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Thermodynamics of Electrochemical Cells If in a cell n equivalents of reactants are converted into products, then the quantity of electricity that flows through the cell is nF, where F is the Faraday constant. If this amount of charge is transported through the cell of Emf E volts, the amount of electrical work done by the cell is nEF. Gibbs free energy decrease in a cell reaction is therefore given by; -G=nEF or G=-nEF                                                                                                                   (18) If at constant temperature and pressure (G) P,T < 0 or E cell > 0, the cell reaction can proceed spontaneously. However, if(G) P,T =0 E cell = 0, the cell is in a state of equilibrium.. or Eqn (18) provides a method for determining free energy changes of electrochemical cell reactions. The enthalpy change for a cell reaction may also be deduced from Emf measurements. From Gibbs-Helmoholtz equation we have; H =-G –T [] P      

Application of EMF Measurements i) Determination of Equilibrium Constant Measurement of the standard Emf of the cell, E° Cell , enables one to evaluate the equilibrium constant for the electrode reaction. The relation between the standard free energy change and the equilibrium constant of a reaction is given by: G 0 = -RT In K But the standard free energy is related to the standard electrode potential by the expression: G 0 = -nE 0 F  Hence E 0 = In K At 298K E 0 = log K                                                                                                                   Exercise 4 For the following electrochemical cell Zn/Zn 2+ //Fe 3+ ,Fe 2+ /Pt Whose standard Emf is 1 .534V, the overall cell reaction is Fe 3 + + 1/2Zn  Fe 2+ +1/2 Zn 2+ ii) Determination of Solubility Products This is a useful technique to evaluate the solubility product of sparingly soluble salt such as AgCI. The saturated solution of AgCl in water is so dil

Debye- Hückel  Theory of Electrolytes Assumptions i) Electrolytes are completely dissociated into ions into solutions ii) The solutions are dilute, with a concentration of 0.01 m or lower iii) on average, each ion is surrounded by ions of opposite charge, forming an ionic atmosphere. Because γ+ nor γ- could be measured directly, the final result is expressed in terms of the mean ionic activity coefficient of the electrolyte  as follows logγ± = -0.509 z + z_√I                                                                            (34) This equation is known as the Debye-Hückel limiting law where     signs denote the magnitude but not the signs of the product z+z-. The quantity I called the ionic strength, is defined as follows                                                                                    (35) where mi and zi are the molality and charge of the ith ion in the electrolyte respectively Exercise 6 Calculate the mean activity coefficie

Ionic Activity For an ideal NaCl solution, the chemical potential, µ NaCl is given by            µ NaCl = µ Na + +µ Cl -                                                                                        (24) Because cations and anions cannot be studied individually, µ Na+ and µ Cl- are not measurable. We can express the chemical potentials of the cation and anion as µ Na+ = µ o Na + + RT ln m Na + µ Cl-   = µ o Cl - + RT ln m Cl - where µ o Na + and µ o Cl - are the standard chemical potentials of the ions. Equation 24  can now be written as µ NaCl = µ o NaCl + RT ln m Na + m Cl - where µ o NaCl = µ o Na + + µ o Cl - In general, a salt with the formula M v+ X v- dissociates as follows: M v+ X v-               v + M z+ + v - X z- where v + and v - are the numbers of cations and anions per unit and z + and z - are the numbers of charges on the cation and anion, respectively. The chemical potential is given by µ = v + µ + + v - µ -  

Application of EMF Measurements Determination of Equilibrium Constant Measurement of the standard Emf of the cell, E° Cell , enables one to evaluate the equilibrium constant for the electrode reaction. The relation between the standard free energy change and the equilibrium constant of a reaction is given by: G 0 = -RT In K But the standard free energy is related to the standard electrode potential by the expression: G 0 = -nE 0 F  Hence E 0 = In K At 298K E 0 = log K                                                                                                                   Exercise 4 For the following electrochemical cell Zn/Zn 2+ //Fe 3+ ,Fe 2+ /Pt Whose standard Emf is 1 .534V, the overall cell reaction is Fe 3 + + 1/2Zn  Fe 2+ +1/2 Zn 2+ Calculate the equilibrium constant

The Concentration Dependence of Cell Emf - The Nernst Equation Consider an electrochemical equilibrium whose overall cell reaction is represented by the scheme - aA+bB cC+dD                                                                                                           (3) where a, b, c and d are the number of moles of the reagents taking part in the reaction The reagent or reagents could be gases, ions or molecules in solution. Solids may also be involved but they are treated as constants.  For 1mole of species A, the free energy is given by G A =G A °+RT in a A                                                                                            (4) where G A is the electrochemical free energy, and G A ° is the standard free energy and a A is the activity of reagent A. For a moles of reagent A, aG A = aG A + aRT ln a A aG A + RT in (a A ) a Similar-expressions can be written for the other three reagents. The overall free energy change is th