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Review of CHM 1316

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 = n R T. Boyle’s Law for isotherms, P 1 V 1 =P 2 V 2 Charles’ Law for isobars, V 1 /T 1 =V 2 /T 2

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Review of CHM 1316

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  1. Review of CHM 1316 Final at 11 AM Monday 7 May 2001

  2. Gases and Chemistry of the Atmosphere Ideal Gas Laws Relation of Temperature to <KE> Earth’s Atmosphere

  3. 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

  4. 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

  5. For Gases P = 1 bar T = 0ºC = 273.15 K Unit amount, n = 1 mole (6.0221023 molecules) For Thermodynamics P = 1 bar T = 25ºC = 298.15 K Unit amount, n = 1 mole (6.0221023 molecules) Standard Conditions

  6. 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

  7. 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

  8. 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

  9. Pure Solids and Liquids Intermolecular forces Crystals and Metals Phase Diagrams

  10. 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)

  11. 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.

  12. 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

  13. 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

  14. 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

  15. 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

  16. Solvents and Solutes Ideal solutions Colligative properties Non-idealities

  17. 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

  18. 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

  19. 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

  20. 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

  21. Thermochemistry Conservation of state functions Enthalpy, the Chemist’s choice Exo- and Endothermicity

  22. 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

  23. 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.

  24. 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

  25. 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

  26. 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

  27. Thermodynamics Entropy and Disorder of the Universe Free Energy, G, points to Equilibrium Temperature Dependence of K

  28. 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

  29. 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

  30. 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!

  31. 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.

  32. Chemical Kinetics Reaction Rate Expressions Mechanisms & Elementary Reactions Rate Constants and Temperature

  33. Simple Rate Expressions

  34. 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. Molecularity

  35. 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

  36. 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

  37. 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.

  38. Electrochemistry Galvanic and Electrolytic Cells Standard Reduction Potentials Nernst Equation & Electrical Work

  39. 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

  40. 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 )

  41. 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

  42. 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

  43. 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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