Chapter 11 Electrochemistry
Electromotive Force (電動勢) 1 joule of work is produced or required when 1 coulomb of charge is transferred between two points in the circuit that differ by a potential of 1 volt.
Galvanic Cells (Voltaic Cells ) • Galvanic cell - an electric cell that generates an electromotive force by an irreversible conversion of chemical to electrical energy; cannot be recharged. • The electron flow from the anode to the cathode is what creates electricity. • In a galvanic cell, the cathode is positive while the anode is negative, while in a electrolytic cell, the cathode is negative while the anode is positive.
Standard Hydrogen Electrode 2H+(aq)+Zn(s) →Zn+2(aq)+H2(g) Oxidation half-reaction Zn(s) →Zn+2(aq)+2e- Standard hydrogen electrode 2H+(aq)+2e-→H2(g) The cathode consists of a platinum electrode in contact with 1 M H+ ions and bath by hydrogen gas at 1 atm. We assign the reaction having a potential of exactly 0 volts.
The Cell Potentials E0cell=E0(cathode)-E0 (anode) The value of E0 is not changed when a half reaction is multiplied by an integer. 2Fe+3+2e-→2Fe+2E0(cathode)=0.77 V Cu →Cu+2+2e- -E0 (anode)=-0.34 V Cu+2Fe+3 →2Fe+2+Cu+ E0cell=E0(cathode)-E0 (anode)=0.43 V reduction oxidation
Cell Diagrams For a copper-zinc voltaic cells Cu’ Zn ZnSO4(aq) CuSO4(aq) Cu 1. A vertical line indicates a phase boundary. 2. A dashed vertical line indicates the phase boundary between two miscible liquid. Dashed line
PtL|H2(g)|HCl(aq)|AgCl(s)|Ag| PtR Anode: H2(g)=2H++2e-(PtL) Cathode: [AgCl(s)+e-(PtR)=Ag+Cl-] ×2 Overall: 2AgCl(s)+ H2(g)=2Ag+ 2H++2Cl- CuL|Cd(s)|CdCl2(0.1M)|AgCl(s)|Ag(s) |CuR Anode: Cd=Cd+2+2e- Cathode: [AgCl+e-=Ag++Cl-] ×2 Overall: Cd+2AgCl=2Ag+Cd+2+2Cl-
Nernst Equation • E0: standard reduction potential • n: moles of electrons • F: Faraday constant 96485 C/mol
Thermodynamic-Free Energy • The maximum cell potential is directly related to the free energy difference between the reactants and the products in the cell.
Reaction Quotient (Q) The positive E (fR>fL ) means that Q<K0. As Q increases toward K0, the cell emf decreases, reaching zero when Q=K0
The Equilibrium Constant of a Cu-Zn Cell Zn+Cu+2(aq)=Zn+2(aq)+Cu E0=0.34V-(-0.76V)=1.10V
AgL Ag+(0.1M) Ag+(1M) AgR PtL Cl2(PL) HCl(aq) Cl2(PR) PtR
Liquid Junction Potential • Liquid junction: the interface between two miscible electrolyte solutions. • Liquid-junction potential: A potential difference between two solutions of different compositions separated by a membrane type separator. • The salt will diffuse from the higher concentration side to the lower concentration side.
H+ H+ Cl- Ag+ ＋ ＋ ＋ ＋ ＋ ＋ ＋ ＋ ＋ － － － － － － － － － － ＋ ＋ ＋ ＋ ＋ ＋ ＋ ＋ ＋ － － － － － － － － － － HCl HCl AgNO3 HNO3 a2 < a1 a2 = a1
Liquid Junction Potential • The diffusion rate of the cation and the anion of the salt will very seldom be exactly the same. • Assume the cations move faster; consequently, an excess positive charge will accumulate on the low concentration side, while an excess negative charge will accumulate on the high concentration side of the junction due to the slow moving anions. • When the cell has a liquid junction, the observed cell emf includes the additional potential difference between the two electrolyte solutions.
How to Solve the Liquid Junction Potential • Liquid junction potentials are generally small, but they certainly cannot be neglected in accurate work. • By connecting the two electrolyte solutions with a salt bridge, the junction potential can be minimized. • A salt bridge consist of a gel made by adding agar to a concentrated aqueous KCl solution.
A Cell Diagrams Containing a Salt Bridge For a copper-zinc voltaic cells Cu’ Zn ZnSO4(aq) CuSO4(aq) Cu A salt bridge is symbolized by two vertical dashed lines.
