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2 Chapter 2 Useful Wrk and Gibbs Energy Niklai Bazhin Additinal infrmatin is available at the end f the chapter 1. Intrductin Devices fr perfrming chemical reactins are widely used t prduce heat and wrk. Heat, in turn, prduces wrk, e.g., in the frm f electric energy in the s-called heat engines. It is the well-knwn fact that the efficiency f heat engines is restricted by Carnt principle. Therefre, it is generally recgnized that heat cannt be fully cnverted t wrk. The efficiency f electric energy prductin due t the burning f fssil fuel f varius kinds varies frm 30 t 50 %. On the ther hand, there are galvanic and fuel cells whse efficiency can reach theretically unity if it implies the rati between the electric energy prduced and the value f a change in Gibbs energy during chemical reactins ccurring in a cell. These devices perate at cnstant temperature and pressure. It is cncluded then that the devices, similar t a galvanic cell, cannt wrk at cnstant and unifrm temperature accrding t the principle f heat engine. These devices assumed t perate nly due t the direct transfrmatin f chemical reactin energy, described by a change in the Gibbs energy, int wrk [1]. This viewpint causes, hwever, numerus cntradictins. The gal f this wrk is t analyze in detail the mechanism f useful wrk and heat prductin in chemical systems functining at cnstant temperature and pressure. 2. Fundamental functins In this Sectin, the fundamental functins f thermdynamics will be characterized, as the fundamental functins play the imprtant rle in the descriptin f the prcess f the energy transfrmatin. This ntin includes fur functins, i.e., internal energy, enthalpy, Helmhltz energy, and Gibbs energy. All f them are the state functins f energy dimensin. It is generally believed that the value with energy dimensin describes energy but this is by n means always the case. Belw, the fundamental functins will elucidate whether these are energy values r nt Bazhin, licensee InTech. This is an pen access chapter distributed under the terms f the Creative Cmmns Attributin License ( which permits unrestricted use, distributin, and reprductin in any medium, prvided the riginal wrk is prperly cited.

3 30 Thermdynamics Fundamentals and Its Applicatin in Science 2.1. Internal energy Accrding t IUPAC [2], "internal energy U is the quantity the change in which is equal t the sum f heat, q, brught t the system and wrk, w, perfrmed n it, U q w ". Because f varius transfrmatins, the internal energy can be cnverted t ther kinds f energy. Hwever, the initial quantity f internal energy shuld be cnserved due t the law f energy cnservatin. Cnservatin is the mst imprtant characteristic f energy. Hence U is energy Enthalpy Accrding t IUPAC, "enthalpy, H =U + pv is the internal energy f a system plus the prduct f pressure and vlume. Its change in a system is equal t the heat, brught t the system at cnstant pressure [2]. It is wrth nting that the change in the value describing energy always crrespnds t the change in energy and nt nly in sme special cases. Generally, a change in enthalpy may be incnsistent with the change in real physical values. Let us cnsider, e.g., the prcess f ideal gas heating at cnstant vlume. The quantity f heat, taken in by ideal gas frm the heat bath, q, equivalently changes nly the internal gas energy, U q, and simultaneusly causes changes in gas enthalpy, H U pv q. Hwever, this change fails t reflect the changes in any physically significant values. Thus, the enthalpy is nt energy but a functin f state having the dimensin f energy. It is easier