General Chemistry
Review for the MCAT
Dr. Paul A. Jelliss
Monsanto Hall 114
(314) 977-2834
jellissp@slu.edu
MCAT
The MCAT: Basic Structure
Verbal Reasoning:
• 85 minutes, 65 questions.
Physical Sciences Ö Physics & Gen. Chem.:
• 100 minutes, 77 questions.
Writing Sample:
• 30 minutes, 2 essays.
Biological Sciences Ö Organic & Biology:
• 100 minutes, 77 questions.
MCAT
2
The Essentials for Class
A functional brain:
• not yet turned to mush?
• it might after this.
Eye(s) & Ear(s):
• preferably attached to aforementioned brain.
Pen/pencil & notepaper:
• to write stuff down when I suggest, e.g. examples.
• we’ll try to make this at least a bit interactive to
keep you awake.
• where else would you rather be early on a cold
February Saturday morning?
MCAT
3
What can we do in 6 hours?
No way can we cover absolutely everything from
two semesters of general chemistry.
• would you really want to relive that entire nightmare
anyway?
We can look at key concepts from gen. chem. and
try some examples which are MCAT-relevant.
Most importantly, RELAX!
•
•
•
but don’t over-do it.
you will learn and test better under moderate anxiety.
Freaking out won’t help!
MCAT
4
General Chemistry on the
MCAT
Intermingled with physics in a Physical
Sciences section (total 77 questions in 100
minutes).
• ~75 seconds per question.
Some passages, some free standing
questions: consider doing the latter first.
Immediately following the verbal section
before lunch.
MCAT
5
Back to the Basics:
Atomic Structure
Atom: smallest unit of any element.
Subunits: protons, neutrons, electrons:
• protons and neutrons are neucleons.
Atomic number (Z): proton number:
• identifies element, X.
• charge of +1.
• mass of ~1 amu (1.66 × 10–27 kg).
6
Back to the Basics:
Atomic Structure
Mass number (A): mass of the atom.
A = Z protons + N neutrons = Σ nucleons.
Neutrons: same mass as protons, no charge.
Written as superscript before the element
symbol:
A
ZX
#electrons = Z in a neutral atom!
7
Isotopes, Atomic Weight, and
Ions
What is an isotope?
Two atoms of the same element that differ in
their number of neutrons:
• 74Be and 94Be.
Atomic weight (not atomic mass) – what’s the
difference?
Weighted average of masses of naturally
occurring isotopes.
Ions: gain or loss of electrons – anion or cation.
8
Average Atomic Weight
Element X has two isotopes of atomic mass
38.6 and 42.6 in 1:3 relative abundance.
What is the atomic weight of X?
•
•
•
•
42.6
41.7
40.6
39.7
9
Isotopes, Atomic Weight, and
Ions – Example
An atom contains 16 protons, 17 neutrons,
and 18 electrons. Which of the following
best indicates this atom?
•
•
•
•
33Cl–
34Cl–
33S2–
34S2–
10
Quantum Numbers:
Electron Zip Code
What is the purpose of quantum numbers?
Quantum numbers designate a unique “zip
code” for each electron in an energy level.
No two can have same zip code.
How many quantum numbers in a zip code?
One zip code Ö four quantum numbers.
• shell, subshell, orbital, spin.
11
The First Quantum Number
What does it designate? What is its symbol?
Principal quantum number designates the shell
(symbol is n).
Related to the size and energy of an orbital (a
three dimensional region around the nucleus in
which the electron is likely to be found).
What are the possible values?
n = 1, 2, 3, 4, 5...∞ (higher values are higher in
energy and farther from nucleus).
12
The Second Quantum Number
What does it designate? Symbol?
Subshell number (symbol is l) describes shape
of electron’s orbital.
Values?
l = 0, 1, 2,…n – 1 (If n = 3, then l = 0, 1, or 2).
s, p, d, and f subshells correspond to l values of
0, 1, 2, and 3 respectively.
Subshells have shape – what are they?
13
The Second Quantum Number
Shapes mnemonic easy to remember:
s is for spherical
d is for daisy
p is for peanut
f is for f---ed up!
14
The Third Quantum Number
What does it designate? Symbol?
Orbital number (symbol is ml ) describes the
three dimensional orientation of an orbital.
Values?
