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Review of CHM 1316

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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

- 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

- [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 –PV

For Gases

P = 1 bar

T = 0ºC = 273.15 K

Unit amount, n = 1 mole (6.0221023 molecules)

For Thermodynamics

P = 1 bar

T = 25ºC = 298.15 K

Unit amount, n = 1 mole (6.0221023 molecules)

- 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

- kinetic energy = ½ mmoleculevrms2 = ½ kT
- k = Boltzmann constant = R/NAv

- 3 Cartesian Directions: KE = (3/2) RT

- distance = v t so heavy takes longer than light

- Dry Air: 78% N2 + 21% O2 +
- 1% Ar and traces, esp. 365 ppm CO2

- Rising hot air cools adiabatically condenses H2O

Pure Solids and Liquids

Intermolecular forces

Crystals and Metals

Phase Diagrams

- London (induced dipole-induced dipole)
- Enhanced by size and weakly held electrons

- Much higher melting points
- XHX “hydrogen bonding” with X=N,O,F

- Strongest forces but ion-dipole often competes (as in dissolution in aqueous solution)

- Solids
- Immobile and often regular arrays

- Molecules migrate but remain cohesive
- Surface tensions yield capillarity

- Free molecular motion fills container
- Found (vapors) in increasing concentration as solids liquefy until PVAPOR = 1 atm defines boiling.

- 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

- Molecular

- 7 Crystal Systems
- A consequence of packing unit cells in 3d

- n = 2d sin give constructive interference patterns
- d measures plane separations (Miller indices)
- Absences in the indices forced by symmetries

- Phases (co)existing at fixed (P,T )
- Coexistence lines of melting, boiling, and sublimation
- Critical Point above which no liquid
- Triple Point where 3 phases coexist

- 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

- Electronic gap to next vacant band can only be bridged with applied voltage, Egap

Solvents and Solutes

Ideal solutions

Colligative properties

Non-idealities

- 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

- Raoult’s Law: Psolvent = XsolventPºsolvent
- Henry’s Law: Psolute = XsoluteKHenry
- 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

- 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 = CsoluteRT
- van’t Hoff factor, i = neff / ndissolved

- 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

- 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 = 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.

- 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

- INDEPENDENT of any process’s path
- Examples: E, H, T, P, V, S, A, and n
- NON State Functions include w and q

- (State Function) the same over all paths
- Pick the easiest to measure or compute

- vi are product stoichiometric coefficients but negative reactant stoichiometric coefficients

- 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

- S = k ln W (Boltzmann’s epitaph)
- Equivalent Ways of finding a molecule

- 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.
- TSUniverse = T Ssystem + T Ssurroundings
- – G T SUniverse = T Ssystem– Hsystem
- Free Energy, G = H – TS, must decrease

- 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!

- 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

ReactionOrder

Applies to overall reaction

Sum of exponents in rate expression is the overall order

Individual exponents are individual orders but not stoichiometric

ReactionMolecularity

Applies only to an elementary reaction

Sum of exponents in rate expression is the molecularity

Exponents are the stoichiometric coefficients!

- 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

- 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

- 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

- 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

- 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 )

- 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

- Work = Charge Potential change
- Mole of electrons worth F (96,450 C)
- Workmax = neFE° = – 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
- neE° / 52.9 mV = log K

- 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