Equilibrium Electrochemistry

Equilibrium Electrochemistry • Electrochemistry: study of the relationship between chemical change and electrical energy Equilibrium Electrochemistry • Investigated through the use of electrochemical cells: that incorporate oxidation-reduction (or redox reaction) to produce electrical energy • Equilibrium electrochemistry: the study of electrochemical equilibrium properties in solutions (inside electrochemical cells 1 Equilibrium Electrochemistry • Thermodynamic principles explain how cells work • The beauty of being able to make very precise measurements of currents and potential differences (‘voltages’) means that electrochemical methods can be used to determine thermodynamic properties of reactions that may be inaccessible by other methods • Whether an electrochemical process releases or absorbs energy, it always involves movement of electrons from one chemical species to another in a redox reaction. • Let’s review redox terminology! Review A redox reaction involves a change in oxidation numbers. Oxidation: loss of electrons Reduction: gain of electrons Oxidizing agent: causes oxidation of another by accepting e- from it Reducing agent: causes reduction by giving eReduction-oxidation always occurs in pairs and the number of electrons gained by the oxidizing agent always equals the number lost by the reducing agent. 2 Example What is being oxidized and reduced in the following: Cd(s) + NiO2(s) + 2H2O(l)  Cd(OH)2(s) + Ni(OH)2(s) Overview of Electrochemical Cells • Electrochemical cells consist of two electrodes (conduct electricity between cell and surroundings) that are dipped into electrolyte (mixture of ions, usually in aqueous solution [but can also be a solid or liquid]) that are involved in the reaction or that carry the charge. – Oxidation: anode – Reduction: cathode • An electrode and its electrolyte comprise an electrode compartment • Salt bridge – used if electrolytes are different (KNO3, KCl) 3 Overview of Electrochemical Cells Two types of cells based on general thermodynamics: 1. Voltaic cell (or galvanic cell): an electrochemical cell that produces electricity as a result of a spontaneous reaction occurring inside it.  G < 0 - flashlights, CD player, car 3. Electrolytic cell: an electrochemical cell in which a nonspontaneous reaction is driven by an external source of current  Voltaic or Galvanic Cells Reaction of zinc metal with Cu2+ solution • Electrons are transferred but system does not generate electrical energy (oxidizing reagent and reducing agent are in physical contact). • If half-reactions are physically separated and connected by external circuit, electrons are transferred by travelling through the circuit, producing an electric current. • Separation of half-reactions is key to a voltaic cell. G > 0 - electroplating 4 Voltaic or Galvanic Cells Voltaic or Galvanic Cells • Two parts are connected by a salt bridge – Tube containing a concentrated solution of electrolyte (KNO3, KCl) which allows ions of electrolyte to migrate • Oxidation (anode): Zn metal bar immersed in a electrolyte (ZnSO4). Zn bar conducts released electrons out of its half-cell. • Reduction (cathode): Cu metal bar immersed in Cu2+ electrolyte (CuSO4). Cu conducts electrons into its half-cell. • Electrode charges are determined by source of electrons and direction of electron flow. (In any voltaic cell, the anode is - and the cathode +.) • Uses a spontaneous reaction (ΔG < 0) to generate electrical energy. Zn2+ • What would happen if no salt bridge? If only a wire, a few electrons pass, but then current stops – – – – Right-hand becomes negative because of the transfer of e- into it Left-hand becomes positive because electron leave This would prevent any further transfer of electrons Adding a salt bridge allows the two half-cells to lose their excess charge and permits more electrons to flow 5 Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s) How Does a Voltaic Cell Work? • By using a light bulb or voltmeter we can see that the Zn/Cu2+ cell generates electrical energy but why? – Why do the electrons flow in the direction shown? • Electrons flow from the zinc rod to the copper rod and the voltmeter registers +1.10 V when switch is first closed. – What is the