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MCAT Chemistry Equation Sheet
ORBITALS AND ELECTRONS
1.
molecules are very small compared to the
INTERMOLECULAR FORCES
distance b/w them
Quantum numbers descriptions
2.
molecules are continuously moving
D
F
:
ISPERSION
ORCES
Describe the attraction between the negatively
3.
pressure of the gas – collisions of the
Quantum
Description
Possible
charged electron cloud of one molecule and the
number
values
molecules with container walls
positively charged nuclei of neighbouring molecules
Principal quantum
energy level
n=1, 2, 3….
D
F
:
IPOLAR
ORCES
4.
molecules do not experience intermolecular
number (n)
Describe the attraction between the negatively
Angular
orbital shape (s,
l = 0, to …n-
forces
charged end of a polar molecule and the positively
momentum
p, d, f)
1
charged ends of neighbouring polar molecules
∝ T
5.
KE
quantum number
ave
H
B
:
YDROGEN
ONDING
PV = nRT
(l)
Involves lone pairs of electrons on an
Ideal-gas law:
Magnetic quantum
orbital
m = -l to +l
electronegative atom of one molecule and a polar
P
V
P
V
Combined gas law:
number (m)
orientation (p
,
=
bond to hydrogen in another molecule, they are
x
1
1
2
2
p
, p
)
T
T
confined to molecules that contain O, N, and F
y
z
1
2
Spin quantum
describes spin of
m
= + ½ or -
atoms.
s
V
V
number (m
)
electron
½
Charles’ law:
=
P = const
P
:
OLARIZABILITY
s
1
2
The ease with which the electron clouds are
T
T
1
2
distorted
Each electron has a unique set of quantum
= P
Boyle’s law:
P
V
V
T = const
M
S
:
OLECULAR
OLID
1
1
2
2
numbers.
Molecules in molecular solids are held in place by
P
P
the types of forces: dispersion forces, dipolar
No ones’ Law:
=
V = const
ELECTRONIC CONFIGURATION
1
2
interactions, and/or hydrogen bonds
T
T
1
2
M
S
:
ETALLIC
OLID
Electron configuration: describes the location of all
STP – standard temperature (0°C or 273.15 K) and
Atoms in metallic solids are held in place by
of the electrons in an element. e.g. Carbon =
delocalised bonding
pressure (1 atm)
2
2
2
1s
2s
2p
N
S
:
ETWORK
OLID
Contains an array of covalent bonds linking every
1 mol of ideal gas occupies V = 22.4 L
Heisenberg Uncertainty Principle: the
atom to its neighbours
standard conditions - 25°C and 1 atm
position and momentum of a particle cannot
I
S
:
ONIC
OLID
both be exactly known at the same time.
Contains cations and anions, attracted to one
Dalton’s law of partial pressure (mixture of the gases)
Pauli exclusion principle: no two electrons
another by coulombic interactions
+ p
+K+ p
P= p
in an atom can have the same set of four
A
B
N
quantum numbers (n, l, m, m
) which means
SOLUTIONS
s
χ
=
⋅ P
that each orbital with quantum numbers (n, l,
p
A
A
m) can hold at most two electrons with
opposite spins.
n
N
moles of solute/volume of
χ
=
=
A
A
molarity (M)
solution. M=n/V
A
n
N
Hund’s rule: when electrons added to
molality (m)
moles of solute/kg of solvent
total
total
orbitals of equal energy, a single electron
moles of solute/total moles
mole fraction (χ)
G
RAHAM
S LAW OF EFFUSION
enters each orbital before a second electron
mass of solute x 100/ total mass
with opposite spin enters any orbital. The
mass percent
1
v
m
of solution
=
spins remain parallel if possible. e.g.
=
2
A
B
KE
m
v
6
parts per million
mass of solute x 10
/total mass
A
A
A
Nitrogen
2
v
m
(ppm)
of solution
↑↓
↑↓
B
A
N =
Raoult’s Law (distillation)
1s
2s
2p
2p
= T
P =
x
y
= KE
KE ∝ T
o
at
T
b/c
, but
X
P
KE
2p
z
A
A
A
A
B
A
B
P
Where
= partial pressure of A in solution
≠ v
= T
A
v
at
T
Aufbau Principle: dictates the order in
X
= mole fraction of A in the liquid
A
B
A
B
A
which orbitals fill. Some exceptions occur in
0
P
= vapour pressure of pure A
What leads to the gas “ideality”: high T & low P & lower
A
the transition elements.
