Atkins & de Paula: Elements of Physical Chemistry: 5e Chapter 9: Chemical Equilibrium: Electrochemistry

End of chapter 9 assignments Discussion questions: 1, 4 Exercises: 1, 3, 9, 12, 13 (include last 3?) Use Excel if data needs to be graphed

Homework assignments Did you: –Read the chapter? –Work through the example problems? –Connect to the publisher’s website & access the “Living Graphs”? –Examine the “Checklist of Key Ideas”? –Work assigned end-of-chapter exercises? Review terms and concepts that you should recall from previous courses

Build Yourself a Table… TERMUNITSSYMBOL Potentialvolts V Resistanceohms  CurrentampI Siemens  -1 (ohm -1 ) S Resistivityohm meter  Conductivityohm -1 meter -1  Molar conductivityS m 2 mol -1 mm Ionic conductivity mol/dm 3 mS m 2 mol -1 + – Terms, Units, & Symbols  is an uppercase

Foundational concepts What is the most important difference between solutions of electrolytes and solutions of non-electrolytes? Long-range (Coulombic) interactions among ions in solutions of electrolytes

The Debye-Hückel theory Activity, a, is roughly “effective molar concentration” 9.1a a J =  J b J /b  b  = 1 mol/kg 9.1b a J =  J b J  = activity coefficient –treating b as the numerical value of molality If a is known, you can calculate chemical potential:  μ J = μ J  + RT ln a J (9.2) 

The mean activity coefficient Mean activity coefficient   = (  +   – ) ½  For MX,   = (  +   – ) ½ For M p X q,   = (  + p   – q ) 1/s s = p+q So for Ca 3 (PO 4 ) 2,   = (  + 3   – 2 ) 1/5

Debye-Hückel theory Fig 9.1 (203) A depiction of the “ionic atmosphere” surrounding an ion The energy of the central ion is lowered by this ionic atmosphere

Debye-Hückel theory Debye-Hückel limiting law: log   = –A|z +  z – |  I ½ –   is the mean activity coefficient –I = ionic strength of the solution I = ½(z + 2 b + + z – 2 b – ) [b = molality] –A is a constant; A = for water –z is the charge numbers of the ions p.203

The extended Debye-Hückel law log   = – + C.I –   is the mean activity coefficient –I = ionic strength of the solution I = ½(z + 2 b + + z – 2 b – ) –A is a constant; A = for water –B & C = empirically determined constants –z = the charge numbers of the ions A |z +  z – | I ½ 1 + B. I ½ p.203

Debye-Hückel theory Fig 9.2 (203) (a) the limiting law for a 1,1-electrolyte (B & C = 1) (b) the extended law for B = 0.5 (c) the extended law extended further by the addition of the C  I term [in the graph, C=0.2]

The migration of ions Ions move Their rate of motion indicates: –Size, effect of solvation, the type of motion Ion migration can be studied by measuring the electrical resistance in a conductivity cell V = IR

The migration of ions V = IR Resistivity (  ) and conductivity (  ) And  = 1/  and  = 1/  Drift velocity, s = u E Where u (mobility) depends on a, the radius of the ion and , the viscosity of the solution

Conductivity cell Fig 9.3 (204) The resistance is typically compared to that of a solution of known conductivity AC is used to avoid decomposition products at the electrodes Conductivity bridge

Do you see any trends? T9.1 Ionic conductivities, /(mS m2/mol)*

T9.2 Ionic mobilities in water at 298 K, u/(10-8 m2 s-1 V-1) Do you see any trends?

The hydrodynamic radius The equation for drift velocity (s) and the equation for mobility (u) together indicate that the smaller the ion, the faster it should move… But the Group 1A cations increase in radius and increase in mobility! The hydrodynamic radius can explain this phenomenon. Small ions are more extensively hydrated. s = u E

Proton conduction through water Fig 9.4 (207) The Grotthus mechanism The proton leaving on the right side is not the same as the proton entering on the left side

Determining the Isoelectric Point Fig 9.5 (207) Speed of a macro- molecule vs pH Commonly measured on peptides and proteins (why?) Cf “isoelectric focusing”

Types of electrochemical rxns Galvanic cell—a spontaneous chemical rxn produces an electric current Electrolytic cell—a nonspontaneous chemical rxn is “driven” by an electric current (DC)

Anatomy of electrochemical cells Fig 9.6 (209) Fig 9.7 (209) The salt bridge overcomes difficulties that the liquid junction introduces into interpreting measurements

Half-reactions For the purpose of understanding and study, we separate redox rxns into two half rxns: the oxidation rxn (anode) and the reduction rxn (cathode) Oxidation, lose e –, increase in oxid # Reduction, gain e –, decrease in oxid # Half rxns are conceptual; the e – is never really free

