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(c) (d)
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Thus, Eq. (c) corresponds to scheme (a) and Eq. (d) to scheme (b). The flow of the charge is due to the chemical forces described by the affinity of the cell reaction, and at the same time to the electrical forces measured by the electrical potential difference. The affinity of the reaction is given by the algebraic sum of the chemical potentials of all the substances participating in the reaction multiplied by the corresponding stoichiometric coefficients (which are positive for reactants and negative for products); it is thus given by the decrease in the Gibbs free energy of the system AG. The sign of the affinity, however, is reversed when the reaction is written in the opposite direction. Thus, for reactions (c) and (d), -AGc=+AGd (3.1.38)
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If the reaction in the cell proceeds to unit extent, then the charge nF corresponding to integral multiples of the Faraday constant is transported through the cell from the left to the right in its graphical representation. Factor n follows from the stoichiometry of the cell reaction (for example n = 2 for reaction c or d). The product nFE is the work expended when the cell reaction proceeds to a unit extent and at thermodynamic equilibrium and is equal to the affinity of this reaction. Thus,
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(3.1.39)
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Considering that (-AG d ) > 0 when ( AGC) < 0, then it is apparent that the sign of the EMF depends on the direction in which the scheme of the cell is written and, consequently, on the direction in which the reaction is written. The EMF is positive when the reaction and the scheme are formulated so as to correspond to a spontaneous reaction (the reaction would occur spontaneously in the direction indicated if the cell were short-circuited). Thus cell (a) has a positive EMF and cell (b) a negative one.
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161 Consider a galvanic cell consisting of hydrogen and silver chloride electrodes: Pt | H2 | HCl(c) | AgCl(s) | Ag | Pt (3.1.40)
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In this cell, the following independent phases must be considered: platinum, silver, gaseous hydrogen, solid silver chloride electrolyte, and an aqueous solution of hydrogen chloride. In order to be able to determine the EMF of the cell, the leads must be made of the same material and thus, to simplify matters, a platinum lead must be connected to the silver electrode. It will be seen in the conclusion to this section that the electromotive force of a cell does not depend on the material from which the leads are made, so that the whole derivation could be carried out with different, e.g. copper, leads. In addition to Cl~ and H 3 O + ions (further written as H + ), the solution also contains Ag + ions in a small concentration corresponding to a saturated solution of silver chloride in hydrochloric acid. Thus, the following scheme of the phases can be written (the parentheses enclose the species present in the given phase):
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-,Ag + )|AgCl(Ag + ,C1")l Ag(Ag+ ,e) 1 Pt(e) (3.1.41)
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The electrodes employed will be considered in greater detail in Section 3.2. Here it is sufficient that this cell can yield electrical energy, because the cell reaction ^H2(2) + AgCl(4)-> H+(3) + CT(3) + Ag(5) (3.1.42)
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takes place spontaneously. Depending on the processes occurring during the cell reaction at the individual electrodes, the cell reaction can be separated into two half-cell reactions formulated as reduction by electrons. For the cell reaction described by Eq. (3.1.42), these reactions are AgCl(4) + e = Ag(5) + Cl~(3) H (3) + e = iH2(2)
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(3.1.43) (3.1.44)
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Subtraction of reaction (3.1.44) from reaction (3.1.43) yields reaction (3.1.42). The EMF, E, is given by the difference in the inner potentials of phases V and 1: E = <t>(l')-<t>(l) (3.1.45)
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If this EMF is compensated by an external electrical potential difference of the same magnitude and of opposite polarity, then no current flows and the system is at equilibrium. The phase equilibria of communicating species are
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