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### Gases and Chemistry of the Atmosphere

### Thermodynamics

### Chemical Kinetics

### Electrochemistry

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 –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)

Standard ConditionsNon-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

Intermolecular Forces

- London (induced dipole-induced dipole)
- Enhanced by size and weakly held electrons
- Dipole
- Much higher melting points
- XHX “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

- 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

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

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 = 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

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 = CsoluteRT
- 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

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

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.
- TSUniverse = 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!

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.

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!

Order vs. MolecularityReaction 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.

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 andNernst Equation

- 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

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

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