Direction of e – flow in electrochemical cells Fig 9.8 (213)

Reactions at electrodes Fig 9.9 (213) An electrolytic cell Terms: –Electrode –Anode –Cathode

Fig 9.10 (213) Standard Hydrogen Electrode Is this a good illustration of the SHE? Want to see a better one? A gas electrode

19.3 E 0 = 0 V 2e - + 2H + (1 M) 2H 2 (1 atm) Reduction Reaction Standard hydrogen electrode (SHE) Standard Hydrogen Electrode

19.3 E 0 = 0 V Standard hydrogen electrode (SHE) Standard Hydrogen Electrode H 2 (1 atm) 2H + (1 M) + 2e - Oxidation Reaction

H 2 gas, 1 atm Pt electrode SHE acts as cathodeSHE acts as anode Standard Hydrogen Electrode

Metal-insoluble-salt electrode Fig 9.11 (214) Silver-silver chloride electrode Metallic Ag coated with AgCl in a solution of Cl – Q depends on a Cl ion

Variety of cells Electrolyte concentration cell Electrode concentration cell Liquid junction potential

Redox electrode Fig 9.12 (215) The same element in two non-zero oxidation states

The Daniell cell Fig 9.13 (215) Zn is the anode Cu is the cathode

The cell reaction Anode on the left; cathode on the right Cell Diagram Zn (s) + Cu 2+ (aq) Cu (s) + Zn 2+ (aq) [Cu 2+ ] = 1 M & [Zn 2+ ] = 1 M Zn (s) | Zn 2+ (1 M) || Cu 2+ (1 M) | Cu (s) anodecathode

Measuring cell emf Fig 9.13 (217) Cell emf is measured by balancing the cell against an opposing external potential. When there is no current flow, the opposing external potential equals the cell emf.

The electromotive force The maximum non-expansion work (w’ max ) equals  G [T,p=K] (9.12) Measure the potential difference (V) and convert it to work to calculate  G  r G = –  FE (F = kC/mol) E = – rGrG FF

The electromotive force  r G = –  FE  r G =  r G  + RT ln Q E = E  – ln Q E  = At 25°C, = mV E is independent of how the rxn is balancedRT FFFF rGrGrGrG FFFF RTF

Cells at equilibrium ln K =  FE  RT At equilibrium, Q = K and a rxn at equilibrium can do no work, so E = 0 So when Q = K and E = 0, the Nernst equation E = E  – ln Q, becomes…. RT FF

Cells at equilibrium ln K =  FE  RT Is simply an electrochemical expression of  r G  = – RT ln K

Cells at equilibrium If E  > 0, then K > 1 and at equilibrium the cell rxn favors products If E  < 0, then K < 1 and at equilibrium the cell rxn favors reactants 218

Standard potentials SHE is arbitrarily assigned E  = 0 at all temperatures, and the standard emf of a cell formed from any pair of electrodes is their difference: E  = E  cathode – E  anode OR E  = E  right – E  left Ex 9.6: Measure E , then calculate K

The variation of potential with pH If a redox couple involves H 3 O +, then the potential varies with pH

Table 9.3 Standard reduction potentials at 25°C (1)

Table 9.3 Standard reduction potentials at 25°C (2)

The determination of pH The potential of the SHE is proportional to the pH of the solution In practice, the SHE is replaced by a glass electrode (Why?) The potential of the glass electrode depends on the pH (linearly)

A glass electrode Fig 9.15 (222) The potential of a glass electrode varies with [H + ] This gives us a way to measue pK a electrically, since pH = pK a when [acid] = [conjugate base]

The electrochemical series A couple with a low standard potential has a thermodynamic tendency to reduce a couple with a higher standard potential A couple with a high standard potential has a thermodynamic tendency to oxidize a couple with a lower standard potential

E 0 is for the reaction as written The more positive E 0 the greater the tendency for the substance to be reduced The more negative E 0 the greater the tendency for the substance to be oxidized Under standard-state condi- tions, any species on the left of a given half-reaction will react spontaneously with a species that appears on the right of any half-reaction located below it in the table (the diagonal rule)

The half-cell reactions are reversible The sign of E 0 changes when the reaction is reversed Changing the stoichio- metric coefficients of a half-cell reaction does not change the value of E 0 The SHE acts as a cath- ode with metals below it, and as an anode with metals above it

The determination of thermodynamic functions By measuring std emf of a cell, we can calculate Gibbs energy We can use thermodynamic data to calculate other properties (e.g.,  r S  )  r S  =  F(E  – E  ’) T – T ’

Determining thermodynamic functions Fig 9.16 (223) Variation of emf with temperature depends on the standard entropy of the cell rxn

Key Ideas

The End …of this chapter…”

Box 9.1 pp207ff Ion channels and pumps