Value of ml = –l...0...+l inclusive.
•
•
•
If l = 0, then ml = 0
If l = 1, then ml = –1, 0, 1
If l = 2, then ml = –2, –1, 0, 1, 2
15
The Fourth Quantum Number
What does it designate? Symbol?
Spin number (symbol is ms ) designates
electron’s intrinsic magnetism.
Values?
1
1
Value of ms = + 2 or – 2 only.
Every orbital can accommodate 2 electrons.
If an orbital is full, the electrons it holds are
“spin-paired”.
©ª
16
Assigning Quantum Numbers: Rules
Aufbau principle: What is it?
Electrons occupy the lowest energy orbitals
available:
• 1s-2s-2p-3s-3p-4s-3d-4p-5s-4d-5p-6s-4f-5d6p-7s-5f-6d-7pHund’s Rule: Basic point?
Electrons in same subshell occupy available
orbitals singly before pairing up.
Pauli Exclusion Principle: Think exclusion?
No two electrons can have same set of four
quantum numbers.
17
Fill in order of increasing n + l
Assigning Quantum Numbers: Rules
1s
2s
2p
3s
3p
3d
4s
4p
4d
4f
5s
5p
5d
5f
6s
6p
6d
7s
7p
18
Ground State Electron
Configurations
Use previous three rules to write.
How would oxygen look?
1s22s22p4
Frequently, shortcut designations are used
instead of writing out the entire configuration
– P for example:
• [Ne]3s23p3
19
Electron Configurations:
Anomalies
Sometimes the anticipated electron
configuration is not the actual one: stability
through filled or half-filled subshells.
What are some exceptions?
The exceptions: Cr, Cu, Mo, Ag, Au.
What is Cr expected?
[Ar]4s23d4
But what is it really?
Cr actual: [Ar]4s13d5
20
Electron Configurations: Ions
Anions accommodate the gained electrons in
the first available orbital with the lowest
available energy.
F (Z=9) has config. 1s22s22p5 while F– has
config. 1s22s22p6
• configuration exactly like Ne (F– and Ne are called
isoelectronic).
• iso- = same, -electronic = configuration.
21
Electron Configurations: Ions
Cations lose electrons from the most unstable
orbital: How would Li+ look?
Li (Z = 3) has config. 1s22s1 and Li+ has
config. 1s2
How about Ti+?
For transition metals, the valence s electrons
are always lost first, before any d electrons.
Ti+ (Z = 22) expected [Ar]3d14s2 but Ti+
actually: [Ar]3d24s1
22
Electron Configurations:
Examples
Which of the following gives the electron
configuration of an aluminum atom?
• 1s22s22p1
• 1s22s22p2
• 1s22s22p63s23p1
• 1s22s22p63s23p2
23
Electron Configurations:
Examples
What is the electron configuration of an atom
of copper?
Remember, Cu is an exception!
Expected: [Ar]3d94s2
Actual: [Ar]3d104s1
Moral: beware of stability in transition metals!
24
Diamagnetic and Paramagnetic
Atoms
Diamagnetic: all electrons are spin paired
(even number of electrons):
• atom repelled by a magnetic field.
Paramagnetic: not all electrons are spin-paired:
• atom attracted by a magnetic field.
Know the difference – these are easy points!
25
Electron Energy Levels and
Spectra
Ground state: define?
• Lowest possible energy.
Excited state?
• At least 1e– in higher energy level.
Absorption: + or – energy change?
• Incoming photon absorbed by electron, jumping to
higher energy level.
Emission: + or – energy change?
• Electron dropping to lower energy level emits
photon.
26
Electron Energy Levels and
Spectra
Formula for the energy of a photon?
• E = hν = hc/λ…define the terms!
• Planck’s constant, h = 6.63 ×10–34 J.s
Emission vs. absorption spectra: What’s the
difference?
• Emission: electrons dropping to lower energy
levels emit light of specific frequencies which are
separated into bright lines by a prism.
• Absorption: specific frequencies of white light are
absorbed by gaseous element based on differences
between quantized energy levels – dark bands.
27
Electromagnetic Spectrum
From lowest to highest energy level?
Radiowaves € microwaves € infrared €
visible light € ultraviolet € X-rays € gamma
rays.
Visible light, from lowest to highest frequency?
