1. Chapter 20: Thermodynamics
1.1. Spontaneity
1.1.1. Spontaneous change: occurs under specified conditions w/out a continuous input of energy from the surroundings
1.1.2. "Spontaneous" does NOT mean "instantaneous"
1.1.3. A chemical rxn proceeding toward equilibrium is spontaneous
1.1.4. First Law of Thermodynamics does NOT predict spontaneous change
1.1.4.1. Law of conservation of energy
1.1.4.2. ΔEsys + ΔE surr = 0 = ΔEuniv
1.1.4.3. Change in internal energy: ΔE= q + w
1.1.5. The sign of ΔH does NOT predict spontaneous change
1.1.5.1. Exothermic (ΔH < 0) and endothermic (ΔH > 0) processes can be spontaneous
1.2. Entropy
1.2.1. Definition
1.2.1.1. Freedom of particle motion & dispersal of particle energy
1.2.1.1.1. Entropy Incr. as: - solid --> liq. --> gas - A salt dissolves
1.2.1.1.2. A change in the freedom of motion of particles in a system affects the direction of a spontaneous process
1.2.1.2. Incr. # of microstates --> incr. entropy
1.2.1.3. Entropy (S) is a state function
1.2.1.3.1. ΔS(sys) = S(final) - S(initial)
1.2.1.3.2. ΔS(sys) = q(rev) / T q = heat absorbed
1.2.1.4. Extensive property: depends on amount
1.2.1.4.1. Standard molar entropy (S°) (units of J/mol*K)
1.2.2. Second Law of Thermodynamics
1.2.2.1. All processes occur spontaneously in the direction that incr. the entropy of the universe
1.2.2.2. ΔS(univ) = ΔS(sys) + ΔS(surr) > 0 for any real spontaneous process
1.2.3. Third Law of Thermodynamics
1.2.3.1. A perfect crystal has zero entropy at absolute zero (0 K)
1.2.3.2. At equilibrium, ΔS(univ) = 0 (no net change)
1.2.4. Predicting Relative S°
1.2.4.1. S° incr. as T incr.
1.2.4.2. S° incr. as state changes from solid to liquid to gas
1.2.4.3. ΔS°vap >> ΔS°fus
1.2.4.4. S(sol'n) > S(solute) + S(solvent)
1.2.4.5. Dissolving a gas in a liquid: entropy decr.
1.2.4.6. Dissolve gas in another gas: entropy incr.
1.2.4.7. Entropy incr. w/ size (down a group on the periodic table) & chemical complexity (for compounds)
1.2.5. Calculating Entropy Change of a Reaction
1.2.5.1. Standard entropy of reaction, ΔS°rxn: entropy change that occurs when all reactants & products are in their standard states
1.2.5.2. Predicting the sign of ΔS°rxn
1.2.5.2.1. # mol gas incr. --> ΔS°rxn is positive
1.2.5.2.2. # mol gas decr. --> ΔS°rxn is negative
1.2.5.3. Hess's Law: ΔS°rxn = ΣmS°(products) - ΣnS°(reactants)
1.2.5.4. The only way for an endothermic reaction (ΔHsys > 0) to occur spontaneously is if ΔSsys is positive & large enough to outweigh the negative ΔSsurr
1.2.5.4.1. Solid ionic compound dissolved: ΔSsys >> 0 --> ΔSuniv > 0
1.3. Free Energy (G)
1.3.1. G = H - TS
1.3.2. Free energy change (ΔG)
1.3.2.1. Measure of the spontaneity of a process & the useful energy available from it
1.3.2.2. The sign of ΔG
1.3.2.2.1. ΔSuniv > 0: spontaneous: ΔG < 0
1.3.2.2.2. ΔSuniv = 0: equilibrium: ΔG = 0
1.3.2.2.3. ΔSuniv < 0: nonspontaneous: ΔG > 0
1.3.3. Gibbs Equation
1.3.3.1. ΔGsys = ΔHsys - TΔSsys
1.3.3.2. Standard free energy change ΔG°sys = ΔH°sys - TΔS°sys
1.3.4. Standard free energy of formation, ΔG°f
