydroxides: MOH  M+ + OH
metal oxides: MO + H2O  M2+ + 2 OHo weak bases

ammonia (amines): NH3 + H2O  NH4+ + OH
anions: A- + H2O  HA + OH
acid and base properties of salts
strong bases
others
M+
(spectator ions) M+ + H2O  H+ + MOH
X 
7 strong (spectator)
neutral
acidic
HX-  H+ + X2acidic
acidic
X- + H2O  HX + OHbasic
?

weak acid–weak base: HF + NH3  F- + NH4+
o KaHF x KbF- = KbNH3 x KaNH4+ = Kw = 1 x 10-14
o from standard conditions equilibrium shifts from
stronger acid and base to weaker acid and base

Lewis concept–acid = electron pair acceptor and base =
electron pair donor: Fe2+ + :SCN-  Fe:SCN+
Aqueous systems

ionization of a weak acid (HA)
o HA(aq)  H+(aq) + A-(aq), Ka = [H+][A-]/[HA]
o polyprotic acids (H2A): [H+]E from first ionization

Ka1: [H+][HA-]/[H2A]

Ka2: [H+][A2-]/[HA-]

hydrolysis of a weak bases (A- or B)
o basic anion (A-—except from strong acids)
A-(aq) + H2O(l)  HA(aq) + OH-(aq),
Kb = [HA][OH-]/[A-]
o basic molecules (B—derived from NH3)
B(aq) + H2O(l)  HB+(aq) + OH-(aq),
Kb = [HB+][OH-]/[B]

ionization of water
H2O(l)  H+(aq) + OH-(aq), Kw = [H+][OH-] = 1 x 10-14

dissociation of a salt (MX)
o MX(s)  M+(aq) + X-(aq), Ksp = [M+][X-]
o spectator ions: Na+, K+, NO3o common ppt.: AgCl, PbCl2, Hg2Cl2, BaSO4, SrSO4

formation of complex ions
M+(aq) + :X(aq)  M:X+(aq), Kf = [M:X+]/[M+][:X]
Equilibrium problems

determine direction ( or  from [ ]o
o substitute [ ]o into equilibrium expression = Q
o if Q > K, then , if Q < K, then 

determine K, given [ ]E
o write expression from equation
o substitute [ ]E, solve for K

determine K, given [ ]o and one [ ]E
o set up an "ICE Box" (shaded boxes are given)
[]
A
+
2B

C
+
3D
[A]o
[B]o
[C]o
[D]o
I
C
-
-2
[C]E – [C]o = 
3
[C]E
E
[A]o - 
[B]o – 2
[D]o + 3
o write expression, substitute [ ]E , solve for K

determine one [ ]E, given other [ ]E and K
o write expression, substitute given [ ]E and K, solve
for missing [ ]E

determine [ ]E, given [ ]o and K
o set up an "ICE Box" (shaded boxes are given)
[]
A
+
2B

C
+
3D
[A]o
[B]o
[C]o
[D]o
I
-x
-2x
+x
+3x
C
[A]o – x
[B]o – 2x
[C]o + x
[D]o + 3x
E
o write expression, substitute [ ]E and K, solve for x
o substitute x back into formulas solve for [ ]E
Titration curve and calculations
0.1 M HCl added to 0.1 M NaOH (upper) or 0.1 M NH3 (lower)
pH pure NaOH
14 [OH-] = [NaOH] = 0.10 M
13
[OH-] = (nOH- – nH+)/Vtotal
12 pure NH3
11 Kb = [OH-]2/[NH3]
10
Buffer
9
Kb = [OH-](nH+)/(nNH3 – nH+)
8
½ way
pure water
7
pKb = pOH
[OH-] = [H+] = 10-7 M
6
equivalence
5
pure conjugate acid
4
Ka = [H+]2/(nNH3/Vtotal)
3
2
excess HCl
1
[H+] = (nH+ – NOH-)/Vtotal
0
mL HCl