Red € orange € yellow € green
blue € indigo € violet
• ROYGBIV
Trends are important, not values.
28
Nuclear Structure and Decay
Protons and neutrons held together by strong
nuclear force which overcomes the electrical
repulsion between the protons.
What is radioactive decay?
Unstable nuclei undergo a transformation by
altering the number and ratio of protons and
neutrons or lowering their energy.
What are parent and daughter nuclei?
Anyone done the different types in class?
29
Alpha Decay: α
An alpha particle, denoted by α, consists of 2
protons and 2 neutrons, equivalent to a He
nucleus, which is ejected.
Alpha decay reduces the parent’s atomic
number by 2 and mass number by 4.
210 Po € 206
4 He
+
84
2
82Pb
∆Z = –2, ∆A = –4
30
Beta Decay: β–
When unstable nucleus contains too many
neutrons, it may convert a neutron into a
proton and an electron (β– particle) which is
ejected: 10n € 11p + 0–1e–
Atomic number of daughter nucleus is 1
greater than parent, but mass number same.
14 C € 14 N + 0 e–
6
–1
7
∆Z = +1, ∆A = 0
31
Positron Decay: β+
When unstable nucleus contains too few
neutrons, it may convert a proton into a neutron
and positron (β+ particle) which is ejected: 11p
€ 10n + 0+1e+
Positron is electron’s antiparticle – identical to
electron, but charge is positive.
Atomic number of daughter nucleus is 1 less
than parent, but mass number same.
18 F € 18 O + 0 e+
8
9
+1
∆Z = –1, ∆A = 0
32
Electron Capture
Conversion of a proton into a neutron by an
unstable nucleus by capturing an electron (e–)
from the closest shell: 11p + 0–1e– € 10n
Atomic number of daughter nucleus is 1 less
than parent, but mass number same – just like
positron emission.
51 Cr + 0 e– € 51 V
24
–1
23
∆Z = –1, ∆A = 0
33
Gamma Decay: γ
Nucleus in excited state (often after alpha or
beta decay) emits energy in form of photons of
electromagnetic radiation.
Gamma photons (γ rays) have neither mass nor
charge, and their ejection changes neither
atomic mass or number.
31 Si € 31 P + β– € 31 P + γ
15
14
15
∆Z = 0, ∆A = 0
34
Radioactive Decay: Example
Radioactive calcium-47, a known β– emitter, is
administered in form of 47CaCl2 by I.V. as a
diagnostic tool to study calcium metabolism.
What is the daughter nucleus of 47Ca2+?
• 46K+
• 47K+
• 47Ca2+
• 47Sc2+
35
Radioactive Decay: Example
Memory device:
• β+ decay starts with proton and makes it a neutron.
• β– decay starts with neutron and makes it a proton.
36
Radioactive Decay: Half Life
What is a half-life?
The time it takes for one-half of some sample
of radioactive substance to decay.
Shorter half lives mean faster decay.
Half life denoted by t1/2.
Make a chart to solve these problems – forget
the formula unless you do e-functions in your
head!
37
Radioactive Decay: Half Life
Time
0
Amount of Sample
Remaining
100 %
1 half-life Ö t1/2
1/2 = 50 %
2 half-lives Ö 2t1/2
(1/2)2 = 1/4 = 25 %
3 half-lives Ö 3t1/2
(1/2)3 = 1/8 = 12.5 %
4 half-lives Ö 4t1/2
(1/2)4 = 1/16 = 6.25 %
38
Half Life: Example
Radiolabeled vitamin B-12 containing
radioactive cobalt-58 is administered to diagnose
a defect in a patient’s vitamin B-12 absorption.
If the half-life is 72 days, approximately what
percentage of the radioisotope will remain in the
patient a year later?
• 3%
• 5%
• 8%
• 10 %
39
The Mole
Mole: amount of substance ¨ contains same #
of elementary entities as carbon-12 atoms in
exactly 12 g carbon-12.
Avogadro’s constant, NA = 6.022 × 1023 mol–1.
Molar mass: mass (g) of 1 mole of substance.
mass (g)
# moles =
molar mass (gmol–1)
40
Chemical Compounds
Chemical compound ¨ pure substance,
can be broken into 2/more elements.
Molecule ¨ smallest unit of a compound,
still retains properties (formula unit for
ionic compounds).
