Chem 6A Equation Sheet (Final Exam) 1 Prof. Crowell

Chem 6A Final Exam Equation Sheet Constants and Conversions:

Speed of light in vacuum: c = 2.99792 x 108 m/s Plancks Constant: h = 6.62607 x 10-34 J-s Elementary Charge: e = 1.60218 x 10-19 C Electron Mass: me = 9.10938 x 10-31 kg Proton Mass: mp = 1.67262 x 10-27 kg Neutron Mass: mn = 1.67493 x 10-27 kg Avogadros #: NA = 6.02214 x 1023 mol-1 Atomic Mass Unit: 1 amu = 1.66054 x 10-27 kg Boltzmanns Constant: kB or k = 1.38066 x 10-23 J/K Acceleration of free fall: g = 9.80665 m/s2 Molar Volume, Ideal Gas (@273.15 K, 1 atm): Vm = 22.414 L Std Atmosphere: 1 atm = 101 325 Pa Molar Gas Constant: R = 8.31447 J/K-mol = 0.0820574 L-atm/K-mol = 0.0831447 L-bar/K-mol

1( 300 ) / 208E at K kT hc cm Rydberg Constant: RH = 1.096776 x 107 m-1 Conversions: Mass: 1 metric ton = 103 kg, 1 ton (US) = 2000 lb, 1 kg = 2.20462 lb, 1 lb = 16 oz = 453.5924 g Volume: 1L = 1 dm3 = 103 cm3 = 10-3 m3 = 1.057 qt, 1 cm3 = 1 mL, 1 m3 = 35.3 ft3, 1 gal = 3.78541 L Length: 1 cm = 10-2 m, 1 m = 10-6 m, 1 nm = 10-9 m, 1 = 10-10 m, 1 pm = 10-12 m, 1 in = 2.54 cm Pressure: 1 atm = 101,325 Pa, 1 bar = 105 Pa = 105 N/m2, 1 atm = 1.01325 bar, 0.98692 atm = 1 bar, 1 atm = 760 torr, 1 torr = 133.32 Pa, 1 psi = 6895 Pa = 6.895 kPa Energy: 1 erg = 10-7 J, 1 eV = 1.60218 x 10-19 J, 1 eV = 96.485 kJ/mol, 1 cm-1 = 1.98645 x 10-23 J, 1 cal = 4.184 J, 1 L-atm = 101.325 J, 1 J = 1 V-C, 1 J = 1 Pa-m3 = 1 N-m = 1 kg-m2/s2 Power: 1 hp = 745.7 W = 745.7 J/s, 1 kWh = 3600 kJ; Dipole: 1 D = 1 Debye = 3.33564 x 10-30 C-m

Chem 6A Equation Sheet (Final Exam) 2 Prof. Crowell

Soluble Ionic Compounds: 1. All common compounds of Group 1A ions (Li+, Na+, K+, etc.) & the ammonium ion (NH4

+) are soluble.

2. All common nitrates (NO3-), acetates (C2H3O2

-), and most perchlorates (ClO4-) are soluble.

3. All common chlorides (Cl-), bromides (Br-), and iodides (I-) are soluble, except those of Ag+, Pb2+, Cu+, and Hg2

2+. All common fluorides (F-) are soluble, except those of Pb2+ and Group 2A.

4. All common sulfates (SO42-) are soluble, except those of Ca2+, Sr2+, Ba2+, Ag+, and Pb2+.

Insoluble Ionic Compounds: 1. All common metal hydroxides (Mn+ + OH-) are insoluble, except those of Group 1A (Li+, Na+, K+, etc.) and the larger members of Group 2A (i.e. Ca2+ and larger). 2. All common carbonates (CO3

2-) & phosphates (PO43-) are insoluble, except those of Group 1A & NH4

+.

3. All common sulfides (S2-) are insoluble, except those of Group 1A, Group 2A, and NH4+.

Strong Acids: HBr, HCl, HI, HNO3, H2SO4, H2SeO4, HClO4, HClO3 Strong Bases: NaOH, KOH, Ca(OH)2, Sr(OH)2, Ba(OH)2, Group I & II oxides (MO) & amides (MNH2)

Rules for Assigning an Oxidation Number (O.N.) 1. For an atom in its elemental form (Na, O2, Cl2, etc.): O.N. = 0 2. For a monatomic ion: O.N. = ion charge 3. The sum of O.N. values for the atoms in a molecule or formula unit of a compound equals zero. The sum of O.N. values for the atoms in a polyatomic ion equals the ions charge.

