Nuclear and Atomic Chemistry Electron Configurations

Radioactive Decay Stoichiometry / Lewis Structures

Z = # protons = atomic number, N = # neutrons,A = Z + N = mass number

Periodic Trends & Bonding Molecular Geometry (VSEPR theory)

electronegativity of some common atoms: F > O > (N ≈ Cl) > Br > (I ≈ S ≈ C) > H

intermolecular forces (D = dipole, I = induced, i = instantaneous): ion–ion > ion–D > D–D (incl. H-bonds) > D–ID > iD–ID (London)

MCAT G-Chem Formula Sheet

© 2001 by T

he Princeton R

eview, Inc.

Unauthorized reproduction prohibited.

7s

6s

5s

4s

3s

2s

1s

7p

6p

5p

4p

3p

2p

6d

5d

4d

3d

5f

4f

e quantum numbers: ,

2, 1, ,

[

, (

or

in subshell ,max # of electrons

in energy level ,max #

s

s

−

= = −= ↔ = ↔= ↔ = ↔= − − − −

= + −

= +

n m m

n n

s p

d f

m

m

n

, ,

, ,

, ,

, ]

, ( ), ),

l

K l K

l l

l l

l l K l l

ll

l

l

1 0 1

0 1

2 3

1 1

4 2

12

12

of electrons of electrons = 2 2n

Decay Description N A∆ ∆ ∆Zeject He

n p ep n e

EC p e nX* X+

α αββ

γ γ

= − − −→ + + −→ + − ++ → − +

→

− −

+ +

−

24 2 2 4

1 1 01 1 01 1 0

0 0 0

Atomic Radius Electron Affinity

Ionization Energy

increases

more

negativeincreases

Electronegativity

increases

Acidity Basicity

increases

increases

# ;

%

( )

' ((#

molesmass in grams

MW molarity:

moles of soluteL of solution

% composition by mass of Xmass of X

mass of molecule

formal charge:

(# of valence e s), # of bonding e 's), of lone-pair e 's)

= =

= ×

= − += ==

− −

−

M

FC V B LV BL

100

12

Linear Trigonalplanar

Tetrahedral Trigonalbipyramid Octahedral

Bent See-saw Squarepyramid

Trigonalpyramid

T-shaped Squareplanar

Bent

Geometric Family

0

1

2

# lonepairs oncentralatom

shape =

shape =

shape = geometry

Constants or equations in a shaded

box do not need to be mem

orized.

Avogadro' s number:

amu (u) gram

1 u g kg

u, u

# protons, # neutrons

mass defect:

nuclear binding energy:

eV J, 1 MeV eV

A

A

p n

p n nucleus

B MeV

1 u

photon

N

N

m m

Z N

m Zm Nm m

E m

E hf

= ×=

= × = ×= =

= == + −

= ×

= × ==

− −

−

6 02 10

1

1 66 10 1 66 10

1 0073 1 0087

1 1 6 10 10

23

24 27

931

19 6

.

. .

. .

( )

( )

.

∆

∆

==

= −

hc

E nZn

λ

electron energy levels: eV) for any 1-electron (Bohr) atom

2

2 13 6( .

Gases Colligative PropertiesSTP: T = 0 °C = 273 K, P = 1 atm = 760 torr = 760 mmHgAvogadro’s law:

Boyle’s law: V ∝ 1/P (at constant T )Charles’ law: V ∝ T (at constant P )Combined: P

1V

1/T

1 = P

2V

2/T

2BP elevation: ∆T

b = k

bim

Ideal-Gas law: PV = nRT FP depression: ∆Tf = –k

fim

Dalton’s law of partial pressures: P = Σ pi

Graham’s law of effusion:Raoult’s law:vapor pressure depression:osmotic pressure: Π = iMRT

KineticsThermochemistry

T (in K) = T°C + 273, 1 cal ≈ 4.2 J, q = heat

q = mc ∆T = C ∆T (if no phase change)q = n ∆H

phase change (∆T = 0 during phase change)

enthalpy change: ∆H = heat of rxn at const P∆H < 0 ⇔ exothermic, ∆H > 0 ⇔ endothermicstandard state: one most stable at 25°C, 1 atm