1s
molecular weight or small size of gas molecules
2s 2p
Colligative properties (melting/boiling points
Real gases:
3s 3p 3d
etc)
4s 4p 4d 4f
have intermolecular attractions (non-elastic
Freezing point depression: salt on the sidewalk in winter
5s 5p 5d 5f
collisions) called Van der Waals forces
lowers the freezing point of H
O to prevent the water
6s 6p 6d 6f
2
from freezing
contain molecules that have volume (or
∆T
THE GAS PHASE
= k
mi
f
f
measurable size)
Boiling point elevation: salt in pasta water increases the
boiling point of H
O so that the water boils hotter (and
2
2
U
P
:
n
NITS OF
RESSURE
(
)
your pasta cooks more quickly).
+ a
⎟ ⋅ V
− nb
= nRT
P
∆T
1atm = 760 mmHg = 760 torr = 101.325 kPa =
= k
mi
real
real
2
b
b
V
1.01325 barr
Osmotic pressure: increase in pressure due to a solvent
crossing a membrane into a more concentrated solution
ΠV=nRT
I
DEAL GAS POSTULATES
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MCAT Chemistry Equation Sheet
ORBITALS AND ELECTRONS
1.
molecules are very small compared to the
INTERMOLECULAR FORCES
distance b/w them
Quantum numbers descriptions
2.
molecules are continuously moving
D
F
:
ISPERSION
ORCES
Describe the attraction between the negatively
3.
pressure of the gas – collisions of the
Quantum
Description
Possible
charged electron cloud of one molecule and the
number
values
molecules with container walls
positively charged nuclei of neighbouring molecules
Principal quantum
energy level
n=1, 2, 3….
D
F
:
IPOLAR
ORCES
4.
molecules do not experience intermolecular
number (n)
Describe the attraction between the negatively
Angular
orbital shape (s,
l = 0, to …n-
forces
charged end of a polar molecule and the positively
momentum
p, d, f)
1
charged ends of neighbouring polar molecules
∝ T
5.
KE
quantum number
ave
H
B
:
YDROGEN
ONDING
PV = nRT
(l)
Involves lone pairs of electrons on an
Ideal-gas law:
Magnetic quantum
orbital
m = -l to +l
electronegative atom of one molecule and a polar
P
V
P
V
Combined gas law:
number (m)
orientation (p
,
=
bond to hydrogen in another molecule, they are
x
1
1
2
2
p
, p
)
T
T
confined to molecules that contain O, N, and F
y
z
1
2
Spin quantum
describes spin of
m
= + ½ or -
atoms.
s
V
V
number (m
)
electron
½
Charles’ law:
=
P = const
P
:
OLARIZABILITY
s
1
2
The ease with which the electron clouds are
T
T
1
2
distorted
Each electron has a unique set of quantum
= P
Boyle’s law:
P
V
V
T = const
M
S
:
OLECULAR
OLID
1
1
2
2
numbers.
Molecules in molecular solids are held in place by
P
P
the types of forces: dispersion forces, dipolar
No ones’ Law:
=
V = const
ELECTRONIC CONFIGURATION
1
2
interactions, and/or hydrogen bonds
T
T
1
2
M
S
:
ETALLIC
OLID
Electron configuration: describes the location of all
STP – standard temperature (0°C or 273.15 K) and
Atoms in metallic solids are held in place by
of the electrons in an element. e.g. Carbon =
delocalised bonding
pressure (1 atm)
2
2
2
1s
2s
2p
N
S
:
ETWORK
OLID
Contains an array of covalent bonds linking every
1 mol of ideal gas occupies V = 22.4 L
Heisenberg Uncertainty Principle: the
atom to its neighbours
standard conditions - 25°C and 1 atm
position and momentum of a particle cannot
I
S
:
ONIC
OLID
both be exactly known at the same time.