Atom ¨ smallest unit of an element.
Any compound always contains same %
composition by mass, e.g. iron (III) oxide:
Fe = 69.9 % O = 30.1 %
41
Empirical Formula
Find lowest multiple(s) of whole atoms ¨
2-step process:
• c assume 100 g compound:
1 mol
= 1.25 mol
Fe = 69.9 g ×
55.9 g
1 mol
= 1.88 mol
O = 30.1 g ×
16.0 g
• d convert numbers to lowest whole multiple(s):
1.88 mol O
3 mol O
1.5 mol O
¨ Fe2O3
=
=
1.25 mol Fe 1.0 mol Fe 2 mol Fe
42
Molecular Formula
For many (usually organic) compounds,
actual molecular formula usually not
empirical (simplest ratio), e.g. glucose:
Empirical: CH2O molecular: C6H12O6
molecular mass
= integer n ¨ CnxHnyOnz
empirical mass
For glucose ¨ n = 6.
43
Balanced Chemical Equations
Inorganic chemistry ¨ conservation of matter:
2H2 + O2 → 2H2O Stoichiometric
Organic chemistry:
coefficients
C3H8 + O2 → CO2 + H2O
c C3H8 + O2 → 3CO2 + H2O
d C3H8 + O2 → 3CO2 + 4H2O
e C3H8 + 5O2 → 3CO2 + 4H2O
Balance O last – why?
44
Chemical Reactions
Stoichiometric factors:
4Fe(s) + 3O2(g) → 2Fe2O3(s)
How many moles O2 required to react
completely with 5 mol Fe?
3 mol O2
= 3.75 mol O2
5 mol Fe ×
4 mol Fe
How many moles Fe2O3 are produced
when 5 mol Fe react completely?
2 mol Fe2O3
= 2.50 mol Fe2O3
5 mol Fe ×
4 mol Fe
45
Limiting Reagent
279 g Fe & 128 g O2 are allowed to react.
Which is the limiting reagent?
2 mol Fe2O3 160 g Fe2O3
1 mol Fe
279 g Fe ×
×
×
55.9 g Fe
4 mol Fe
1 mol Fe2O3
= 400. g Fe2O3 ¨ Fe is limiting.
1 mol O2 2 mol Fe2O3 160 g Fe2O3
×
×
128 g O2 ×
32.0 g O2
3 mol O2
1 mol Fe2O3
= 427 g Fe2O3 ¨ O2 is in excess.
46
Yield
Theoretical yield ¨ maximum yield
allowed by limiting reagent (in grams).
Percentage yield:
actual yield
× 100 % = percentage yield
theoretical yield
Measure of how successfully reaction
proceeds in forward direction.
47
Yield
When 279 g Fe & 128 g O2 are allowed to
react, only 300. g of Fe2O3 are recovered.
What is the percentage yield?
300. g
× 100 % = 75.0 %
400. g
48
Types of Chemical Reaction
1.
2.
3.
4.
Precipitation reactions.
Neutralization reactions.
Gas-forming reactions.
Redox reaction
49
Precipitation Reactions
Formation of insoluble product:
Pb(NO3)2(aq) + 2KI(aq) → PbI2(s) + 2KNO3(aq)
Pb2+(aq) + 2NO3–(aq) + 2K+(aq) + 2I–(aq) →
PbI2(s) + 2K+(aq) + 2NO3–(aq)
Spectator ions
Net ionic reaction: Pb2+(aq) 2I–(aq) → PbI2(s)
50
Neutralization Reactions
Strong acid + strong base → salt + water
HCl(aq) + NaOH(aq) → NaCl(aq) + H2O(l)
H+(aq) + Cl–(aq) + Na+(aq) + OH–(aq) →
Na+(aq) + Cl–(aq) + H2O(l)
Spectator ions
Net ionic reaction: H+(aq) + OH–(aq) → H2O(l)
51
Gas-forming Reactions
Reaction where one of the products is a gas:
Na2CO3(aq) + 2HCl(aq) →
CO2(g) + H2O(l) + 2NaCl(aq)
2Na+(aq) + CO32–(aq) + 2H+(aq) + 2Cl–(aq) →
CO2(g) + H2O(l) + 2Na+(aq) + 2Cl–(aq)
Spectator ions
Net ionic reaction: CO32– (aq) + 2H+ (aq) →
CO2(g) + H2O(l)
52
Redox Reactions
Reactions involving transfer of electrons
and changes in oxidation state.