EquilibriumLaws of Thermodynamics (E = energy, S = entropy):

1) Euniverse is constant. ∆Esystem = q + W. 2) Spontaneous rxn ⇒ ∆S universe > 0 3) S = 0 for pure crystal at T = 0 K

Gibbs Free Energy: ∆G = ∆H – T∆S [const. T ]∆G < 0 ⇔ spontaneous∆G = 0 ⇔ at equilibrium∆G > 0 ⇔ reverse rxn is spontaneous

∆G o ≈ –RT ln K ≈ –2.3RT log K ≈ (–5.7 kJ

mol ) log K

Redox and ElectrochemistryRules for determining oxidation state (OS ):* 1) sum of OS ’s = 0 in neutral molecule; sum of OS ’s = charge on ion 2) Group 1 metals: OS = +1;

Group 2 metals: OS = +2Acids and Bases 3) OS of F = –1pH = –log [H+] = –log [H3O

+] 4) OS of H = +1pOH = –log [–OH] 5) OS of O = –2Kw = [H+][–OH] = 1 × 10–14 at 25 °C 6) OS of halogens = –1; OS of O family = –2pH + pOH = 14 at 25 °C If one rule contradicts another, rule higher in

list takes precedence. [*These rules work 99% of the time.]

F = faraday ≈ 96,500 C/mol e–

∆G = –nFEcell

Ecell > 0 ⇔ spontaneous Ecell < 0 ⇔ reverse rxn is spontaneous

Nernst equation:

Faraday’s Law of Electrolysis: The amount of chemical change is proportional to the amount of electricity that flows through the cell.

V n∝V nat STP L)= ( .22 4

v vmm

mm2 1

1

2

1

2, ,rms rmsrate of effusion of gas 2rate of effusion of gas 1

= ⇒ =∆P PA A A

oX= − −( )1P PA A A

oX=

mole fraction: Xmoles of Stotal molesS =

molality: moles of solute

kg of solvent

normality: equivalents (eq)

L of solution

m

N

=

=

∆ ∆ ∆H n H n Hrxno

f,productso

f,reactantso= ∑ − ∑

for generic balanced reaction A B C D,

equilibrium constant: C] D]

A] B]

(gas rxns use partial pressures in expression)

is a constant at a given temperature.equilibrium favors reactantsequilibrium favors products

reaction quotient: C] D]

A] B]

Law of Mass Action (Le Châtelier's principle):

rxn proceeds forwardrxn at equilibriumrxn proceeds in reverse

eqat eq at eq

at eq at eq

eq

eq

eq

eq

eq

eq

eq

a b c d

K

K

KKK

Q

Q KQ KQ K

c d

a b

c d

a b

+ +

=

< ⇔> ⇔

=

< ⇔= ⇔> ⇔

[ [

[ [

[ [

[ [

11

excludingpure solidsand liquids

concentration ratereactant]time

or [product]

time

reaction ratecoeff

reactant]time

or coeff

[product]time

rate law for step: rate reactant

Arrhenius equation: 1

coeff1

a

= − +

= − +

== −

∆ ∆

∆ ∆

[

[

[ ]

1 1

rate-determining kk Ae E RT

L

K K K

K K K

K K K

K K

K K

N V

a a a

b b b

a b w

a[conjugate base]

[weak acid] aweak acid]

[conjugate base]

b[conjugate acid]

[weak base] bweak base]

[conjugate acid]

a a

H AHA]

p

OH][HBB]

p

ion-product constant for water

Henderson–Hasselbalch equations:

pH p p

pOH p p

acid–base neutralization:

= = −

= = −

= =

= + = −

= + = −

+ −

− +

[ ][ ][

, log

[ ][

, log

log log

log log

[

[

== N Vb b

E En

Q≈ −o 0 06.log