1.3.4.1. When 1 mol of a compound is made from its elements w/ all components in standard state
1.3.4.2. ΔG°rxn = ΣmΔG°f(prod.) - ΣnΔG°f(reacts)
1.3.4.3. ΔG°f of an element in its standard state is zero
1.3.4.4. An eq. coefficient (m,n) multiplies ΔG°f by that number
1.3.4.5. Reversing a reactin changes the sign of ΔG°f
1.3.5. Work
1.3.5.1. ΔG = W(max)
1.3.5.2. ΔG is the max. useful work done by a system during a spontaneous process
1.3.5.2.1. Spont. rxn (ΔGsys is negative) does work on surroundings (-W)
1.3.5.3. ΔG is the minimum work done to a system to make a nonspont. process occur
1.3.5.3.1. Nonspont. rxns occur only if the surroundings do work on the system (+W)
1.3.6. Reaction Spontaneity
1.3.6.1. Most exothermic rxns are spont. because the large negative ΔH makes ΔG negative
1.3.6.2. ΔH ΔS -TΔS ΔG Rxn spontaneity - + - - Spont. at all T + - + + Nonspont. at all T + + - - Spont. at high T or + Nonspont. at low T - - + - Spont. at low T or + Nonsp. at high T
1.3.6.3. The temperature at which a rxn becomes spont.
1.3.6.3.1. Set ΔG = 0 and solve for T
1.3.6.3.2. ΔH = TΔS
1.3.6.3.3. T = ΔH/ΔS
1.3.7. Equilibrium & Rxn Direction
1.3.7.1. ΔG = RT ln(Q/K) = RT lnQ - RT lnK
1.3.7.2. ΔG° = -RT lnK
1.3.7.3. ΔG = ΔG° + RT lnQ
2. Chapter 21: Electrochemistry
2.1. Redox Reactions
2.1.1. Oxidation: loss of e-
2.1.1.1. Reducing agent is oxidized (gives e-)
2.1.1.2. Oxidized substance ends up w/ a higher O.N.
2.1.2. Reduction: gain of e-
2.1.2.1. Oxidizing agent is reduced (takes e-)
2.1.2.2. Reduced substance ends up w/ a lower O.N.
2.1.3. Half-reaction method
2.1.3.1. 1) Divide the skeleton ionic rxn into two half-rxns, each containing the oxidized & reduced forms of one of the species
2.1.3.2. 2) Find the oxidation # of each atom
2.1.3.3. 3) Balance the atoms other than O & H
2.1.3.4. 4) Account for the change in O.N. by adding electrons on one side of each equation
2.1.3.5. 5) Find the LCM of the electrons' coefficients, multiply each equation to match that # of e-
2.1.3.6. 6) Sum the equations and cancel out the electrons
2.1.3.7. 7) Balance the charges by adding some H+ ions to one side
2.1.3.8. 8) Balance the # of O atoms by adding some H2O to one side
2.1.3.9. 9) Check the # of H atoms on each side
2.1.3.10. 10) In basic sol'n, add an OH- ion on both sides for each H+ ion present. The OH- on the same side as the H+ combine to form H2O. Excess H2O is canceled.
2.2. Electrochemical Cells
2.2.1. Two electrodes are dipped into an electrolyte
2.2.1.1. Anode: Oxidation
2.2.1.2. Cathode: Reduction
2.2.2. Voltaic (galvanic cell)
2.2.2.1. Uses a spontaneous rxn (ΔG < 0) to generate electrical energy. The system does work.
2.2.2.2. Electrons flow through the wire from anode to cathode
2.2.2.3. Anode: negative charge
2.2.2.3.1. Oxidation: X --> X+ + e-
2.2.2.4. Cathode: positive charge
2.2.2.4.1. Reduction: e- + Y+ --> Y
2.2.2.5. Salt bridge: joins the half-cells; "liquid wire"
2.2.2.6. Output of a Voltaic Cell
2.2.2.6.1. Cell potential, Ecell: the voltage of the cell (electromotive force, emf); difference in electric potential between the two electrodes
