THERMODYNAMIC ASPECTS OF CHEMICAL REACTIONS, AS APPLIED TO THE SMELTING AND REFINING OF LEAD A. B. CHATTERJEA & B. R. NIJHAWAN National Metallurgical Laboratory, Jamshedpur Abstract entropy of the system. All systems tend to reach maximum stability. The free energy With a reference to the formulae employed in chemical thermodynamics , available data on thermo- of - any system, therefore, tends to attain a dynamics of chemical reactions involved in the minimum value under conditions of constant extraction and refining of lead are brought together. pressure and temperature. Hence, the Equilibrium constants of the reactions have been change in free energy AG is indicative of the calculated from the standard free energy data to direction and extent to which a chemical explain the desideratum of optimum working con- ditions required during roasting , smelting and reaction, phase transformation and change of refining of lead . Graphs showing the changes with state can proceed. It is the driving force of temperature of standard free energies of formation any chemical reaction. The standard free of oxides, sulphides, chlorides , fluorides, sulphates, energy change of a reaction (A.G°) is related carbonates and silicates have been incorporated for to standard enthalpy change of a reaction ready reference. ( OH°) and standard entropy change of a reaction (AS°) at constant temperature and Introduction pressure by the equation A PPLICATION of the laws of thermo- AGO = AH°-TAS° ...... (2) dynamics permits the study of che- Whether a reaction can proceed in the mical reactions involved in different desired direction or not depends on two metallurgical processes . Thermodynamics factors, viz. the sign of the free energy change thus provides a useful method of predeter- and the availability of a suitable reaction mining the possibility of a chemical reaction path. If the free energy is lowered by the to occur under given conditions of tempera- reaction proceeding in the intended direction ture, pressure and composition . Review of and a path is available, the necessary pre- thermodynamical factors of chemical reac- requisites exist for the reaction to proceed. tions involved in the smelting and refining If the free energy change is not favourable, of lead has been dealt with based on the the mere existence of a reaction path is not conventional processes in use thereof. In enough. Similar reasoning applies to the doing so it has not been possible to include other case where the free energy change is physico-chemical studies of all aspects of lead favourable, but the reaction path is either not metallurgy. available or not straightforward or when the chances of the reactants meeting each other Free Energy of Reaction are small. Available portion of the total energy of a system is known as free energy (G) (F by Equilibrium Constant and Free Energy some American authors) and is defined by For any chemical reaction at given tem- the relation perature and pressure G=H-TS......... ( 1) bB+cC=dD+eE where H is the heat content and S is the in which b, c, d and e represent the number 108 CHAtrERJEA & NIJIIAWAN-THERMODYNAMIC ASPECTS OF CHEMICAL. REACTIONS 109 of molecules of the reactants B and C, and the known value of heat of reaction AH° and products D and E taking part in the re- the value of change in entropy OS°, when action, the change in free energy at a given the substances are in their standard states. temperature and pressure is given by the The variation of the equilibrium constant equation with temperature is expressed by van't Hoff d e equation AGT -_ AGO. -}- RTlnab x aE , ... (3) aBxae d1nK _ LH° (7) dT RT2 '"" where ae = activity of a constituent E; If AH ° is positive , i.e. endothermic reac- T = absolute temperature ('K); and R = tion, lnK, or - AG° becomes more negative gas constant (1-987 cal./degree/mole/mole). AG' and the reaction proceeds further with the is conventionally expressed in cal . per gram rise of temperature . If AH is negative, atom. When the reaction attains a state of ° then - AG°/T becomes more positive with equilibrium, the free energy change AGT is the increase of temperature . The possibility zero, and, therefore, of AH ° changing sign with temperature d e should be considered . From equation (6) AG°_-RTinDXaE _ - RT1nK ... (4) aB xaG LH° log K - 4-575T plus-constant ° or log K = - 4 -575 T ...... (4a) as the heat of the reaction does not change appreciably with temperature and pressure. where K is the equilibrium constant of the When logarithm of the equilibrium constant reaction. This equation shows the relation is plotted against the reciprocal of absolute of standard free energy change AG° to the temperature, a straight line is obtained, the equilibrium constant (K) of a chemical slope of which multiplied by 4-575 will give reaction. K