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Review of CHM 1316
Final at 11 AM
Monday
7 May 2001
Gases and Chemistry of the
Atmosphere
Ideal Gas Laws
Relation of Temperature to <KE>
Earth’s Atmosphere
Ideal Gas Law, PV=nRT
 Boyle’s Law for isotherms, P1V1=P2V2
 Charles’ Law for isobars, V1/T1=V2/T2
 Avogadro’s Law for moles, V1/n1=V2/n2
 For adiabatic processes (q=0)
• T1/P1 = T2/P2 where  = CP/CV ~ 1.4
• So T falls as P falls with altitude in atmosphere
Pressure, Work, Energy
 [P] = 1 Pa (Pascal) = 1 N m-2 (force/area)
• Gravitational force (weight) of Earth’s
atmosphere above every m2 is 101,325 Pa
 1 atm = 101.325 kPa = 760 mm Hg (torr)
• 1 bar = 100 kPa = 0.986923 atm
 R = 0.08206 atm L mol-1 K-1
• R = 8.314 J mol-1 K-1
 [PV] = Nm = J = energy; work  – PV
Standard Conditions
 For Gases
 For Thermodynamics
 P = 1 bar
 P = 1 bar
 T = 0ºC = 273.15 K
 T = 25ºC = 298.15 K
 Unit amount, n = 1
 Unit amount, n = 1
mole (6.0221023
molecules)
mole (6.0221023
molecules)
Non-ideal Gases
 Many “equations of state” for real gases
 Van der Waals’ a good approximation:
 [ Preal + a (n/Vreal)2 ] [ Vreal – n b ] = n RT
 Pideal exceeds Preal by gas-gas attraction, a
 Vreal exceeds Videal by molecular volume, b
Equipartition Theorem
 kinetic energy = ½ mmoleculevrms2 = ½ kT
• k = Boltzmann constant = R/NAv
 KINETIC ENERGY = ½ Mvrms2 = ½ RT
• 3 Cartesian Directions: KE = (3/2) RT
 Effusion (from puncture) and Diffusion
(through gas): v12/v22 = M2/M1 (Graham)
• distance = v t so heavy takes longer than light
 CV (monatomic gas) = (3/2) R
Earth’s Atmosphere
 Dry Air: 78% N2 + 21% O2 +
• 1% Ar and traces, esp. 365 ppm CO2
 Sat’d Air 95% of above + 5% water vapor
 Troposphere: weather by buoyancy
• Rising hot air cools adiabatically condenses H2O
 Stratosphere: stagnant by O3 + hv  O + O2
 Traces NOX & SOX give Acid Rain
 Growing CO2 traps IR; warms Earth
Pure Solids and Liquids
Intermolecular forces
Crystals and Metals
Phase Diagrams
Intermolecular Forces
 London (induced dipole-induced dipole)
• Enhanced by size and weakly held electrons
 Dipole
• Much higher melting points
• XHX “hydrogen bonding” with X=N,O,F
 Ionic
• Strongest forces but ion-dipole often competes (as in
dissolution in aqueous solution)
Phase Properties
 Solids
• Immobile and often regular arrays
 Liquids
• Molecules migrate but remain cohesive
• Surface tensions yield capillarity
 Gases
• Free molecular motion fills container
• Found (vapors) in increasing concentration as solids
liquefy until PVAPOR = 1 atm defines boiling.