2.2.2.6.2. Ecell > for a spontaneous process
2.2.2.6.3. If Ecell = 0, the rxn has reached equilibrium & the cell will do no more work
2.2.2.6.4. Standard cell potential (E°cell)
2.2.3. Electrolytic cell
2.2.3.1. Uses electrical energy to drive a nonspontaneous rxn (ΔG > 0). The surroundings do work on the system.
2.2.3.1.1. Electrons flow from Cathode to Anode
2.2.3.1.2. ΔG is (+) and Ecell is (-)
2.2.3.2. Anode: positive charge
2.2.3.2.1. Oxidation: A- --> A + e-
2.2.3.3. Cathode: negative charge
2.2.3.3.1. Reduction: e- + B+ --> B
2.2.3.4. Electrolysis: splitting a substance w/ the input of electrical energy; decompose a compound into its elements
2.2.3.4.1. Recall diatomic elements: H2, N2, O2, F2, Cl2, I2, Br2
2.2.3.4.2. Electrolysis of Pure Molten Salts
2.2.3.4.3. Electrolysis of Mixed Molten Salts
2.2.3.4.4. Electrolysis of Water
2.2.3.4.5. Electrolysis of Aqueous Salt Sol'ns
2.2.3.4.6. Stoichiometry of Electrolysis
2.3. Free Energy & Electrical Work
2.3.1. The signs of ΔG and Ecell are opposite for a spont. rxn.
2.3.2. Electrical work: Wmax = -Ecell x charge (in Joules)
2.3.3. The charge of 1 mol of electrons (Faraday constant): F = 96500 J/V*mol e-
2.3.4. ΔG = -nFEcell (n moles e-)
2.3.4.1. ΔG° = -nFE°cell when all components are in standard state
2.3.4.2. E°cell = (RT/nF) lnK (R = 8.314 J/mol K)
2.3.4.2.1. Positive E°cell: rxn proceeds spont. to the right at standard state
2.3.4.3. Reaction Parameters at Standard State ΔG° K E°cell Rxn at standard state < 0 >1 > 0 Spontaneous 0 1 0 At equilibrium >0 <1 < 0 Nonspontaneous
2.3.4.4. Effect of Concentration on Cell Potential (under nonstandard conditions):
2.3.4.4.1. ΔG = ΔG° RT lnQ
2.3.4.4.2. Nernst Equation: Ecell = E°cell - (RT/nF) lnQ
2.3.4.4.3. Q contains only species w/ concentrations/pressures that can vary. Solids do not appear
2.3.4.4.4. Converting pressure to molarity: n/V = P/RT, R = 0.0821 atm L/mol K
3. Chapter 18: Acids and Bases
3.1. All pH calculations
3.1.1. 1. All correct starting concentration
3.1.1.1. M = n/L
3.1.1.2. M1V1 = M2V2
3.1.2. 2. Remove spectator ions
3.1.2.1. Cations: Li+, Na+ K+, Rb+, Cs+, Ba2+, Sr2+
3.1.2.2. Anions: Cl-, Br-, I-, No3-, ClO4-
3.1.3. 3. Neutralization
3.1.3.1. H+ + OH- --> H2O(l) SA + SB
3.1.3.2. w.a. + OH- --> c.b.
3.1.3.3. w.b. + H+ --> c.a.
