* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Review - The University of Texas at Dallas
Molecular Hamiltonian wikipedia , lookup
Thermophotovoltaic wikipedia , lookup
Rate equation wikipedia , lookup
State of matter wikipedia , lookup
Gibbs paradox wikipedia , lookup
Franck–Condon principle wikipedia , lookup
Eigenstate thermalization hypothesis wikipedia , lookup
Vapor–liquid equilibrium wikipedia , lookup
X-ray photoelectron spectroscopy wikipedia , lookup
Chemical equilibrium wikipedia , lookup
Enzyme catalysis wikipedia , lookup
Electrolysis of water wikipedia , lookup
George S. Hammond wikipedia , lookup
Marcus theory wikipedia , lookup
Thermodynamics wikipedia , lookup
Equilibrium chemistry wikipedia , lookup
Physical organic chemistry wikipedia , lookup
Electrochemistry wikipedia , lookup
Heat transfer physics wikipedia , lookup
Work (thermodynamics) wikipedia , lookup
Chemical thermodynamics wikipedia , lookup
History of thermodynamics wikipedia , lookup
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 – PV 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 (6.0221023 molecules) mole (6.0221023 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 • 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 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. 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! 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