Solid Organization
 Amorphous (absence of order, e.g., glass)
 Crystalline (repeating “unit cell” patterns)
– Molecular
• London or Dipolar binding
– Atomic (“macroscopic molecules”)
• Covalent (diamond) or Metal binding
– Ionic (also “macroscopic”)
• Cation/Anion binding
• Easily shattered along glide planes
Regularity
 7 Crystal Systems
• A consequence of packing unit cells in 3d
 Coherent X-ray scattering (Bragg angles)
• n = 2d sin  give constructive interference patterns
• d measures plane separations (Miller indices)
• Absences in the indices forced by symmetries
 Geometries and dimensions of molecules in
unit cells prove molecular structure
Phase Diagrams
fixed (P,T )
 Coexistence lines of
melting, boiling, and
sublimation
 Critical Point above
which no liquid
 Triple Point where 3
phases coexist
Critical
point
Pressure (atm)
 Phases (co)existing at
10_252
Pc = 218
Solid
Liquid
1.00
P3 = 0.0060
Gas
Triple
point
Tm
T3
Tb
Tc
0
0.0098
100
374
Temperature ( ° C)
Metal Bonding
 Infinite in extent throughout metal crystal
 Overlap of NAv valence orbitals gives bands
of whole crystal (molecular) orbitals
 Metal properties if
• ½ filled MO since kT sufficient to excite electrons
• Fully filled MO but overlaps empty bands
 Semiconductor properties if
• Electronic gap to next vacant band can only be
bridged with applied voltage, Egap
Solvents and Solutes
Ideal solutions
Colligative properties
Non-idealities
Impetus to Dissolve
 Endothermic breaking of pure bonding
offset by solvent-solute interactions
 Adhesive forces compete with cohesive
 “Like dissolves like” ensures comparable
force magnitudes
 Water, the “universal solvent”
• Polarity surrounds and insulates ions
• Hydrogen bonds dissolve oxygen-containing solutes
 Entropy wins
Ideal Solutions
 Raoult’s Law: Psolvent = Xsolvent Pºsolvent
 Henry’s Law: Psolute = Xsolute KHenry
 Valid if cohesion = adhesion
 Valuable to measure chemical activity of
solution components by vapor pressures
 Violated as a rule:
• + deviation if cohesive > adhesive forces
• – deviation if cohesive < adhesive forces
Colligative Properties
 Depend only on mole fraction not identities
 Freezing Point Depression
• Tfp;solvent = – kfp;solvent msolute
 Boiling Point Elevation
• Tbp;solvent = + kbp;solvent msolute
 Osmotic Pressure
• solvent = Csolute RT
• van’t Hoff factor, i = neff / ndissolved
Measures of Solutes
 Mole fraction, Xi = ni / (  nj )
– Measures apples and apples
 Molarity, Mi = ni / 1 Lsolution
– Valuable for dispensing
– Suffers if solution densities vary with conc.
 Molality, mi = ni / 1 kgsolvent
– While V may not be conserved, mass always is!
– Aqueous m=M at infinite dilution
Thermochemistry
Conservation of state functions
Enthalpy, the Chemist’s choice
Exo- and Endothermicity
Energy
 E = q + w
• q, heat: transfer of energy by T
• w, work; transfer of energy by organized force
 EUniverse = 0 is Thermodynamics’ 1st Law
 Heat Capacity, CV = (dE/dT)V ~ E/T
 E = qV or heat transferred at fixed volume
 Exothermic process sheds heat, E < 0
 Endothermic process absorbs heat, E > 0
Work
 Work = travel through force = F x
 Surface (tension) Work = +  A that
increases energy with surface area
 Pressure-Volume Work increases energy
with decreasing volume (against expansive
force) so w = – P V
 Electrical work = Q E where E is an
electrical potential difference through which
charge Q travels.
Enthalpy, H
 H = E + PV
 H = E + P V (assuming P fixed)
 H = qP or heat transferred at fixed P
 CP = (dH/dT)P ~ H / T is the heat
capacity at fixed P
 Exothermicity means H < 0 (fixed P)
 Endothermicity means H > 0
State Functions
 INDEPENDENT of any process’s path
 Examples: E, H, T, P, V, S, A, and n
• NON State Functions include w and q
 The basis of Hess’s Law:
• (State Function) the same over all paths
• Pick the easiest to measure or compute
 H =  vi Hf
• vi are product stoichiometric coefficients but
negative reactant stoichiometric coefficients
Standard° States
 Elements
• The state most stable at 1 bar and 25ºC
• Enthalpy° of formation (from elements) = 0.00
 Gases: 1 bar at 25ºC
 Pure condensed phases: 1 bar at 25ºC
 (Ideal) Solutes: 1 M at 1 bar and 25ºC
Thermodynamics
Entropy and Disorder of the Universe
Free Energy, G, points to Equilibrium
Temperature Dependence of K
Entropy and Disorder
 S = k ln W (Boltzmann’s epitaph)
• Equivalent Ways of finding a molecule
 S increases with heat, qrev, but cold systems
are more influenced than hot, already
chaotic, ones: S = qrev / T
 Disorder means more Ways of finding the
Universe, and Disorder (Entropy) never
decreases! (2nd Law)
 Ssolid < Sliquid << Sgas and Ssimple < Scomplex
Surroundings are Disordered
 Chaos takes energy, but energy is
conserved.
 SUniverse must increase, but individual
entropies of system and surrounding can
decrease as long as their sum does not.