3.1.3.4. SCAN chart: Start Change (limiting reactant) After Neutralization
3.1.4. 4. Do the calculation
3.1.4.1. a) H+ --> pH (SA)
3.1.4.2. b) OH- --> pOH --> pH (SB)
3.1.4.3. c) HA + H2O <=> H3O+ + A- Eqm calc. using Ka(HA) --> pH (WA)
3.1.4.4. d) B + H2O <=> OH- + BH+ Eqm. calc. using Kb(B) --> pOH --> pH (WB)
3.1.4.5. e) A- + H2O <=> OH- + HA Eqm. calc. w/ Kb(A-) = Kw/Ka(HA) --> pOH --> pH
3.1.4.6. f) BH+ + H2O <=> H3O+ + B Eqm. calc w/ Ka(BH+) = Kw/Kb(B) --> pH
4. Chapter 19: Ionic Equilibria in Aqueous Solutions
4.1. Acid-Base Buffers
4.1.1. Buffer Solution: a conjugate acid-base pair within a 10:1 concentration ratio of each other (WA w/ conj. base or WB w/ conj. acid
4.1.2. Added H3O+ or OH- causes only a small change in the buffer-component concentration ratio & a small change in pH
4.1.3. Ideal Buffer: 1:1 concentration ratio
4.1.4. Common-ion effect: an ion is added to a solution that already contains it, and the equilibrium position shifts away from forming it (Le Chatelier's principle)
4.1.5. Ka = [H3O+] [A-] / [HA]
4.1.6. Henderson Hasselbalch Equation: solve directly for pH
4.1.6.1. pH = pKa + log([A-]/[HA])
4.1.6.2. Ideal buffer: pH = pKa because [base] = [acid]
4.2. Titrations
4.2.1. Monitoring pH w/ Acid-Base Indicators
4.2.1.1. An indicator changes color over a range of ~2 pH units
4.2.2. SA-SB Titration Curve
4.2.2.1. pH = 7 at equivalence (end) point
4.2.3. WA-SB Titration Curve
4.2.3.1. Buffer region
4.2.3.2. Half-way equivalence point: at midpoint of the buffer region; half of the initial WA has reacted, so [HA] = [A-] and pH = pKa
4.2.3.3. Equivalence point: pH > 7.00 The sol'n contains A-, which acts as a WB
4.2.4. WB-SA Titration Curve
4.2.4.1. Halfway equivalence point: pOH = pKb
4.2.4.2. Equivalence point: pH < 7.00
4.2.5. Polyprotic Acid Titration Curve
4.2.5.1. 2 equiv. pts. & 2 buffer regions
4.2.5.2. The pH at the midpoint of each buffer region is equal to the pKa of that acidic species
4.3. Solubility Equilibria
4.3.1. "Slightly soluble" ionic compounds
4.3.2. Qsp: ion-product expression For PbF2(s) <=> Pb(2+)(aq) + 2F-(aq): Qsp = Qc[PbF2(s)] = [Pb2+(aq)][F-(aq)]^2
4.3.3. Ksp: solubility-product constant
4.3.3.1. Saturated sol'n: Qsp = Ksp (at equilibrium)
4.3.3.2. Ksp depends on temperature only
4.3.4. Special case: sulfide ion, S(2-) reacts completely w/ water : S(2-)(aq) + H2O(l) --> HS-(aq) + OH-(aq)
4.3.5. Determining Solubility (S) from Ksp:
4.3.5.1. Ksp = [C]^p * [A]^q
4.3.5.2. Set up SCE chart: Use "S" instead of "x"
4.3.5.3. Pay attention to stoich. ratios... # moles
4.3.5.4. S = molar solubility
4.3.5.5. Higher Ksp --> greater solubility
4.3.6. Adding a common ion decr. the solubility of a slightly soluble ionic compound
4.3.7. Effect of pH on Solubility
4.3.7.1. In acidic sol'n, most ionic compounds are more soluble
4.3.7.2. NO EFFECT FOR: Cl-, Br-, I-, ClO2-, NO3-
4.3.8. Prediction the formation of a precipitate
4.3.8.1. If Qsp > Ksp, sol'n is saturated; no change
4.3.8.2. If Qsp > Ksp, a precipitate will form until saturation
4.3.8.3. If Qsp < Ksp, no precipitate will form (sol'n is unsaturated)
4.4. Complex Ion Equilibria
4.4.1. Complex ion: central metal ion covalently bonded to two or more anions/molecules (ligands)
4.4.1.1. Hydrated metal ions: salt dissolves in water --> H2O ligands around metal ion
4.4.1.2. Cr(NH3)6 (3+)
4.4.2. Formation constant, Kf = Kc / [H2O]^n (The concentration of water is constant in aqueous reactions)
4.4.3. A ligand incr. the solubility of a slightly soluble ionic compound if it forms a complex ion w/ the cation