As a general rule electrochemical cell potentials

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As a general rule, electrochemical cell potentials follow the Nernst Equation , × = - × × 0 R T E E lnQ n F (4.11) E 0 is the electric potential for the reaction of interest under standard conditions, R = 8.3145 J/mol -K is the universal gas constant, n is the number of electrons transferred from reactants to products, and F = 96.500 kJ/V·mol = 23.061 kcal/V mol (4.12) is the “ Faraday ” associated with the energy carried by a mole of electrons moving through a potential difference of 1 V ( V = volt). Further, in the Nernst Equation (4.11), Q is the reaction quotient. This is the ratio of actual concentrations for the reaction prevalent at a given extent (relative progress). Inserting numerical values for the constants and assuming room temperature is 25 ° C ( T = 298 K ), Equation 4.11 can be written as
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Chemistry 132 Lab Manual Page 42 = - × 0 10 0.059V E E log Q n (4.13) Note that the natural log of Equation 4.13 has been converted to logarithm for base 10. For a generic overall cell reaction of the type A B C D n A(s) n B (aq) n C(s) n D (aq) + + + ® + (4.14) Equation 4.13 for the cell potential becomes E cell = E cell 0 0.059V n log 10 D + (aq) n D B + (aq) n B (4.15) The concentrations (activities) of solids have unit values and drop out of the equation. The standard cell potential E 0 cell is measured at standard conditions, i.e., at 25 0 C, 1 atm of pressure, and 1 M concentration. The quantity n is the number of electrons transferred at either electrode. When the concentrations [D + ] = [B + ] = 1.00 M, then D + nD = B + nB and E cell equals the standard cell potential. This suggests a viable experimental method for its determination. Measurement of Cell Voltages In this first part of the experiment, the voltages of several different cells are to be measured. As discussed above, the potential of any half-cell reaction may be adopted as a suitable standard, E = 0 . The potentials of all other cells can then be deduced from a relative measurement. In the experiment, five different half-cells will be studied. One of the overall cell reactions is Cu(s) Ag (aq) Cu (aq) Ag(s) + + + ® + 2 2 2 (4.16) Equation 4.15 predicts a cell potential of E cell = E cell 0 0.059V 2 i log 10 Cu 2 + (aq) Ag + (aq) 2 (4.17) For this reaction the number of exchanged electrons is n=2 . E Cell would equal the standard cell potential when the copper and silver salt solutions have 1 M concentrations, since the logarithmic term would vanish. If one decreases the Cu 2+ concentration, keeping [Ag + ] at 1 M, the potential of the cell will increase by about 0.03 V (volts) for each factor of ten decrease in the Cu 2+
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Chemistry 132 Lab Manual Page 43 concentration. Ordinarily it is not convenient to change concentrations of an ion by several orders of magnitude at once, so in general, concentration effects in cells are relatively small. However, if a species is added that forms a complex with Cu 2+ aq , then [ Cu 2+ ] aq
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