Electromotive force temperature coefficients

ACTIVITY COEFFICIENT. A fractional number which when multiplied by the molar concentration of a substance in solution yields the chemical activity. This term provides an approximation of how much interaction exists between molecules at higher concentrations. Activity coefficients and activities are most commonly obtained from measurements of vapor-pressure lowering, freezing-point depression, boiling-point elevation, solubility, and electromotive force. In certain cases, activity coefficients can be estimated theoretically. As commonly used, activity is a relative quantity having unit value in some chosen standard state. Thus, the standard state of unit activity for water, dty, in aqueous solutions of potassium chloride is pure liquid water at one atmosphere pressure and the given temperature. The standard slate for the activity of a solute like potassium chloride is often so defined as to make the ratio of the activity to the concentration of solute approach unity as Ihe concentration decreases to zero. 

LiHgaa (Hq.). Lewis and Keyes2 computed the partial molal heat of solution of Li (c) in LiHggg (liq.) from the temperature coefficient of the electromotive force of cells. 

This equation indicates that, if the electromotive force has a positive sign and the temperature coefficient of the electromotive force of the reaction has a negative sign, the reaction enthalpy will be negative AHH IOi < 0 and hence the reaction is exothermic. 

Isothermal temperature coefficient — (d / dT)isoth is the derivative of the - electromotive force with respect to the temperature for the following isothermal cell [i] ... 

These equations are called the phenomenological equations, which are capable of describing multiflow systems and the induced effects of the nonconjugate forces on a flow. Generally, any force Xt can produce any flow./, when the cross coefficients are nonzero. Equation (3.175) assumes that the induced flows are also a linear function of non-conjugated forces. For example, ionic diffusion in an aqueous solution may be related to concentration, temperature, and the imposed electromotive force. 

Electromotive force measurements of the cell Pt, H2 HBr(m), X% alcohol, Y% water AgBr-Ag were made at 25°, 35°, and 45°C in the following solvent systems (1) water, (2) water-ethanol (30%, 60%, 90%, 99% ethanol), (3) anhydrous ethanol, (4) water-tert-butanol (30%, 60%, 91% and 99% tert-butanol), and (5) anhydrous tert-butanol. Calculations of standard cell potential were made using the Debye-Huckel theory as extended by Gronwall, LaMer, and Sandved. Gibbs free energy, enthalpy, entropy changes, and mean ionic activity coefficients were calculated for each solvent mixture and temperature. Relationships of the stand-ard potentials and thermodynamic functons with respect to solvent compositions in the two mixed-solvent systems and the pure solvents were discussed. 

The Li-component activity coefficient, YLi> can be determined from electromotive force (emf) data taken by Saboungi (32) at temperatures of 497, 539, 596, and 659 C in Pb-Li mixtures with Pb atom fractions above 45%. In Figure 21, Yl is shown as a function of (1/T) at five liquid compositions. The lines in Figure 21 are least-square fits to allow extrapolation to the temperature region of interest to IGF reactor designers, 400 to 500°C. 

The Seebeck coefficient were calculated from measurement of electromotive force with temperature difference of lOK. The electrical resistivity and Hall measurement were performed by van der Pauw method. The thermal conductivity were calculated from the thermal diffusivity, the specific heat and the density. The thermal diffusivity and the specific heat were measured by laser flash method and differential scanning calorimeter (DSC), respectively. 

To measure the Seebeck coefficient a, heat was applied to the sample which was placed between the two Cu discs. The thermoelectric electromotive force (E) was measured upon applying small temperature difference (JT <2 E) between the both ends of the sample. The Seebeck coefficient a of the compound was determined from the E/JT. The electrical resistivity p of the compound was measured by the four-probe technique. The repeat measurement was made rapidly with a duration smaller than one second to prevent errors due to the Peltier effect [3]. The thermal conductivity k was measured by the static comparative method [3] using a transparent Si02 ( k =1.36 W/Km at room temperature) as a standard sample in 5x10 torr. 

It should be noted in the method that the U- or II-shaped specimen is never p-n device but a single p- or n- type material. This was aimed to remove possible errors due to Seebeck and Peltier effects in the resistivity measurement where a large temperature gradient is given to a specimen. An apparent Seebeck coefficients were calculated as the temperature derivatives from the measured electromotive forces. 

By means of the Gibbs-Helmholtz equation (38) it is obviously possible to compute the heats of the reaction, — AH, from the electromotive force of a cell in which the reaction takes place, and the temperature coefficient of the electromotive force of the cell. If the temperature range is not too great equation (38) can be replaced by... 

In particular, the relativdy large temperature coefficient of the electromotive force has found a complete thermodynamical explanation it is the conversion of 7 mols of... 

Harned and Owen presented tabulated values for the mean activity coefficients of HCl at temperatures from 0 to 60°C for maximum molalities from 2 to 4. The coefficients are from observed electromotive forces for molalities greater than. 001 the values for molalities less than. 002 were extrapolated from plots. 

In practice, the Seebeck electromotive force is related to the temperature difference by a polynomial equation, where the polynomial coefficients (i.e., c , c, Cj, C3, etc.) are empirical constants determined by experiment and that characterize the thermocouple selected. 

The standard molar entropies of aqueous electrolytes, 2°°, are preferably obtained from the temperature coefficients of the electromotive forces of galvanic cells. The absolute values for individual ions are based on 5°°(H", aq) = —22.2 1.4 J K moP at 298.15 K, from data for thermocells [1]. The S °° values increase with the masses of the ions but are small or negative for multi-charged ions. 

The final units arc appropriate for a temperature coefficient of electromotive force. 

Standard-state entropies of aqueous ions are by convention referenced to S°(H (aq)) = 0. Alternatively, the temperature coefficient of the electromotive force of an equilibrium reaction involving the ion can be used to calculate the entropy of the reaction, and from the reaction entropy as well as necessary auxiliary data the entropy of formation of the ion can be calculated. Four actinide aquo-ion entropies (Th , Pu, UOj, and NpO ) have been determined by the former method. The other aquo-ion entropies of uranium, neptunium, and plutonium have been connected by the latter method. 

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