driving force? • Spontaneous reaction occurs due to different abilities of metals to give up their electrons and ability of electrons to flow through circuit. – Electrons flow from anode to cathode because of a difference in electrical potential energy – Higher in anode than in cathode 6 Cell Potential Cell Potential and Standard Cell Potential • Difference in potential energy per electrical charge between two electrodes is measured in volts (1 V = 1 J C-1) • Electrical energy can do work and is proportional to the difference in electrical potential between the two electrodes. • Difference is measured with a voltmeter – Reading is known as cell potential (Ecell) or electromotive force (emf) or voltage of the cell – The “pull” or driving force on the electrons. • A cell potential measured under standard state conditions is called the standard cell potential (E°cell) • 298 K, 1 atm for gases, 1 M solns, pure solids E°cell = E°ox + E°red 7 Standard Hydrogen Electrode Standard Potential Tables F2 + 2e–  2F– +2.87 2H+ + 2e–  H2 e– +1.81 Pb2+ +1.69 Sn2+ Co3+ Au+ + + e–  Co2+  Au Ce4+ + e–  Ce3+ Br2 + 2e–  2Br– Ag+ + e–  Ag Cu2+ + 2e–  Cu AgCl + e–  Ag + Cl– Sn4+ + 2e–  Sn2+ +1.61 +1.09 + 2e– + 2e–  Pb  Sn In3+ + 3e–  In Fe2+ + 2e–  Fe +0.80 Zn2+ + 2e–  Zn +0.34 V2+ + 2e– + e– V +0.22 Cs+ + e–  Cs +0.15 Li+  Li 0.0000 -0.13 -0.14 -0.34 -0.44 -0.76 -1.19 -2.92 -3.05 8 Calculation of Cell Potentials SOLUTIONS OF ELECTROLYTES Molecular and Ionic substances • Electrolyte – a substance which when dissolved in a solvent dissociates into ions, e.g. NaCl • Nonelectrolyte – a substance which does not dissociate into ions when dissolved in a solvent, e.g. sugar. • Strong electrolyte – a substance which dissociates completely into ions when dissolved, e.g. NaCl • Weak electrolyte – a substance which dissociates partially into ions when dissolved, e.g. acetic acid 9 Molecular and Ionic substances Measuring conductivity • The conductance of a solution is obtained by measuring its resistance using a modified Wheatstone bridge circuit. Variable condenser Conductivity cell Variable resistance Detector A X B AC source 10 Measuring conductivity Variation of Conductivity with Concentration κ C This is the general shape of a conductivity concentration curve for both weak and strong electrolytes. The curves for both types show a maximum but cannot be plotted on the same scale because the curve for a strong electrolyte lies well above that for a weak one. Concentration/mol m-3 Conductivity of KCl/Sm-1 Conductivity of acetic acid/Sm-1 • • • 0.1 1.3 1.07 1 12 4.1 10 102 103 2 x 103 120 1120 9820 18520 14.3 46 132 160 N.B. In many cases a saturated solution is obtained before the maximum is reached, so only the left hand part of the curve is obtainable. Substances with high conductivities are strong electrolytes (e.g. mineral acids, alkalis and most salts). The opposite is mostly organic acids and bases). 11 Variation of Conductivity with Concentration Variation of Conductivity with Concentration • Although the κ against c graph has the same shape for strong and weak electrolytes the causes are different. κ C • Although the κ against c graph has the same shape for strong and weak electrolytes the causes are different. – Weak electrolytes (not completely ionized): Increase in concentration gives more solute particles but the degree of ionization decreases – Strong electrolytes (completely ionized): Increase in concentration causes an increase in solute particles but a decrease in ionic freedom and ionic speeds. • Weak electrolytes (not completely ionized): Increase in concentration gives more solute particles but the degree of ionization decreases % Ionization Weak electrolyte Conc • Strong electrolytes (completely ionized): Increase in concentration causes an increase in solute particles but a decrease in ionic freedom and ionic speeds. 12 Variation of Molar conductivity with Concentration Concentration/mol m-3 0.1 Λ, KCl/S m2 mol-1 0.01291 0.01273 0.01224 0.01120 0.00983 Λ, acetic acid/S m2 mol-1 0.0107 1 10 102 103 2 x 103 3 x 103 0.00926 0.00883 0.00410 0.00143 0.00046 0.000132 0.00080 0.000054 0 Variation of Molar conductivity with Concentration Strong electrolytes c Weak electrolytes General shape of molar conductivity versus dilution curves for strong and weak electrolytes. 