and mre crrect t assume that the enthalpy is the part f a calculating means used t describe thermdynamic prcesses Helmhltz energy Accrding t IUPAC, "Helmhltz energy (functin), A, is the internal energy minus the prduct f thermdynamic temperature and entrpy: A = U - TS. It was frmerly called free energy" [2]. Let us see why this quantity was called free energy. Accrding t the first law [3] U q w, (1) where q is the heat, entering the system, and w is the ttal wrk perfrmed n the system by the surrundings. Usually, the ttal wrk is given as the sum f tw terms: expansin wrk ( p V) and s-called useful wrk ( w useful) w p V w useful. (2) If the prcess ccurs at cnstant vlume, the expansin wrk is absent and w describes the useful wrk. In the case f reversible prcess [3] Thus, eq. (1) is f the frm in the case f reversible prcess q T S. (3)

4 Useful Wrk and Gibbs Energy 31 wuseful U S ( U S) A, (4) where A is the change in Helmhltz energy at cnstant temperature and vlume. Since the term "energy" means the capacity f the system t perfrm wrk, frm eq. (4) it is frmally cncluded that A is the energy (but in this case eq. (4) can have the secnd explanatin A is the numerical characteristic f wrk and nt the wrk itself). Further, frm eq. (4) it was cncluded that nly the part f internal energy U minus TS can be used t prduce wrk. Therefre, the TS quantity was called "bund energy" and (U - TS) "free energy". The meaning f these ntins will be cnsidered in mre detail using the Gibbs energy as an example because it is mre ften used in chemical applicatins Gibbs energy Accrding t IUPAC [2], "Gibbs energy (functin), G ( H TS), is the enthalpy minus the prduct f thermdynamic temperature and entrpy. It was frmerly called free energy r free enthalpy". The reasns fr the appearance f the term "Gibbs energy" are similar t thse discussed when cnsidering the Helmhltz energy except fr the fact that the Gibbs energy describes the reversible useful wrk perfrmed at cnstant temperature and pressure. This is readily bserved by substituting eq. (3) and eq. (2) int eq. (1) with regard t V p 0 wuseful H S ( H S) G, (5) where G is the change in Gibbs energy at cnstant temperature and pressure in the reversible prcess. Unfrtunately, the wrd "energy" as defined by IUPAC fr a Gibbs energy (and als fr a Helmhltz energy), causes great cnfusin. The Gibbs energy G = H TS cnsists f tw terms, the enthalpy and the entrpy ne. The rigin f bth f the terms is quite different despite the same dimensin. The enthalpy, cnsidered abve, is nt energy. Cnsider nw the prblem f TS nature. In the case f the reversible prcess T S q, but in the case f the irreversible prcess T S q and additinal cntributins t T S can arise withut change in energy. Fr example, it is well knwn the increase f the entrpy in the prcess f ideal gas expansin in vacuum withut heat cnsumptin (q = 0). Let us cnsider anther example. Let the ideal gas-phase system invlves a spntaneus prcess f the mnmlecular transfrmatin f substance A int B. As suggested a change in enthalpy tends t zer in this reactin. Thus, the internal energy, temperature, pressure, and vlume will nt underg changes in this prcess. Hwever, the entrpy will increase due t the entrpy f the mixing, because the entrpy is a functin f state. The value f the TS prduct will increase accrdingly. Hwever, the energy and even the bund energy cannt arise frm nthing, whereas the entrpy, being a functin f state, can increase thus reflecting a change in system state withut any changes in the internal system energy. Therefre, the TS term is nt the energy, which als implies the absence f the term "bund" energy.

