VOLTAIC CELL. 214 VOLTAIC CELL. the zinc electrode is in the opposite direction. These two thermo-eleetromotive forces per de- gree C. are veiy nearly equal to each other, and the temperature coefficient of the Daniell cell is accordingly very small. The curves of Fig. 14 represent "the changes in the electromotive force of a Daniell cell produced by heating the two sides separately. Curve A is for the zinc side, and curve B for the copper side. The two changes have opposite signs, but both are plotted as positive ordinates in the figure, since their difference expresses the change of electromotive force when the whole cell is heated. In Fig. 15 curve A is again the curve for zinc (zinc sulphate), and curve B is the curve for mercury (mercurous sulphate), in the same solu- tion of zinc sulphate. In other words, the cell was set up as a Clark standard cell without any crystals of the zinc salt. The difference in the values of these thermo-eleetromotive forces for say 10° and 40°, divided by the temperature dif- ference, 30°, gives the change in electromotive force of this type of Clark cell for 1° 0. It is 0.00055 volt. The actual change determined by heating the whole cell, as already stated, is 0.00056 volt; and if a much smaller term, de- pending on the square of the temperature dif- ference, be taken into account, the result will be identical with that obtained from the curves of Fig. 15. The same method of synthesis applied to a cell composed of zinc in a solution of zinc chloride and mercury in contact with mercurous chloride (calomel), which has a small positive tempera- ture coefficient, again gives a result agreeing per- fectly with the coefficient obtained by direct measurement. It thus appears that the heat generated or absorbed by a voltaic cell, corresponding with the sign of the temperature coefficient, may be local- ized in the cell. In the Daniell cell, the passage of a current generates heat at the zinc electrode, where the current flows against the thermo-elee- tromotive force at that point; at the same time heat is absorbed at the copper electrode, because the thermo-electromotive force there is in the same direction as the current, and energy is given to the circuit. Tliis energy is supplied by the heat of the cell itself. On account of these two opposite heat effects, a difference of temperature is established between the two sides of the cell proportional to the quantity of electricity that has passed through it. If a current is passed through the cell from some outside source, in the opposite direction, the heat effects at both elec- trodes will be reversed. These results have been established by experiment. If heat is generated on one side and absorlied at the other in equal quantities, then the temperature of the ('ell as a whole will remain unchanged, the temperature coefficient is zero, and the chemical energy trans- formed equals the electrical eni'rgy given out. Nernst's Theory. The modern theory of dis- sociation has given rise to another view of vol- taic cells in the hands of Nernst and his school. Van't Hoff accounts for the phenomena of os- motic pressure by the theory that the molecules and ions in a solution exert a pressure which conforms in all respects to the laws of Boyle and Gay-Lussac for gases. According to this view, the ions are forced out of the solution against the electrodes in a voltaic cell and give up their charges to them. Further, it is assumed that metals exhibit a tendency to go into the ionic state when immersed in an electrolyte. This tendency is known as electrolytic solution pressure. It is analogous to vapor pressure, and measures the tendency of a metal to pass into the state of free ions in an electrolyte. Let P denote the solution pressure, and p the osmotic pressure due to the metallic ions present in the electrolyte. If now P is greater than p, some of the metal will go into the solution as positively charged ions, leaving the metallic mass negatively charged. If P equals •/), no more ions are formed and the metal does not become charged. If P is less than j), the osmotic pressure drives the positive ions out against the smaller solution pressure, and" the metal to which they give up their charges be- comes positively charged. The charging of the metal is equivalent to the production of a differ- ence of potential between the metal and the solution. Starting from the well-known gas equation, pv := RT, and assuming that when the ions pass from the pressure P to the pressure p, work is done to the same extent as if the ions were in the gaseous state, Nernst found that the electro- motive force between a metal and an electrolyte may be expressed by the following formula : E = 0.0002 -log-. n ^ p In this equation n is the valence of the metal. Taking into consideration the potential differ- ence at both electrodes, we have as the equation for the electromotive force of a voltaic cell, neg- lecting the small potential difference at the con- tact of the two electrolytes, /I P 1 P' E = 0.0002 T (iloe ^.log — V
^ p 11 ^ p J
The C4ibbs-Helmholtz and the Xernst formiilas denote two methods of viewing the action taking place in a voltaic cell. They are not antago- nistic, but complementary. Nernst's formula gives perhaps a more detailed insight into the mechanism of a cell ; Helmholtz's, especially when the heat effects are localized, considers a voltaic cell entirely from the point of view of the chemical and thermal energy involved. The Nernst formula gives no definite account of the temperature coefficient of a cell, nor of the rela- tion of this coefficient to the electrical energy evolved. The thermodynamic method of Ciibbs and Hclmholtz furnishes the most secure founda- tion for the investigation of the transformations of energy in a voltaic cell, without exposing to view, however, the exact mechanism beyond the application of fliermo-electromotive forces to the problem. (■ONCENTRATION Cet.i.s. In the extreme case in which there is no chemical cnergj' to convert into work, the cell becomes a device for the conver- sion of heat alone into the energj- of the current. It is then known as a concentration cell. Thus, when two electrodes of the same metal are im- mersed in a solution of a salt of this metal, the concentration of the solution at one electrode being greater than at the other, the cell has a small electromotive force which will produce a (Turrent. hen the solutions are so dilute that