0 c Strong electrolytes Weak electrolytes Dilution i.e. c-1 • For a strong electrolyte a maximum is reached at low concentrations and the Λo value can be obtained by extrapolation. • The maximum for weak electrolytes is obtained at concentrations which are too low for experimental measurements. • The maximum value for the molar conductivity of an electrolyte, reached at low concentrations, is known as the molar conductivity at zero concentration, Λo. It may also be known as the molar conductivity at infinite dilution, Λ∞. It is the conducting power of 1 mole of an electrolyte which is completely split up into noninteracting ions. • For weak electrolytes, Λ∞ values must be obtained indirectly. 13 Worked Examples Worked Examples 14 Worked Examples IONICS 3. The limiting molar conductivities (in S cm2 mol-1) at 298 K of KCl, KNO3 and AgNO3 are 149.9, 145.0 and 133.4 respectively. (i) Calculate the limiting conductivity of AgCl. (ii) If the conductivity of saturated solution of AgCl in water at that temperature was found to be 1.83 x 10-6 S cm-1, find the solubility and solubility product of AgCl at this temperature. 4. The resistance of 0.002 mol dm-3 aqueous acetic acid solution at 25 °C in a cell (cell constant 0.2063 cm-1) measured was found to be 2930 S-1 and the molar conductivity of acetic acid at infinite dilution at 25 °C is 387.9 S cm2 mol-1. Estimate the value of degree of dissociation under those conditions. 15 Kohlrausch’s Law Kohlrausch’s Law 16 Mechanism of Electrolytic Conductance Mechanism of Electrolytic Conductance 17 Mechanism of Electrolytic Conductance Ostwald's Dilution Formula (1888) 18 Strong Electrolytes • Arrhenius theory inconsistent • Ostwald dilution law is not obeyed by acids stronger than acetic acid. • The heats of neutralization of strong acids were too constant to be consistent with the Arrhenius theory. • The fall in Λ with increasing concentration for strong electrolytes must therefore be attributed to some cause other than a decrease in the degree of dissociation. • Debye-Hückel theory – decrease in Λ of a strong electrolyte is due to mutual interference of the ions which becomes more pronounced as the concentration increases. Strong Electrolytes • Arrangement of ions in solution is not completely random Na+ Cl- Cl- Na+ Na+ Na+ ClCl- Na+ • relaxation or asymmetry effect – retardation in the motion of an ion by oppositely charged ions. _ + + + + _ _ _ + + _ _ + + + + 19 Strong Electrolytes Transference or Transport numbers: t+ and t- • Electrophoretic effect – ions are attracted to solvent molecules by ion-dipole forces, when they move they drag solvent with them – ionic atmosphere moves in a direction opposite to the central ion and therefore drags solvent in the opposite direction – central ion has to travel upstream and therefore moves more slowly. • Ion association – because of strong electrostatic attractions pairs of ions can become associated in solution e.g. Na+ and SO42-. 20 Transference or Transport numbers: t+ and t- Transference or Transport numbers: t+ and tElectrolysis with inert electrodes • If a current of 96487 n C is passed through an electrolyte, CA, n mol of C+ will be discharged at the cathode and n mol of A- will be discharged at the anode. The C+ ions will carry 96487 ntC C towards the cathode whilst the A- ions will carry 96487 ntA C towards the anode. 21 Transference or Transport numbers: t+ and tAnode compartment C+ loss of ntC A- ntA in Cathode compartment C+ ntC in n out n out Loss of n - ntC Loss of n - ntA = (n(1-tC) = n(1 – tA) = ntA = ntC A- loss of ntA CA ntC mol lost CA ntA mol lost Determination of Transport numbers: Hittorf method • Hittorf method utilises the changes in concentrations of electrolytes in the neighbourhood of cathode and anode as a result of the difference in the velocities of the two ions of an electrolyte for determination of transport numbers. central • The solution to be electrolysed is placed in the cell, and a small current is passed between the electrodes for a short period of time (to minimise thermal, and resulting diffusion effects). • The solution is run through the taps and analysed for concentration changes 22 Hittorf method - example • Determination of Transport numbers: Moving Boundary Method The electrolysis of HCl takes place in a Hittorf cell. The Anode and the Cathode are each 500 ml acid. 100 mA of current flows through the electrolyte for 1 hour. The following concentrations were measured before electrolysis of HCl; 10 mmol in each compartment. [Λ∞ (H+) = 349.8 S cm2 mol-1 and Λ∞ (Cl-) = 76.4 S cm2 mol-1) (i) Calculate the limiting conductivities t- and t+ (ii) No of moles of H2 at cathode (iii) Concentration of HCl after electrolysis Soln t- = Λ∞ (Cl-) / [ Λ∞ (Cl-) + Λ∞ (H+) ] and from here t+ can be calculated nanode = canoed. Vanode = After electrolysis: H+ + Cl-  ½ H2 + ½ Cl2 nHCl = -It/F (Faradays law) 23 Determination of Transport numbers: Moving Boundary Method Moving boundary - example 24 Ionic Mobilities Ionic Mobilities 25 Ionic Mobilities Equilibrium Electrochemistry • Galvanic cell – an electrochemical cell that produces electricity as a result of a spontaneous reaction occurring inside it • Electrolytic cell – an electrochemical cell in which a nonspontaneous reaction is driven by an external source of current • A cell in which the overall cell reaction has not reached equilibrium can do electrical work as the reaction drives electrons through an external circuit. The work that a given transfer of electrons can accomplish depends on the potential difference between the two electrodes. • The potential difference is called the cell potential (measured in V). 26 Equilibrium Electrochemistry Gibbs Energy and Electrical Work E°cell G° K Rxn Under Stand State Conditions Positive Negative >1 Spontaneous (favours products) 0 0 =1 Favours reactants and products equally Negative Positive <1 Nonspontaneous (favours reactants) 27 Nernst Equation • Cell need not operate at standard state conditions. – We can calculate potential of a cell in which some or all components are not in std states. – Need to understand how cell potential changes with concentration and/or temperature changes. 0.0592 E  E  logQ n Nernst Equation • We have seen earlier that  a yaz   revG   revG   RT ln Ya Zb   a A aB    revG   RT ln Q u • where Q is the reaction quotient. • It follows that if we divide through by –νF: E  revG RT  ln Q F F E  E  RT ln Q F 28 Concentration cells • Consider the concentration cell Cells at equilibrium • If the reaction is at equilibrium then Q = K. • A chemical reaction at equilibrium cannot do work and hence it generates a zero potential difference between the electrodes of the galvanic cell. • where the solutions L and R have different molalities. The cell reaction is a Q  L  1 aR RT a L E ln F aR • Setting E = 0 and Q = K in the Nernst equation gives: . ln K  FE  RT If R is the more concentrated solution, E > 0. 29 Application 1: Solubility products Application 1: Solubility products E  Eo  RT RT . ln(a Ag  .aCl  )  E o  . ln K SP F F 30 Application 2: Measurement of activity coefficients Application 2: Measurement of activity coefficients RT RT ln[m u ]2  ln    F F 2 RT 2 RT ln m u  ln    E  F F E  E  • where γ±, equal to (γ+ γ-)1/2, is the mean activity coefficient. • The above equation can be written E  E  RT ln[a a ]u F E 2 RT 2 RT ln m u  E   ln   F F 31 Application 2: Measurement of activity coefficients Application 2: Measurement of activity coefficients Example: Calculation of the emf of a cell E  2 RT ln m u F 2 RT ln   F Calculate the emf at 25 °C of the cell, Zn(s)  ZnSO4 (1.0 m)  CuSO4(0.1 m) H2(g)  Cu(s), Eº Molality/mol kg‐1 • At any molality the y-value minus Eº yields  2 RT ln   F • from which the activity coefficient can be evaluated. 32 Application 4: Temperature coefficients of cell emfs  G    S   T  P  dE o   r S o     dT  F Application 3: Evaluating a standard potential   Go  E o   r   F    dE o      r H o  F  E o  T    dT    33 Application 2: Measurement of activity coefficients Example: Calculation of the emf of a cell The standard potential of the cell Pt(s)H2(g)  HBr(aq)  AgBr(s)  Ag(s) was measured over a range of temperatures and data were found to fit the following equation. ECell/V = 0.07131 - 4.99 x 10-4 (T/K -298) - 3.45 x 10-6 (T/K 298)2 The cell reaction is, AgBr(s) + ½H2(g) → Ag(s) + HBr(aq) Evaluate the standard reaction Gibbs energy, enthalpy and entropy at 298 K. 34