5 32 Thermdynamics Fundamentals and Its Applicatin in Science Since neither enthalpy nr TS are the energy quantities, the difference between them cannt represent energy. Thus, G cannt represent energy precisely in terms f this ntin. Nte that in the irreversible prcess, ccurring at cnstant temperature and pressure, the Gibbs energy decreases and thus, is nt cnserved. This is readily demnstrated by e.g., the afrementined example f a mnmlecular transfrmatin f substance A int B. Thus, cnservatin, as the mst imprtant criterin fr energy quantity, fails fr the Gibbs energy. It is cncluded then that the Gibbs energy is nt energy [4] but a functin f state. In this regard, the Gibbs energy des nt differ frm heat capacity. The ntins f the nn-existing in reality quantities f free energy" and "bund energy" cause nly cnfusin and are, at present, bslete [5]. Nevertheless, the ntins that the Gibbs energy is the energy and thus, beys cnservatin laws, prve t be lng-lived, which causes errneus interpretatin f a number f prcesses sme f which are f paramunt imprtance. Let us cnsider nw the reactin f adensine triphsphate (ATP) hydrlysis in water slutin which is f great cncern in bichemistry ATP + H2O = ADP + Pi. Under the standard cnditins [6] r G 7, r H 4 kcal ml-1. Accrding t D. Haynie [6, p. 143], "measurement f the enthalpy change f ATP hydrlysis shws that H 4 kcal ml -1. That is, the hydrlysis f ne mle f ATP at 25 º results in abut 4 kcal ml -1 being transferred t a slutin in the frm f heat and abut 3 kcal ml -1 remaining with ATP and Pi in the frm f increased randm mtin." The heat f 4 kcal ml -1 is actually released int slutin due t hydrlysis. Unfrtunately, it is then assumed that the Gibbs energy is cnserved which makes his difference in r H and r G f 3 кcal ml-1 be lcated n the degrees f freedm f prduct mlecules. Hwever, in this cnnectin, the prduct mlecules culd appear in the nn-equilibrium excited states and transfer this energy t slvent mlecules which wuld result in the emissin f 7 kcal ml -1 rather than 4 kcal ml -1 which cntradicts the experiment. There are n additinal 3 кcal ml -1 n the degrees f freedm f AТ and Pi because the Gibbs energy is nt cnserved Cnclusins Thus, amng the fur quantities, that claims t be called energy quantity, nly the internal energy deserves this name. The ther functins, i.e., enthalpy Н, Helmhltz energy A, and Gibbs energy G are the parts f a mathematical apparatus fr calculating varius quantities, such as useful wrk, equilibrium cnstants, etc. This als means that the useful wrk is nly calculated by using functins A and G, but cannt arise frm the change in either the Helmhltz r the Gibbs energy. The physical nature f the wrk perfrmed shuld be cnsidered separately. Since the Helmhltz energy and the Gibbs energy are nt energies, then, t avid misunderstanding, it is better t exclude the wrd energy frm the name f crrespnding functins and t use the secnd variant f the name f these functins accrding t IUPAC: a Helmhltz functin and a Gibbs functin [7].

6 Useful Wrk and Gibbs Energy Direct cnversin f chemical reactin energy t useful wrk This Sectin is devted t the discussin f the generally accepted thery f the direct cnversin f energy [1, 8] prduced by chemical reactin t useful wrk. Fr simplicity, hereafter exergnic ( G 0) and exthermic ( rh 0) reactins will be cnsidered. r The useful wrk f the chemical reactin ccurring at cnstant temperature and pressure in the reversible cnditins can be calculated thrugh the change in the Gibbs functin (5). When the interest is the useful wrk perfrmed by the system in the envirnment ( w ), then useful wuseful rh rs r G. (6) Frm eq. (6) it fllws frmally that the useful wrk f the reversible system in the envirnment is the sum f the enthalpy member ( rh) and the entrpy member T rs. In this cnnectin it is interesting t discuss the varius situatins which arise in dependence n the relatin between ( rh) and T rs. Frm eq. (6) it fllws, that fr rs 0 the useful wrk in the envirnment exceeds ( rh) : wuseful rh. Therefre, the system must drag the thermal energy frm the envirnment in the vlume T rs t perfrm useful wrk. What is the physical reasn fr thermal energy cnsumptin? Why des the system cnsume thermal energy f vlume T rs neither mre r less? Hw can tw different cntributins prduce the same useful wrk? The secnd case f rs 0 is als f interest. In this case wuseful rh and the system must evlve the part f reactin heat t the envirnment. Why cannt the system use the ttal reactin heat fr useful wrk prductin if this energy is at its dispsal? Why can the system transfer energy f vlume T S and neither mre r less t the envirnment? r The third case is r H 0. Here the system can use nly the thermal energy f the envirnment t prduce useful wrk. In the furth case rs 0 and the system perfrms wrk frmally due t the reactin heat ( H) withut exchanging thermal energy with the envirnment. But it is nt the case. r As mentined in the Intrductin, at present, it is generally accepted that the high efficiency f reversible devices is incnsistent with the ntins that heat can be used t prduce wrk and that such devices realize the direct cnversin f chemical system energy int wrk. But belw it will be shwn that in all the cases, the useful wrk results frm the heat f vlume dragged frm the envirnment. r G 4. A mechanism f useful wrk prductin - A Van t Hff Equilibrium Bx In this Sectin, it will demnstrate the mechanism f prducing useful reversible wrk which invlves n ntins f the direct cnversin f reactin energy int useful wrk. T this end, let us cnsider a Van t Hff equilibrium bx (VHEB) [9 11]. A thermdynamic