Estimate the Liquid Junction Potential from EMF Measurement Ag AgCl(s) LiCl(m) NaCl(m) AgCl(s) Ag m(LiCl)=m(NaCl), E0=0 Anode: Ag+Cl- (in LiCl(aq))=AgCl+e- Cathode: AgCl+e-=Ag+Cl- (in NaCl(aq))
Applications of Electrochemistry • pH meter • ATP Synthase • Potential for a resting nerve cell
Determination of pH Pt H2(g) soln. X KCl(sat.) Hg2Cl2(s) Hg Pt’ 1/2H2(g)+1/2Hg2Cl2=Hg(l)+H+(aq,X)+Cl-(aq) The cell reaction and emf Ex: Junction potential between X and the saturated KCl solution
If a second cell is set up to except that solution X is replaced by solution S, the emf Es of this cell will be:
Reference electrode: saturated calomel electrode (SCE) Sensing electrode: Ion Selective Electrode (ISE) Pt Ag AgCl(s) HCl(aq) glass soln. X KCl(sat.) Hg2Cl2(s) Hg Pt’
Determine the pH of a Solution by a pH Meter • When the glass electrode is immersed in solution X, an equilibrium between H+ ions in solution and H+ ions in the glass surface is set up. • This charge transfer between glass and solution produces a potential difference between the glass and solution.
Ion Selective Electrodes (ISE) for PH Meter • An ion selective electrode contains a glass, crystalline, or liquid membrane whose nature is such that the potential difference between the membrane and an electrolyte solution it is in contact with is determined by the activity of one particular ion. • It is dependent on the concentration of an ionic species in the test solution and is used for electro-analysis.
Marcus theory for Electron transfer reactions • Rudolph A. Marcus was awarded the 1992 Nobel Prize in chemistry
Membrane Equilibrium In a closed electrochemical system, the phase equilibrium condition for two phases a and b
Free-energy change during proton movement across a concentration gradient • The movement of protons from the cytoplasm into the matrix of the mitochondrion.
Proton Pumping • Proton pumping maintains a pH gradient of 1.4 units, then DpH = + 1.4 • DG = -2.303RTΔpH =- 2.303 (8.315 × 10-3 kJ/mol)(298K)(1.4) = - 7.99 kJ/mol Proton concentration gradient
Free-energy change during solute movement across a voltage gradient • In mitochondria, electron transport drives proton pumping from the matrix into the intermembrane space. • There is no compensating movement of other charged ions, so pumping creates both a concentration gradient and a voltage gradient. • This voltage component makes the proton gradient an even more powerful energy source.
Membrane Potential • Dym = yin – yout=0.14 V • DG =-nF Dym=-(1)(96485)(0.14 ) = - 13.5 kJ/mol
Proton-motive force • Proton-motive force (DP) is a Dy that combines the concentration and voltage effects of a proton gradient. • DG=-nFDP = - 2.303 RT DpH + nFDym =(-7.99 kJ/mol)+( - 13.5 kJ/mol) = -21.5 kJ/mol
ATP synthesis • Mitochondrial proton gradient as a source of energy for ATP synthesis • Estimated consumption of the proton gradient by ATP synthesis is about 3 moles protons per mole ATP. • DG = 50 kJ/mol for ATP synthesis • DG = 50 + 3(- 21.5) = - 14.5 kJ/mol • The synthesis of ATP is spontaneous under mitochondrial conditions.
Potential for a resting nerve cellGoldman-Hodgkin-Katz equation P: permeability (穿透率) D: diffusion coefficient (擴散係數) t: thickness of membrane (薄膜厚度)
Concentrations cell △E(K+)=-95 mV △E(Na+)=+57 mV △E(Cl-)=-67 mV Resting Nerve Cell of a Squid P(K+) /P(Cl-)=2 P(K+)/P(Na+)=25 The observed potential for a resting squid nerve cell is about -70 mV at 25oC.
Resting Nerve Cell of a Squid • The observed potential for a resting squid nerve cell is about -70 mV at 25oC. • Hence Cl- is in electrochemical equilibrium, but K+ and Na+ are not. • Na+ continuously flows spontaneously into the cell and K+ flows spontaneously out. • Na+-K+ pump
Batteries • Secondary batteries: Voltaic cells whose electrochemical reactions can be reversed by a current of electrons running through the battery after the discharge of an electrical current. • A secondary battery can be restored to nearly the same voltage after a power discharge.
Lead Storage battery Anode reaction Pb+HSO4-→ PbSO4+H++2e- Cathode reaction PbO2+HSO4-+3H++2e- → PbSO4+2H2O Cell reaction Pb+PbO2+ 2H++2HSO4-→ 2PbSO4+2H2O
Dry Cell Battery Anode reaction Zn→ Zn2++2e- Cathode reaction 2NH4++2MnO2+2e- → Mn2O3+2NH3+H2O Cell reaction 2MnO2+2NH4Cl+Zn→ Zn(NH3)2Cl2 + Mn2O3 +H2O