The Concentration Dependence of Cell Emf - The Nernst Equation

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
GA=GA°+RT in aA                                                                                           (4)
where GA is the electrochemical free energy, and GA° is the standard free energy and aA is the activity of reagent A.
For a moles of reagent A,
aGA = aGA + aRT ln aA
aGA + RT in (aA)a
Similar-expressions can be written for the other three reagents.
The overall free energy change is the free energy of the products minus free energy of the reactants:
G =Gproducts - Greactants
G = G0 + RT In
Recall  G =-nEF and G° = -nE°F
Hence
 E=E0 -                                                                                     (5)
Equation (5) is known as the Nernst equation and gives the dependence of the electrode or cell potential in terms of activities or concentrations of the reactants and products. E° is known as the standard e.m.f of the cell and it is the cell potential when the activities are all unity.
At 25°C equation (5) reduces to
E=E0 –

E=E0 –                                                                                                                                                                                                                                                 (6)
Also by definition,
G° = -RT In K = -nE0F, therefore
E0 =                                                                                         (7)
where K is the equilibrium constant for the electrode or the cell reaction and hence equation (6) can also be written as:
E=                                                                     (8)
Exercise 1
For the following cell at 298K,

Zn(s)/Zn(aq)2+ (a = I )//Pb(aq)2+ (a = 1 )/Pb(s)

(i) Write individual electrode reactions and the overall cell reaction.
(ii) Calculate E°cell.
(iii) Calculate G° of the cell reaction.
(iv) In which direction is the cell reaction spontaneous?
Given E0Zn2+/Zn = 0.762V and E0Pb2+/Pb =-0.126V


Comments

Post a Comment

Popular posts from this blog

Application of EMF Measurements

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
Read more

Limiting Molar Conductances of Weak Electrolytes

Limiting Molar Conductances of Weak Electrolytes One of the immediate application of Kohlrausch’s law at infinite dilution is the   determination of the limiting molar conductance at infinite dilution m   of weak electrolytes. These values cannot be determined by extrapolation of a plot of m versus √C (see fig 2) as in the case of strong electrolytes. In the case of weak electrolytes, an indirect method is employed For example in the case of acetic acid, its m  may be determined indirectly as follows; m ( CH 3 COOH) = m  (CH 3 COONa) + = m (HCl) - m (NaCl) =91.0+425.0-126.5 = 389.5 -1 cm 2 mol -1 or simply; m ( CH 3 COOH) =  CH3COO - + H + = 40.9 + 348.6 = 389.5 -1 cm 2 mol -1
Read more

Validity and Reliability of a Test

Validity and Reliability of a Test    Introduction   An important part of social science research is the quantification of human behavior that is, using measurement instruments to observe human behavior. The measurement of human behavior belongs to the widely accepted positivist view, or empirical-analytic approach, to discern reality. Because most behavioral research takes place within this paradigm, measurement instruments must be valid and reliable. Reliability Reliability is the extent to which measurements are repeatable –when different persons perform the measurements, on different occasions, under different conditions, with supposedly alternative instruments which measure the same thing. In sum, reliability is consistency of measurement (Bollen, 1989), or stability of measurement over a variety of conditions in which basically the same results should be obtained. Methods of testing reliability   Because reliability is consistency of measurement over time o
Read more