Contains cations and anions, attracted to one
Dalton’s law of partial pressure (mixture of the gases)
Pauli exclusion principle: no two electrons
another by coulombic interactions
+ p
+K+ p
P= p
in an atom can have the same set of four
A
B
N
quantum numbers (n, l, m, m
) which means
SOLUTIONS
s
χ
=
⋅ P
that each orbital with quantum numbers (n, l,
p
A
A
m) can hold at most two electrons with
opposite spins.
n
N
moles of solute/volume of
χ
=
=
A
A
molarity (M)
solution. M=n/V
A
n
N
Hund’s rule: when electrons added to
molality (m)
moles of solute/kg of solvent
total
total
orbitals of equal energy, a single electron
moles of solute/total moles
mole fraction (χ)
G
RAHAM
S LAW OF EFFUSION
enters each orbital before a second electron
mass of solute x 100/ total mass
with opposite spin enters any orbital. The
mass percent
1
v
m
of solution
=
spins remain parallel if possible. e.g.
=
2
A
B
KE
m
v
6
parts per million
mass of solute x 10
/total mass
A
A
A
Nitrogen
2
v
m
(ppm)
of solution
↑↓
↑↓
B
A
N =
Raoult’s Law (distillation)
1s
2s
2p
2p
= T
P =
x
y
= KE
KE ∝ T
o
at
T
b/c
, but
X
P
KE
2p
z
A
A
A
A
B
A
B
P
Where
= partial pressure of A in solution
≠ v
= T
A
v
at
T
Aufbau Principle: dictates the order in
X
= mole fraction of A in the liquid
A
B
A
B
A
which orbitals fill. Some exceptions occur in
0
P
= vapour pressure of pure A
What leads to the gas “ideality”: high T & low P & lower
A
the transition elements.
1s
molecular weight or small size of gas molecules
2s 2p
Colligative properties (melting/boiling points
Real gases:
3s 3p 3d
etc)
4s 4p 4d 4f
have intermolecular attractions (non-elastic
Freezing point depression: salt on the sidewalk in winter
5s 5p 5d 5f
collisions) called Van der Waals forces
lowers the freezing point of H
O to prevent the water
6s 6p 6d 6f
2
from freezing
contain molecules that have volume (or
∆T
THE GAS PHASE
= k
mi
f
f
measurable size)
Boiling point elevation: salt in pasta water increases the
boiling point of H
O so that the water boils hotter (and
2
2
U
P
:
n
NITS OF
RESSURE
(
)
your pasta cooks more quickly).
+ a
⎟ ⋅ V
− nb
= nRT
P
∆T
1atm = 760 mmHg = 760 torr = 101.325 kPa =
= k
mi
real
real
2
b
b
V
1.01325 barr
Osmotic pressure: increase in pressure due to a solvent
crossing a membrane into a more concentrated solution
ΠV=nRT
I
DEAL GAS POSTULATES
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ACID-BASE EQUILIBRIA
Chemical Reaction: some bonds break, and new
ln
2
=
[A] = 0.5[A]
,
t
bonds form
0
1
2 /
k
S
F
:
TATE
UNCTION
S
-O
R
E
:
A property that depends only on the state of the
A
A
:
ECOND
RDER
ATE
XPRESSION
RRHENIUS
CID
2
Rate = k[A]
, this can be converted to
system
Anything that produces hydrogen ions in aqueous
P
F
:
solution
ATH
UNCTION
1
1
=
kt
Arrhenius Base:
A property that depends on how a change takes
[A]
[A]
place
Anything that produces hydroxide ions in aqueous
0
Molar Heat Capacity:
solution
B
:
IMOLECULAR ELEMENTARY REACTION
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A + B → products
The amount of heat needed to raise the temperature
B
-L
A
:
RØNSTED
OWRY
CID
Elementary rate = k[A][B]
of 1 mol of substance by 1 Kelvin (1K)
A species that donates a proton is an acid
U
:
NIMOLECULAR ELEMENTARY REACTION
B
-L
B
:
C → products
W
(
):
RØNSTED
OWRY
ASE
Elementary rate = k[C]
ORK
W
A species that accepts a proton is a base
Energy used to move an object against an opposing
F
S
R
-D
:
IRST
TEP IS
ATE
ETERMINING
Amphiprotic Species: a chemical species that can