7 34 Thermdynamics Fundamentals and Its Applicatin in Science system must prvide realizatin f the reversible prcess. This means that all changes in the system are infinitely slw at infinitely minr deviatin frm equilibrium. It is assumed that in the system the fllwing reactin ccurs ia i jbj, (7) i where A i are the reagents and B j are the prducts. The reactin takes place in the reactr (Fig. 1) where the reagents and prducts are in equilibrium. The chemical prcess is affrded by reservirs with reagents and prducts cntained in the system. Fr simplicity, the reagents and prducts are assumed t be in standard states. The system shuld have instruments t transprt bth the reagents frm standard vessels t reactr and the prducts frm reactr t standard vessels. In additin, the system shuld have tls t perfrm wrk, because the reversible prcess must be fllwed by reversible wrk prductin. The instruments and tls fr perfrming wrk can be used tgether. The reactr, transprting instruments, and tls fr perfrming wrk can be placed either separately r tgether. T prvide cnstant and unifrm temperature, it is necessary t lcate the system, including reactr, standard vessels, transprting instruments, and tls in a thermstat, which can als imply the envirnment f cnstant temperature. j Figure 1. Prductin f useful wrk and heat in a clsed reversible system. Ast (Bst) indicate the reagents Ai (prducts Bj) in the standard states; Aeq (Beq) indicate the reagents Ai (prducts Bj) in the equilibrium states, which crrespnd t the equilibrium at the reactr; the green figures in circles indicate the step numbers (see text)

8 Useful Wrk and Gibbs Energy 35 Let us cnsider reversible chemical prcess in a clsed system (Fig. 1). The realizatin f the reversible chemical prcess cnsists in reversible transfrmatin f the reagents t prducts via chemical reactin. Let us cnsider the clsed system Clsed system The prcess f reversible wrk prductin includes six stages. Step 1. A small amunt f substance Ai is remved frm the vessel with reagent Ai in the standard state upn reversible prcess. Gaseus substances can be remved frm a standard vessel and put int a prtable cylinder with pistns [11]; slid r liquid substances are placed in lck chambers. Then, the change in the Gibbs functin and the wrk are zer ( G1 i 0, w1 i 0) because a minr prtin f substance Ai is in the same standard state as the residual reagent. Step 2. Reagent Ai is transfrmed reversibly frm the standard int the equilibrium state in the reactr. Fr example, fr ideal gas, the gas pressure will vary frm a standard value t the equilibrium partial value in the reactr. In this stage, the reversible wrk w 2i is prduced and G2i 0. The wrk w can be dne nly due t thermstat heat 2i because there are n ther energy surces in the system (reactin is in the equilibrium). This wrk depends n the difference in the physical states f reagent Ai in the initial and equilibrium states. All reagents Ai participate in all stages in quantities prprtinal t i. Fr ideal gas, the useful wrk is w RTln( p / p ), (8) 2 i i i,eq i,st where p i,eq is the equilibrium pressure f i-th gas in the reactr, and p i,st is the pressure f i-th gas in a standard vessel. Fr gaseus cmpnents, e.g., the prcess f reversible gas expansin (cmpressin) in a prtable cylinder fr prducing the maximum useful wrk, must prceed t the value p i,eq. If expansin (cmpressin) stps at pi pi,eq, then the inlet f gas int the reactr causes irreversible gas expansin and thus, the useful wrk will be less than the maximum ne. When due t expansin (cmpressin) the final pressure is less than p i,eq, then the inlet f gas int the reactr causes the irreversible inlet f the i-th gas frm an equilibrium mixture in the reactr t the prtable cylinder, which als leads t a decrease in useful wrk. The slid and liquid substances can be transprted by lck chambers. The pressure abve either slid r liquid substances is varied frm 1 bar t the value f the ttal equilibrium pressure in the reactr. The pressure is created using a minr prtin f equilibrium reactin mixture. The thermstat enthalpy varies as fllws: H2,thermstat i w2i. Step 3. Reagent Ai is reversibly intrduced int the reactr. Gaseus cmpnents are intrduced int the reactr thrugh semipermeable membranes using prtable cylinders [11]; the slid r liquid nes by means f lck chambers. Hence, G 3 i 0, w 3 i 0.

