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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 = 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

Review of CHM 1316

Final at 11 AM

Monday

7 May 2001

gases and chemistry of the atmosphere

Gases and Chemistry of the Atmosphere

Ideal Gas Laws

Relation of Temperature to <KE>

Earth’s Atmosphere

ideal gas law pv n r t
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
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

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
non ideal gases
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
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
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

Pure Solids and Liquids

Intermolecular forces

Crystals and Metals

Phase Diagrams

intermolecular forces
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
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
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
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
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
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

Solvents and Solutes

Ideal solutions

Colligative properties

Non-idealities

impetus to dissolve
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
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
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
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

Thermochemistry

Conservation of state functions

Enthalpy, the Chemist’s choice

Exo- and Endothermicity

energy
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
slide23
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
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
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
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

Thermodynamics

Entropy and Disorder of the Universe

Free Energy, G, points to Equilibrium

Temperature Dependence of K

entropy and disorder
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
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
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
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

Chemical Kinetics

Reaction Rate Expressions

Mechanisms & Elementary Reactions

Rate Constants and Temperature

order vs molecularity
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
reaction mechanism
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
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
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

Electrochemistry

Galvanic and Electrolytic Cells

Standard Reduction Potentials

Nernst Equation & Electrical Work

galvanic cells
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
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
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
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
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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