force, w= Fd
The predicted rate law for the overall reaction is the
both donate and accept protons
F
L
T
:
rate expression for that first step
IRST
AW OF
HERMODYNAMICS
Lewis Acid:
A
E
(E
):
E
= q
+ w
CTIVATION
NERGY
sys
sys
sys
A
Anything that accepts a pair of electrons
Energy barrier, the minimum energy that must be
Exothermic Process:
Lewis Base:
supplied before the reaction can occur
If the chemicals release heat, this heat gain raises
Anything that donates a pair of electrons
Activated Complex: the molecular arrangement at
the temperature of the surroundings
W
E
C
(K
):
ATER
QUILIBRIUM
ONSTANT
the point of highest energy along the energy level
E
P
:
W
NDOTHERMIC
ROCESS
−14
+
K
= [H
O
][OH
] = 1.00×10
(at 298 K)
diagram
If the chemicals absorb heat, this heat loss lowers
w
3
S
A
:
TRONG
CIDS
the temperature of the surroundings
Acids that donate protons to water molecules
∆T, q = nC
q
= C
T
CHEMICAL EQUILIBRIUM
calorimeter
cal
quantitatively
E
:
NTHALPY
Strong Base:
A thermodynamic quantity whose change equals the
A substance that generates hydroxide ions
heat flow at constant pressure,
E
C
:
QUILIBRIUM
ONSTANT
quantitatively in aqueous solution.
∆H = ∆E + ∆(PV)
[ ] [ ]
d
e
H S
:
D
E
P
CALES
eq
eq
=
o
S
E
F
:
pH = −log[H
] pOH = −log[OH
= −log K
K
+
TANDARD
NTHALPY OF
ORMATION
H
O
] pK
[ ] [ ]
eq
f
3
a
a
a
b
A
B
= −log K
pK
pH + pOH = 14.00 K
K
= K
pK
+
eq
eq
Enthalpy change accompanying the formation of
b
b
a
b
w
a
pK
= 14.00
one mole of a chemical substance from pure
K
applied only at equilibrium, K
is independent of
b
eq
eq
elements in their most stable forms under standard
W
A
:
initial conditions, K
is related to the stoichiometry.
EAK
CID
eq
conditions
Acid that reaches equilibrium when only a small
P
L
S
:
URE
IQUID AND
OLID
H
’ L
:
ESS
AW
fraction of its molecules transfer protons to water
The concentrations of pure liquids or solids are
The enthalpy change for any overall process is
W
B
:
EAK
ASE
always equal to their standard concentrations,
equal to the sum of enthalpy changes for any set of
Generates hydroxide ions by accepting protons from
therefore division by standard concentration results
steps that leads from the reactants to the products
water but reaches equilibrium when only a fraction
in a value of 1
M
H
S
:
of its molecules have done so
OLAR
EAT OF
OLUTION
L
K
:
ARGE
EQ
Measures net energy flow that occurs as substance
A
A
E
:
PPLICATIONS OF
QUEOUS
QUILIBRIA
Indicates that the reaction goes virtually to
dissolves
B
S
:
completion
UFFER
OLUTION
M
H
V
:
OLAR
EAT OF
APORIZATION
Contains both a weak acid and its conjugate base
L
C
P
:
E
HÂTELIER
S
RINCIPLE
The heat needed to vaporize one mole of a
as major species in solution,
When a change is imposed on a system at
[ ]
substance at its normal boiling point
equilibrium, the system will react in the direction that
A
M
H
F
:
⎜ ⎜
⎟ ⎟
=
+
OLAR
EAT OF
USION
initial
pH
p
K
log
reduces the amount of change.
[ ]
Heat needed to melt one mole of a substance at its
a
H
A
T
:
EMPERATURE
initial
normal melting point
The only variable that causes a change in the value
S
:
B
C
:
UBLIMATION
UFFER
APACITY
of K
an increase in temperature always shifts the
+
A phase change in which a solid converts directly to
eq,
The amount of added H
O
or OH
the buffer
3
equilibrium position in the endothermic direction.
a vapour without passing through the liquid phase,
solution can tolerate without exceeding a specified
∆E
= ∆H
− RT
pH range.