9 36 Thermdynamics Fundamentals and Its Applicatin in Science The useful wrk prductin and the change in thermstat enthalpy place nly at step 2: ( H ) take 2,thermstat w (9) 2 H 2,thermstat, where w2 w2i and H2,thermstat H2 i,thermstat. i i The same prcedure is used t bring prducts frm the standard vessels t reactr. Step 4. An equivalent amunt f prduct BJ is reversibly remved frm the reactr. After this step is G 4 j 0, w 4 j 0. Step 5. Prduct BJ, remved frm the reactr, is reversibly transfrmed frm the equilibrium state int the standard ne t perfrm wrk w 5 j. The change in the Gibbs functin is nt zer, G5 j 0. The change in the thermstat enthalpy is H5 j,thermstat w5j. Step 6. Prduct BJ, remved frm the reactr, is reversibly intrduced int the standard vessel. In this case is G6 0 and w6 0. j j The change in the thermstat enthalpy upn thermal energy cnversin int useful wrk at step 5 is w 5 H 5,thermstat, where and w5 w5j, H5,thermstat H5 j,thermstat j (10) j The change in the thermstat enthalpy at the secnd and fifth steps beys the equatin where Q is the heat dragged by tls. dragged H 2,thermstat H 5,thermstat Q dragged, (11) Fr the reversible prcess, the maximal useful wrk is numerically equal t and, hence, the heat dragged by tls frm thermstat in the vlume r G, eq. (5) w useful w 2 w 5 r G r H r S Q dragged. (12) The prcess has resulted in the useful wrk f the reactin, r G, but the reactin did nt ccur yet. T put it therwise, reactin wrk was perfrmed withut reactin. Only the thermal energy f the thermstat (envirnment) may be the surce f wrk. This means that the prcess f useful wrk prductin and the reactin itself may be temprally and spatially separated. Thus, eq. (6) numerically cnnects reactin parameters and the magnitude f the wrk. Hwever, n reactin energy is needed t prduce the wrk. There is n need t subdivide energy surces int reactin surce ( r H ) and thermal T rs, because there is nly ne energy surce: the thermal energy f thermstat (envirnment).