is a ratio which indicates the the heat of reaction in calories. extent to which a chemical reaction can Thermodynamic data, therefore, provide proceed. The high magnitude of K, there- means of ascertaining the possibility of any fore, indicates that the reaction proceeds chemical reaction taking place under given substantially to the right-hand side of the conditions. It must be mentioned that the equation. The unit in which K is expressed reaction rate will depend on factors such as is generally related to the active mass (or the form of the reactants and is not predict- activity). Change of the equilibrium con- able from thermodynamic considerations stant (K) with temperature is given by the alone, e.g. the diffusion of the reactants and equation products from the zone of reaction may determine the rate of reaction. Metallurgical log "K 1 775 x TG° ..... (5) reactions usually take place at high tempera- If for any chemical reaction at a particular tures at which diffusion rates are high. So, temperature AG° can be found, K can be de- if the free energy change is favourable, a termined, and vice versa. It is thus possible metallurgical reaction is expected to pro- from equation (4) to calculate equilibrium gress at a reasonable rate in the desired activities for a reaction. direction.. From equations (2) and (4) it follows that as" AH° Activity 1nK = - RT ..... (6) By activity is meant the effective concen- which shows that the equilibrium constant tration of a constituent, which may not of any temperature T can be calculated from always be equal to its concentration. Activ- 11o SYMPOSIUM ON NON -FERROUS METAL INDUSTRY IN INDIA ity is always referred to a standard state. AG° = IT + AH° - AaT1nT - It represents the effective concentration in AbT2 AcT3 (9) any desired state when compared to the 2 6 ... effective concentration in the state chosen as where I and H° are integration constants. the standard or reference state. In a large The value of the other three constants a, b number of instances, the pure substance is and c can be calculated from specific heat taken to be the standard state. In such data of the constituents while H° and I can cases, if the solution obeys Raoult's law, the be evaluated from one value of heat effect on activity is equal to the mole or atom fraction. the reaction and a known value of G° at a When considering dilute solutions, it is some- specified temperature respectively. It is thus times inconvenient to refer to the pure sub- possible to calculate the standard free energy stance as the standard state. Hence, we have change of a chemical reaction at a given tem- the infinitely dilute solution standard, and perature, but the equation is cumbersome. the 1 per cent solution (vide Chipman ) standard. In dilute solutions, the activity Graphical Representation of Standard is proportional to the considerations till the Free Energy Changes with Temperature latter become excessive. This is expressed by Henry's law. Activity of a pure solid or Standard free energies of formation of liquid is conventionally considered as unity, various compounds at different temperatures and that of a gas as equal to its partial have been expressed in the form of equation pressure. (9) by Kelly". The ratio of activity (az) to its concentra- Ellingham2 plotted the standard free energy tion is called the activity coefficient (Y1) changes with temperature in a graphical form. where the concentration is defined by the From such a chart, one can directly see the mole fraction (N; ). conditions for a chemical reaction to occur. As 11° and S° change only slightly with tem- Yi - a. ........... (8) perature, such a plot will result approximate- Ni ly in straight lines having a slope of S°, These remarks can be generally applied to because of the relation heterogeneous systems. dAG° _ - A$° In equation (3), when the reactants and dT products are not in their standard states and, If AG° is plotted downwards, as is common therefore, the activities are not unity, the practice, the slope will be - bS°. With the Cree energy change of the reaction AG can abrupt change of entropy at transition, be obtained by adding an activity correction fusion, vaporization and sublimation tern- to AG°. It follows from equation (3) that peratures, the slope is usually changed. AGr AGT + RT1nJa, where Ja is the The standard free energy for chemical reac- activity function at temperature T. An tion is related to standard electrode potential activity correction chart has been shown ( or decomposition voltage) of an electrolytic with a AG°/T diagram for chlorides (Fig. 4 ). cell in which the reaction is carried out by The correction has to be multiplied by the the following equation: number of molecules. This is to be added for products of reaction and subtracted for AG° _ -jnE°F .