Fe2+(aq) → Fe3+(aq) + e– ¨ reductant
MnO4–(aq) + 5e– → Mn2+(aq) ¨ oxidant
MnO4–(aq) + 5e– → Mn2+(aq) + 4H2O(l)
MnO4–(aq) + 8H+(aq) + 5e– → Mn2+(aq) + 4H2O(l)
5Fe2+(aq) → 5Fe3+(aq) + 5e–
5Fe2+(aq) + MnO4–(aq) + 8H+(aq) →
Net ionic reaction 5Fe3+(aq) + Mn2+(aq) + 4H2O(l)
53
The Periodic Table
54
Groups of the Periodic Table
Periods are horizontal rows.
Groups (families) are vertical columns.
Metals, nonmetals and metalloids: which
are which?
What are the electrons in an atom’s
outermost shell called?
Valence electrons: primarily responsible for
chemical behavior.
55
56
Groups of the Periodic Table
Group
Group I
Group II
Group VII
Group VIII
Name
Alkali Metals
Alkaline Earth Metals
Halogens
Noble Gases
Valence Config
ns1
ns2
ns2np5
ns2np6
The s block
The d block
The p block
The f block
Representative Elements
Transition Metals
Representative Elements
Rare Earth Metals
ns1–2
(n–1)dxnsy
ns2np1–6
(n–2)fx(n–1)dynsz
57
58
Groups of the Periodic Table
The Octet Rule: What is an octet?
Great stability in ns2np6 electron
configuration.
All noble gases have a complete octet:
• 8 valence electrons.
• One exception: what is it?
59
Periodic Trends: Nuclear Shielding
What is nuclear shielding?
Each filled shell between the
nucleus and valence shell
“shields” the valence
electrons from full effect of
protons.
Effective nuclear charge, Zeff
• Valence electrons feel a
reduction in the positive
elementary charge (Z) in the
nucleus.
e.g. Mg
60
Periodic Trends:
Atomic and Ionic Radius
What properties of an atom determine radius?
Radius is a function of total pull of protons on
valence electrons: what does the trend look like?
More protons to the right within a period means
stronger pull Ö smaller radius:
• Number of shells doesn’t change in a period.
More shells downward within a group means
more shielding Ö larger radius.
61
Periodic Trends:
Ionization Energy
What is an ionization energy?
Amount of energy necessary to remove the
least-tightly bound electron: IEn (n = 1,2,3..)
What is IE related to?
Smaller radii means least-tightly bound
electron is closer to nucleus, held tighter, and
requires more energy to ionize.
Filled valence shells have high IE: reluctant to
relinquish stability – IE2 vs. IE1
62
Periodic Trends:
Electron Affinity
Anyone want to define it?
The energy associated with the addition of an
electron – negative and positive values.
How is electron affinity related to octet stability?
Becomes more negative the closer the atom is to
an octet configuration: what does this mean?
Positive values: energy required for atoms to
accept an electron – anions of these are unstable.
63
Periodic Trends:
Electronegativity
Definition or description?
An atom’s ability to pull electrons to itself when
forming a covalent bond.
Greater attraction means higher electronegativity.
Notice a pattern?
Trend follows same pattern as IE.
A Hobbit mnemonic Ö FONCl BrISCH:
• F > O > N ~ Cl > Br > I > S > C > H
64
Periodic Trends: Example
Which of the following will have a greater
value for phosphorus than for magnesium?
I
II
III
Atomic radius
Ionization energy
Electronegativity
•I only
•I and II only
•II and III only
•I, II, and III
65
Lewis Dot Structures
Anyone remember the rules?
Pay attention to valence electrons.
skeleton structure Ö central atom (lowest χ).
total valence e– count (group #s).
# valence e– pairs = valence e–/2.
make single covalent bonds.
remaining pairs Ö terminal atoms Ö lone pairs (octet
rule!).
6. left over e– Ö central atom.
7. if still < 8 e– then turn lone pair Ö bond pair Ö
multiple bonds (C, N, O, P, S).
1.
2.
3.
4.
5.
66
Lewis Dot Structures:
Formal Charge
Anyone know what it is?
