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Electrolysis of Hydrochloric Acid: Faradaic and Non-Faradaic Currents Consider the electrolysis of hydrochloric acid using platinum electrodes. Initially when the applied potential is less than the cell Emf no electrolysis takes place and hence there will be no hydrogen or chlorine gas in contact with the respective electrodes. The electrodes will not be in equilibrium with the solution. When an external Emf  is applied across the electrodes, hydrogen ions move towards the cathode and are discharged (reduced) to form hydrogen gas. H + (aq) +e ------------->1/2H 2(g) Similarly chloride ions move towards the anode are discharged (oxidized) to form chlorine gas. Cl - (aq) ----> 1/2Cl 2(g) + e As soon as traces of these gases appear or are in contact with their respective electrodes the cell behaves as a galvanic (chemical) cell with an Enif which is in opposition to the applied Emf This Emf known as the back Emf, will be given by equation (1) rewritten as; E = E

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

Free Energy Changes and Cell Emf’s The reversible cell e.m.f. (E cell ) is related to the free energy change G by the equation G = -nFE Or  G 0 = -nFE 0 where n is the number of electrons involved in the reaction F is the Faraday constant and E is thereversible e.m.f of the cell. If E cell >0 and hence G<0, cell reaction is spontaneous in the given direction and vice versa. If E cell =0 and hence G= 0, then cell is in a state of equilibrium.

Electrode Reactions and Cell E.m.f The standard procedure is to write the left-hand side electrode as an oxidation reaction and the right-hand side electrode as a reduction reaction. The two half-cell reactions are added to give the overall cell reaction and the overall cell e.m.f. For the cell given above, the individual electrode reactions and the overall cell reaction are: Left electrode:                        H 2(g) 2H + (aq) + 2e E° = 0.00V Right electrode:                      Cu 2 + +2e Cu (s) E° = 0.34V Overall cell reaction:   H 2(g) + Cu 2+ -> 2H + (aq) + Cu (s) E° cell = 0.34V Positive e.m.f of the cell indicates that the reaction has the tendency to occur from left to right, i.e. in the direction indicated. Conversely a negative em.f indicates the reaction occurs from right to left. In the case of positive e.m.f the electrons flow from left to right in the outer-circuit and positive electricity passes from left to right inside the cell. By comb