vap
vap
vap
THERMODYNAMICS
CHEMICAL KINETICS
S
L
T
:
ECOND
AW OF
HERMODYNAMICS
C
S
:
LOSED
YSTEM
Any spontaneous process increases the disorder of
Exchanges energy but not matter with its
the universe
R
M
:
EACTION
ECHANISM
surroundings
E
:
NTROPY
The exact molecular pathway that starting materials
I
S
:
SOLATED
YSTEM
The state function that provides a quantitative
follow on their way to becoming products
Exchanges neither matter nor energy with the
measure of disorder and is symbolized S,
R
-D
S
:
ATE
ETERMINING
TEP
surroundings
q
The slowest elementary step in a mechanism
=
T
S
V
:
TATE
ARIABLES
S
F
-O
R
L
:
T
IRST
RDER
ATE
AW
Conditions that must be specified to establish the
Rate = k[A], where A is a reactant in the overall
state of a system, pressure (P), volume (V),
Entropy Change of the Universe:
reaction, this can be converted to
temperature (T), and amounts of substances (n)
Total entropy change,
∆S
= ∆S
+ ∆S
P
C
S
:
[A]
HYSICAL
HANGE OF
TATE
⎜ ⎜
⎟ ⎟
=
universe
system
surroundings
0
ln
kt
Some of the state variables changes, but the
R
E
:
EACTION
NTROPIES
[A]
chemical composition of the system stays the same
=
o
o
o
S
coeff
S
coeff
S
ST
H
-L
(
), 1
O
:
ALF
IFE
T
RDER
C
C
S
:
reaction
p
r
1/2
HEMICAL
HANGE OF
TATE
When half the original concentration has been
The amounts of reactants and products change
consumed,
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R
E
:
ELECTROCHEMISTRY
EACTION
NTHALPIES
=
o
o
o
H
coeff
H
coeff
H
reaction
p
f
r
f
Oxidation – loss of electrons from a substance and an increase in oxidation
Free Energy (G):
state
A state function whose change for the system predicts spontaneity and is
defined by, Free energy
Reduction – gain of electrons by a substance and a decrease in oxidation
G = H
TS
state
C
F
E
:
HANGE IN
REE
NERGY
Reducing agent – a species that loses electrons and is oxidized
∆G
= ∆H
− T∆S
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sys
sys
sys
∆G
is negative for all spontaneous processes under conditions of constant
Oxidizing agent – a species that gains electrons and is reduced
sys
temperature and pressure.
Anode – electrode where oxidation occurs, half-reaction with the more
o
S
M
F
E
F
:
G
TANDARD
OLAR
REE
NERGY OF
ORMATION
f
negative reduction potential occurs at the anode
The change of free energy when one mole of that substance is formed from
Cathode – electrode where reduction occurs, half-reaction with the more
elements in their standard
positive reduction potential occurs at the cathode
=
o
o
o
G
coeff
G
coeff
G
states,
reaction
p
f
r
f
Cell potential:
E
C
N
-S
C
:
NTROPY
HANGE
ON
TANDARD
ONDITIONS
= E
− E
o
o
o
Concentrations can be expressed in terms of the standard entropy change and
E
cell
cathode
anode
Q:
=
o
S
S
R
ln
Q
,
o
E
:
Gibbs free energy and
reaction
reaction
cell
∆G = −nFE
=
o
o
G
G
R
Tln
Q
cell
reaction
reaction
E
and K
:
Relationship between
I
T
S
:
NFLUENCE OF
EMPERATURE ON
PONTANEITY
cell
eq
RT
°
=
=
E
ln
K
o
o
o
G
H
T
S
cell
eq
nF
T
∆H
∆G˚high
∆H˚ low
Spontaneit
∆S˚
E
as a function of concentrations
˚
T
T
y
cell
RT
+
All T
=
°
E
E
ln
Q
+
+
+
No T
cell
cell
nF
+
+
+
High T
+
Low T
Electrolytic cell – uses electricity to produce an non-spontaneous reaction
Phase Diagram for Water
C
1
mol
e
=
×
×
number
of
mol
e
current
time(s)
s
96,485C
For water
Negative slope for
solid-liquid boundary
liquid
Supercritical fluid
melting
(high density & low
crystallization
viscosity)
Critical point
soli
d
1 atm
vaporization
condensation
Triple point
sublimation
deposition
ga
T
T
Temperature
b
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