Are atoms sharing valence electrons in the
best way possible (formal charge = 0)?
HCN or HNC? Only one is right even
though both satisfy the octet rule.
1
FC = V – 2 B – L
•
•
•
V = # valence electrons (free atom)
B = # bonding electrons
L = # lone pair electrons
67
Lewis Dot Structure: Examples
Which is the best Lewis structure for
CH2O?
A common question! Count valence
electrons first and rule out any with the
wrong number. If more than one accounts
for the right number, use formal charge.
68
Lewis Dot Structure: Examples
Which is the best Lewis structure for the
nitronium ion, NO2+?
69
Polar Covalent Bonds
Covalent bonding: shared electrons.
Polar covalent: unequal sharing.
A bond is polar if electron density between
the atoms is uneven – a function of what?
Dipole moment, µ = δer.
Polar or not?
δ+ X
δ
–
Y
r
•
CCl4…HF…OCS…NO3–
70
Coordinate Covalent Bonds
Still covalent bonding: shared electrons.
How different from covalent bond?
Here one atom will donate both of the
shared electrons in the bond.
Complex contains a Lewis base (ligand)
and Lewis acid – which is which?
Good example: BF3 and NH3
A
B
71
Ionic Bonds
What are they?
One atom gives a valence electron to the
other and electrostatic interaction holds
atoms together.
Usually between a metal and nonmetal, but
always between two atoms with large
electronegativity difference, ∆χ.
NaCl…KCl…etc.
72
VSEPR Theory
Basic premise: electron pairs on a central
atom try to move apart as far as possible.
Electron group geometry vs. molecular
geometry?
•
•
Electron group geometry : electron groups
(bonding and nonbonding) on center atom
determine geometric family.
Molecular geometry: bonding pairs around
center atom determine shape, more specific than
electron groups.
Moral: determine family, then shape.
73
VSEPR Theory: The Families
Electron Groups
Geometric Family
2
Linear
3
Trigonal Planar
4
Tetrahedral
5
Trigonal Bipyramidal
6
Octahedral
74
VSEPR Theory:
Shape & Lone Pairs
75
76
77
78
VSEPR Theory: Examples
Determine the geometric family and predict
the shape of each of the following molecules:
• H2O
• BrF3
• XeOF4
• NH3
• NH4+
• BF3
79
VSEPR Theory: Examples
Draw/think about Lewis structures!
Count electron groups around center atom
for family.
Count bonding groups around center atom to
narrow down family into molecular shape.
• multiple bond counts as one group.
Don’t memorize all of this – visualize!
• except geometry names (familiar?).
80
Hybridization
How do you determine hybridization around a
central atom?
Determine number of electron pairs surrounding
central atom.
Each pair needs an orbital:
•
•
•
•
•
•
s fills first (× 1), then p (× 3), then d (× 5).
2 electron groups ¨
sp hybridized,
3 electron groups ¨
sp2 hybridized,
4 electron groups ¨
sp3 hybridized,
5 electron groups ¨
sp3d hybridized,
6 electron groups ¨
sp3d2 hybridized.
81
Hybridization: Example
Determine the hybridization of the central
atom in each of the following molecules:
• H2O
• BrF3
• XeOF4
• NH3
• NH4+
• BF3
82
Polar Molecules?
CCl4…HF…OCS…NO3– ¨ Polar or not?
83
Solids and Intermolecular
Forces
Differentiate between ionic, network, and
metallic solids.
Ionic: electrostatic attractions (NaCl, CaF2).
Network: lattice of covalent bonds (diamond,
quartz).
Metallic: covalent lattice of nuclei and inner
electrons surrounded by cloud of electrons.
• What are conduction electrons?
84
Solids and Intermolecular
Forces
Intermolecular forces are relatively weak
interactions between neutral/charged molecules.
Four major types: what are they?
• Ion-dipole: polar molecules attracted to ions.
• Dipole-dipole: between positive and negative end of
two polar molecules.
• Dipole-induced dipole: permanent dipole induces
dipole in non-polar molecule.
• London dispersion forces: instantaneous dipole
induces a dipole in neighboring non-polar molecule
(also Van der Waals forces).
85
85
Solids and Intermolecular
Forces: Hydrogen Bonding
When does it occur?
Only between H attached to an N, O, F and the
lone pair of another N, O, or F atom.