Rules for Specific Atoms or Periodic Groups: 1. For Group 1A(1): O.N. = +1 in all compounds 2. For Group 2A(2): O.N. = +2 in all compounds 3. For hydrogen (H): O.N. = +1 in combination with nonmetals, O.N. = 1 in combination with metals & B. 4. For fluorine (F): O.N. = 1 in all compounds. 5. For oxygen (O): O.N. = 1 in peroxides, O.N. = 2 in all other compounds (except with F). 6. For Group 7A(17): O.N. = 1 in combination w/ metals, nonmetals (except O), & halogens lower in the group. Work = force x distance = N-m = kg-m2/s2 = J, Expansion work = - Pex V = Pa-m3 = J E = internal energy = KE + PE = system capacity to do work = total energy storage of a system; Ideal Gas Law: PV nRT First Law of Thermodynamics: E q w Expansion work against a constant external pressure: extw P V Work of reversible isothermal expansion of an ideal gas: ln ( / )f iw nRT V V

m sHeat Capacity: C = ; Molar Heat Capacity: C = ; Specific Heat Capacity: C = q q qT n T m T

At Constant Volume (i.e. using a bomb calorimeter): E = q + w = q Pex V = q = qV At Constant Pressure (i.e. using a coffee-cup calorimeter): H = E + (PV) = q Pex V + Pex V = qP

(constant volume) ; (constant pressure)V PV Pq qE HC C C CT T T T

Enthalpy: - A state function that is a measure of the energy (heat) associated with a constant pressure process. Enthalpy = , ( )H E PV H E PV STP = 1 atm, 273.15 K For an Ideal Gas: H = E + (PV) = E + (nRT) = E + nR T (at const # moles) , ,P m V mC C R E (atom) = Etranslation E (molecule) = Etranslation + Erotation + Evibration Enthalpy of Phase Changes: , , , , , ,; ;fus m liq m solid m vap m gas m liq mH H H H H H

, , , , ,subl m gas m solid m fus m vap mH H H H H When a process is reversed: , , reverse m forward mH H H standard state enthalpy change () Reference State Hf standard enthalpy of formation; Hf for an element in its standard state is zero. The change in enthalpy for a given reaction is: ( ) (reactants)rxn p f R f

p RH n H products n H

Chem 6A Equation Sheet (Final Exam) 3 Prof. Crowell

2 2

2

v ; Einstein Equation: ; ; 2 2

1Photoelectric effect: v ; DeBroglie's Postulate: ; 2 v

Atomic Line Spectra:

photon total photons photons

o

m p hcE KE E h c E N Em

h hKE m h h hp m

7 1H 1 H2 2

1

2 2 2 2 2 2-18

2 2 2 2 2 21 1

1 1 1 = R , n > n , R 1.096776 10

- = 2.18 10 13.6

;

photon final initial Hfinal initial

x mn n

Z Z Z Z Z ZE E E E hc R x J eVn n n n n n

2

2

2 2* *

Schrdinger Equation: ( ) ( ) ; Hamiltonian Operator: 2

1-D Probability Density: (x) = (x) (x) ; 1-D Probability: (x) = (x) (x) ;

n n nH x E x H Vmd dx

= wavefunction = electronic motion; 2 = probability distribution = orbital 2 222 2 2

2 2 2 2Particle in a Box: 1D: 1, 2, 3, ; In 3-D: ;8 8y zx

nx y z

n nnn h hn E EmL m L L L

Heisenberg Uncertainty Principle: xp , Et ;4 4h h 2 2

182 2Hydrogen-like 1 electron atoms: , 13.605 2.18 10

1 2 3, , 1, 1 0 1 ; # radial nodes 1, angular nodes;

Radial Distribution function: (

nl l,m

l

nl

Z Z( r,, ) R (r) Y ( , ) E eV x Jn n

n = , , l < n m = l, l + , l , l n l l

P

2 2 1 1) ; has ; has ;2 2nl spin s spin s

r R (r) r m m 2

21

Many electron atom: 13.6 , ,n

nli eff nl nl

i

(Z ) = eV E Z Z Zn

1 1: ( ) ( ) , 0; : ( ) ( ),IE Atom g ion g e E IE EA Atom g e ion g E EA

Rules for forming cations: Main Group last in, first out; Transition Metals first in, first out.

1 2 12

, ,reactants products

Coulomb's Law: / , Born-Haber Cycle: 0

Lattice Enthalpy: ( ) ( ),

Heats of Reaction using Bond Enthalpy :

Al

LE cycle

rxn LE

rxn BE react BE prod

E k Q Q r H H

Ionic Compound s Gaseous Ions g H H

H H H

, ,bonds broken bonds formedternatively: ;

Bond Enthalpy ( ) Bond Order (1 / Bond Length) IR Frequency rxn BE react BE prod

BE

H H H

H

Electronegativity: ability of an atom in a molecule to attract shared electrons to itself; Electronegativity: 10.5 ( ); ;AB AA BBIE EA E E E FONClBrISCH Lewis Dot Structures: Tval NiVii (charge state); Nextra Tval 2Nsingle; FC Vi NNBE Nbonds Bond Order (BO) = the number of bonding electron pairs shared by two atoms Bond Order = (number of shared electron pairs linking atoms X & Y) / (number of X-Y links) VSEPR Shape Molecular formula Related Shapes Linear AX2 Trigonal planar AX3 AX2E Tetrahedral AX4 AX3E, AX2E2 Trigonal bipyramidal AX5 AX4E, AX3E2, AX2E3 Octahedral AX6 AX5E, AX4E2 Dipole Moment: Q r ; 1 Debye = 3.336 x 10-30 Coulomb-meter Paramagnetism: Atoms, Molecules or Ions with an unpaired electron or electrons Diamagnetism: Atoms, Molecules, or Ions in which all electrons are paired.

11Infrared Spectroscopy: ; vibvibEhcE h hc cmhc