 TSUniverse = T Ssystem + T Ssurroundings
 – G  T SUniverse = T Ssystem – Hsystem
 Free Energy, G = H – TS, must decrease
Free Energy and Partial Pressures
 dE = TdS – PdV becomes
 dG = VdP – SdT or just VdP at fixed T
 dG = VdP = (RT/P) dP = RT d ln(P)
 G = RT  vi ln(Pi/1 atm) = RT ln ( Pv)
 G = G° + RT ln Q = 0 when Q=K
 G° = – RT ln K
 Gibbs Free Energy points to equilibrium
and its constant!
16_353
GA
G
GB
(a)
GA (PA decreasing)
G
GB (PB increasing)
(b)
G
(c)
GA
GB
Equilibrium’s T Dependence
 ln K = – G°/RT
 ln K = – (H°/R) T–1 + S°/R
 d lnK / dT  + (H°/R) T–2
 LeChâtlier confirmed: exothermicity means
a negative right-hand side and K diminishes
with T, favoring the reactants. Vice versa
for endothermicity.
Chemical Kinetics
Reaction Rate Expressions
Mechanisms & Elementary Reactions
Rate Constants and Temperature
Simple Rate Expressions
Order
d[A]/dt
Integral form
0
– k0
[A] = [A]0 – k0t
1
– k1 [A]
ln[A] = ln [A]0 – k1t
2
– k2 [A]2
1/[A] = k2t + 1/[A]0
Order vs. Molecularity
 Reaction Order
 Reaction Molecularity
 Applies to overall
 Applies only to an
reaction
 Sum of exponents in
rate expression is the
overall order
 Individual exponents
are individual orders
but not stoichiometric
elementary reaction
 Sum of exponents in
rate expression is the
molecularity
 Exponents are the
stoichiometric
coefficients!
Reaction Mechanism
 Series of elementary steps to final products
 Elementary = actual atomic rearrangements
then order = molecularity
 Slowest rate = “rate limiting step” and
determines overall rate expression
 Intermediates produced and consumed in
steady state
 Fast equilibrium steps honor K = kf / kr
Temperature Dependence of k
 Rate constant  efficacy of encounter
• Efficacy  orientation and momentum directed
at barrier forces
 k = A exp [ – EACT / RT ]
• ln k = ln A – (EACT / R) T–1
 EACT, activation energy imposed (because
bond energies not linear in bond order)
 Exponential measures fraction of thermal
encounters bearing at least EACT
Catalysis
 Catalytic species encourage reaction but are
not consumed (by the overall reaction).
 Homogeneous catalyst has reactants phase
while heterogeneous is another phase
 Catalysts lower EACT making more
encounters effective; reduce dimensionality.
 Biological catalysts (enzymes) are locks for
reactant keys; shape recognition.
Electrochemistry
Galvanic and Electrolytic Cells
Standard Reduction Potentials
Nernst Equation & Electrical Work
Galvanic Cells
 Oxidation half-cell (anode)
– Supplies electrons
 Reduction half-cell (cathode)
– Consumes same number of electrons supplied
 Salt Bridge
– Permits charge rebalance by transporting
counterions
 Spontaneous e– flow if voltage E > 0
Electrolytic Cell
 Non-spontaneous because E < 0
 So external electromotive force (potential)
must be supplied for cell reaction to be
reversed!
 Galvanic cell can drive electrolytic one but
only if Egalvanic – Eelectrolytic > 0
 Much more often, driving potential is direct
current ( I = C / t , Amp = Coulomb / s )
Half-cell Reactions
 Only proceed when in electrical contact
with one another
 Bear independent potentials whose sum is
the overall cell potential, Eanode + Ecathode
 Standard° Reduction Potentials all relative
to 2 H+ + 2 e–  H2(1 bar), E°  0.00 volts
 E°anode is negative of its SRP;  spontaneity
only if E°cathode is the more positive
Maximum Electrical Work and
Nernst Equation
 Work = Charge  Potential change
 Mole of electrons worth F (96,450 C)
 Workmax = ne F E° = – G°
 G = G° + RT ln Q becomes
 E = E° – (RT/ne F) ln Q
 E = E° – (52.9 mV / ne) log Q at 25°C
 ne E° / 52.9 mV = log K
Stoichiometry of Electrolysis
• How much chemical change occurs with the
flow of a given current for a specified time?
current and time  quantity of charge 
moles of electrons  moles of analyte 
grams of analyte