This is major! N, O, and F only – not C or any
other atom!!
Why does it occur?
Very small hydrogen (low χ) next to fairly small
atom (very high χ) Ö intense partial positive
charge, δ+ latches onto lone pair of electrons with
high δ–.
86
Phase Transitions
Closely related to what property of molecules?
Temperature – measure of internal kinetic
energy.
States or phases: name them!
Solids, liquids, gases all differ in kinetic
energy and intermolecular forces.
Phase change caused by overcoming or
strengthening intermolecular forces – boiling
point, vapor pressure, etc.
87
Phase Transitions: Summary
Evaporation, condensation, fusion,
crystallization, sublimation, deposition:
define!
Evaporation: liquid to gas.
Condensation: gas to liquid.
Fusion (melting): solid to liquid.
Crystallization (freezing): liquid to solid.
Sublimation: solid to gas.
Deposition: gas to solid.
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Phase Transitions: Summary
Gas ¨ liquid ¨ solid: what happens to heat,
KE, and entropy?
Heat released, internal KE decreases,
entropy decreases.
Solid ¨ liquid ¨ gas: what happens to heat,
KE, and entropy?
Heat absorbed, internal KE increases,
entropy increases.
Know the conceptual trends!
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Heats of Phase Changes
A change of phase depends on what two things?
Type of substance and amount of substance.
Heat of transition: ∆H – what does it represent?
∆H is amount of energy required to complete a
phase transition @ const. pressure.
Equation: q = n∆H …what is n? signs on terms?
Positive ∆H and q Ö heat absorbed Ö endothermic
Negative ∆H and q Ö heat released Ö exothermic.
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Calorimetry
Absorption or release of heat: what are two
possible consequences?
Temperature change or phase change, but not
both at same time!
Equation for amount of heat absorbed/released?
q = mc∆T … define the terms!
What is specific heat?
Intrinsic property…resistance to temperature
change:
• High c means small temperature change, holds
absorbed heat better.
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Calorimetry: Example
Equal amounts of heat are absorbed by 10-g
solid samples of four different metals:
aluminum, lead, tin, and iron. Of the four,
which will exhibit the smallest temp change?
• Aluminum (c = 0.90 Jg–1K–1)
• Lead (c = 0.13 Jg–1K–1)
• Tin (c = 0.23 Jg–1K–1)
• Iron (c = 0.45 Jg–1K–1)
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Phase Transition Diagrams
What is plotted on one? What does it show?
Note: during a phase transition, temperature of
substance does not change – sound familiar?
Pressure vs. temperature…shows how phases are
determined by these properties.
Some terms: triple point, critical point.
Triple point: temp. and pressure at which all
phases exist simultaneously in equilibrium.
Critical point: beyond this point, substance has
properties of gas and liquid (high density, low
viscosity)…supercritical fluid.
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Phase Transition Diagrams
94
Phase Diagrams: Water & CO2
One difference between water and other
substances – what?
Let’s draw and label water and carbon
dioxide phase diagrams.
For water, an increase in pressure at constant
temperature can favor liquid phase not the
solid as usual…ice skating!
95
Phase Diagrams: Water & CO2
96
Gases and Kinetic-Molecular
Theory
What is the purpose of the theory?
Sets the conditions for an ideal gas.
Normally, real gases operate like ideal gases,
so these conditions can be applied to
understand gas behavior.
A good example of this application: the ideal
gas law.
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Assumptions of the Theory
First assumption?
Gas molecules take up essentially no volume,
compared to the average spacing between them.
Second assumption?
Constant motion, constant speeds, and random
collisions:
•
•
•
Pressure Ö average force exerted per unit area,
Elasticity Ö KEi = KEf
No intermolecular forces.
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Assumptions of the Theory
Third assumption?
Direct proportionality between average
kinetic energy of gas molecules and
temperature in Kelvin degrees: KE ∝ T
Note that this is average kinetic energy, not
average speed – speed involves additional
factors, as we will see.
99
Ideal Gas Law: Units
What are the units of volume, temperature,
and pressure that are used?
1 cm3 = 1 mL…1 m3 = 1000 L.
Kelvin = Celsius + 273.
1atm = 760 torr = 760 mmHg.
Standard temp. and pressure…?
