Chap10 soln

Physical Chemistry

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10 Equilibrium electrochemistry Solutions to exercises Discussion questions E10.1(b) The Debye–H¨uckel theory is a theory of the activity coefficients of ions in solution. It is the coulombic (electrostatic) interaction of the ions in solution with each other and also the interaction of the ions with the solvent that is responsible for the deviation of their activity coefficients from the ideal value of 1. The electrostatic ion–ion interaction is the stronger of the two and is fundamentally responsible for the deviation. Because of this interaction there is a build up of charge of opposite sign around any given ion in the overall electrically neutral solution. The energy, and hence, the chemical potential of any given ion is lowered as a result of the existence of this ionic atmosphere. The lowering of the chemical potential below its ideal value is identified with a non-zero value of RT ln γ ± . This non-zero value implies that γ ± will have a value different from unity which is its ideal value. The role of the solvent is more indirect. The solvent determines the dielectric constant, , of the solution. Looking at the details of the theory as outlined in Justification 10.2 we see that enters into a number of the basic equations, in particular, Coulomb’s law, Poisson’s equation, and the equation for the Debye length. The larger the dielectric constant, the smaller (in magnitude) is ln γ ± . E10.2(b) The potential difference between the electrodes in a working electrochemical cell is called the cell potential . The cell potential is not a constant and changes with time as the cell reaction proceeds. Thus the cell potential is a potential difference measured under non-equilibrium conditions as electric current is drawn from the cell. Electromotive force is the zero-current cell potential and corresponds to the potential difference of the cell when the cell (not the cell reaction) is at equilibrium. E10.3(b) The pH of an aqueous solution can in principle be measured with any electrode having an emf that is sensitive to H + (aq) concentration (activity). In principle, the hydrogen gas electrode is the simplest andmostfundamental. Acellisconstructedwiththehydrogenelectrodebeingtheright-handelectrode and any reference electrode with known potential as the left-hand electrode. A common choice is the saturated calomel electrode. The pH can then be obtained from eqn 10.43 by measuring the emf (zero-current potential difference), E , of the cell. The hydrogen gas electrode is not convenient to use, so in practice glass electrodes are used because of ease of handling. Numerical exercises E10.4(b) NaCl ( aq ) + AgNO 3 ( aq ) AgCl ( s ) + NaNO 3 ( aq ) NaCl, AgNO 3 and NaNO 3 are strong electrolytes; therefore the net ionic equation is Ag + ( aq ) + Cl ( aq ) AgCl ( s ) r H = f H ( AgCl , s ) f H ( Ag + , aq ) f H ( Cl , aq ) = ( 127 . 07 kJ mol 1 ) ( 105 . 58 kJ mol 1 ) ( 167 . 16 kJ mol 1 ) = 65 . 49 kJ mol 1 E10.5(b) PbS ( s ) Pb 2 + ( aq ) + S 2 ( aq ) K S = J a ν J J Since the solubility is expected to be low, we may (initially) ignore activity coefficients. Hence
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