273 K and 1 atm.
100
Ideal Gas Law
Describes behavior of gases following
kinetic-molecular theory.
What is the equation?
PV = nRT…define the terms.
Gas constant: R = 0.0821 Latm mol–1K–1
Derivations of other laws from the ideal-gas
law – three proportionalities, two have names.
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Other P-V-T Gas Laws
Volume proportional to temperature at
constant pressure – what law?
Charles’ Law Ö V1/T1 = V2/T2
Pressure inversely proportional to volume at
constant temperature – what law?
Boyle’s Law Ö P1V1 = P2V2
Pressure proportional to temperature at
constant volume Ö P1/T1 = P2/T2
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Other P-V-T Gas Laws
Suppose you hold n constant?
Combined gas law Ö P1V1/T1 = P2V2/T2
Avogadro’s Law – what did he propose?
If two equal-volume containers hold gas at the
same pressure and temp., then they contain the
same number of particles (regardless of identity).
What is the consequence of this law?
Standard molar volume:
22.4 L @ 273 K and 1 atm
103
Ideal-Gas Law: Example
How many atoms of helium are present in 11.2
liters of the gas at a pressure of 1 atm and
temperature of 273 K?
• 3.01 × 1023
• 6.02 × 1023
• 1.20 × 1023
• Cannot be determined from information
given.
104
Dalton’s Law of Partial
Pressures
Total pressure of sample of 3 different gases
is due to collisions of all types with container
wall. What does this say for the pressure of
each type of gas?
Dalton’s Law of Partial Pressures;
• P = Pa + Pb + Pc
Corollary: Pa = XaP, where Xa is mole fraction
of gas “a”.
105
Dalton’s Law: Example
A mixture of neon and nitrogen contains 0.5
mol of Ne and 2 mol of N2(g). If total
pressure is 20 atm, what is partial pressure of
neon?
106
Graham’s Law of Effusion
What is effusion?
Escape of a gas molecule through a tiny hole
(comparable in size to the molecule) into an
evacuated region.
Our concerns with Graham’s Law:
• What factors determine speed of effusion?
• What equations will help determine relative rates
of effusion for two gases?
107
Graham’s Law – The Conditions
Temperature in container of gas molecules is
a constant.
Average kinetic energies are equal.
Molar masses of gases may be different.
Given what we know about kinetic energy,
mass must play a role in average speed
• KE = 12 mv2
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Graham’s Law – Formulas
The usable formula:
Rate of Gas A √ Molar Mass Gas B
=
Rate of Gas B √ Molar Mass Gas A
Notice the relationships…
The rate of effusion and molar mass are
inverses, so the faster a gas effuses, the smaller
its molar mass must be.
109
Graham’s Law – Remember…
Molecules of different gases at same temp.
have same average kinetic energy.
Average speed takes into account molar mass.
As temp. of sample is increased, the average
speed will increase:
• Cannot account for wide range of speeds in
individual molecules.
110
Graham’s Law – Some
Examples
A container holds methane and sulfur dioxide
at temp. of 227 °C. Which of following best
describes the relationship between their
speeds, where vm represents methane and vs
sulfur dioxide?
• vs = 16vm
• vs = 2 vm
• vm = 2 vs
• vm = 16vs
111
Graham’s Law – Some
Examples
Chamber A holds a mix of four gases, 1 mol of
each. A tiny hole is made in the side and the
gases are allowed to effuse into an empty
chamber. When 2 mol of gas have escaped,
which gas will have the greatest mole fraction
in Chamber A?
• Cl2
• F2
• N2
• CO2
112
Approaching Ideal Gas
Behavior
Under normal conditions, real gases behave
like ideal gases, so the assumptions of kineticmolecular theory apply:
• molecules are so small compared with surrounding
space that they essentially occupy no volume.
• molecules experience no intermolecular forces.
113
Approaching Ideal Gas
Behavior
But these assumptions fail under certain
conditions, making the real gas not ideal –
name them!
High pressures.
Low temperatures.
Strong intermolecular forces (esp. H-bonds).
High MW and diatomic gases behave less
ideally than low MW and monatomic gases.
114
Ideal Gas Behavior – Example
Of the following, which gas would likely
deviate the most from ideal behavior at high
pressure and low temperature?
• He (g)
• H2 (g)
• O2 (g)
• H2O (g)
115