10 Useful Wrk and Gibbs Energy 37 Fr ( rs 0), the thermal energy dragged by the tls exceeds r H, ( Qdragged rh) ; in the case f ( rs 0), the dragged thermal energy is less than r H ( Qdragged rh) ; in the case f ( rs 0) the energy extracted is equal t r H ( Qdragged rh) and fr ( rh 0) the dragged thermal energy is f vlume T rs ( Qdragged rs). The vlume f extracted thermal energy is cntrlled by chemical equilibrium via. Thus, the mixture in the reactr is mved ff balance t be restred later. As a result, the reactin heat is emitted int the thermstat. Indeed, because f the elementary chemical act in the reactr, the energy released cncentrates at the degrees f freedm f the prduct mlecules. As the reactr temperature is cnstant, this energy is dissipated in the reactr and transferred t the thermstat which causes a r H change in thermstat enthalpy. The ttal change in thermstat enthalpy is r G Hthermstat w2 w5 r H. (13) The cycle is ver. Equatins (12, 13) can be used t calculate the ttal change in thermstat enthalpy H G H T S (14) thermstat r r r. The change in thermstat enthalpy is cntrlled nly by reactin entrpy [11] The main principles f reversible device functining in useful wrk prductin This cnsideratin demnstrates the main characteristics f the reversible prcess f useful wrk prductin at cnstant temperature and pressure in clsed systems: 1. The useful wrk arises frm the stage f the reversible transprt f reagents frm reservir t reactr and frm the stage f the reversible transprt f prducts frm the reactr. 2. The nly energy surce f useful wrk is the thermal energy f thermstat (r envirnment). 3. The heat released by chemical reactins is dissipated t the thermstat; the reactin heat is infinitely small in cmparisn with the vlume f the thermstat thermal energy; therefre n reactin heat is really needed t prduce wrk. 4. Althugh the useful wrk is prduced by the cling f ne bdy (thermstat), the secnd law f thermdynamics is nt vilated, because the prcess is fllwed by a change in the amunt f reagents and prducts. 5. The useful wrk is prduced by heat exchange with thermstat (envirnment) accrding t the scheme reactin heat thermal thermstat energy useful wrk (scheme I) 6. The maximal useful wrk is equal the heat dragged by tls frm thermstat. 7. Useful wrk depends n the difference in the cncentratins f standard and equilibrium states f reagents and prducts. Therefre, the amunt f extracted energy can be calculated via the change in the Gibbs functin.

11 38 Thermdynamics Fundamentals and Its Applicatin in Science 8. There is n direct cnversin f the Gibbs energy int useful wrk. Gibbs energy is equal numerically the thermal energy dragged by systems frm the envirnment fr ding wrk The energy limit f chemical reactins - Open systems Usually, the ttal energy which can be prduced by chemical system, is r H. Hwever, this hlds fr clsed systems nly. Fr pen systems, the case is quite different [11]. The pen system is depicted in Fig. 2. As cmpared with the clsed ne (Fig. 1), the pen system cnsists f tw thermstats: the first ne cntains a reactr and the secnd ne cntains standard vessels with substances A and B and tls. The secnd thermstat can be replaced by the envirnment. In the prcess, steps 1, 2, 5, and 6 ccur in the secnd thermstat (envirnment); steps 3 and 4 take place in the first ne. Thus, the heat is released in the first thermstat nly and the wrk is perfrmed by thermal energy f the secnd thermstat (envirnment). The prcesses f heat and wrk prductin are spatially separated! The energy ptential f the pen system beys the equatin q wuseful rh rg (15) Figure 2. Prductin f useful wrk and heat in the pen reversible system. The designatins see in the subscriptin t Fig. 1 In the case f cal burning, it is pssible t btain the duble ttal energy [11]. Thus, understanding the mechanism f useful wrk prductin in the reversible prcess allws us t predict an increase in the energy ptential f chemical reactins in the pen system.

12 Useful Wrk and Gibbs Energy 39 It is wrth nting that the pen system under study is nt a heat pump. The heat pump cnsumes energy t transfer heat frm a cld bdy t the warm ne. The pen system studied des nt cnsume external energy and prduces heat due t chemical reactins in ne thermstat and perfrms wrk by extractin f thermal energy frm the secnd ne Cnclusins The chemical reactin heat is always released in the reversible chemical prcesses and passes t the envirnment independent f the fact whether the system prduces wrk r nt, whether it is clsed r pen. The discussed mechanism f useful wrk prductin in the reversible systems did nt use such ntins as "free energy", "bund energy", "direct Gibbs energy cnversin". The useful wrk arises nly due t the heat exchange with a thermal basin in the prcess, described by the scheme I. The ttal energy f chemical system can be high and equal t rh rg. 5. The mechanism f electric wrk prductin in a galvanic cell The current thery f galvanic cells [1, 3, 8] is based n a direct transfrmatin f the energy ( r G ) f xidatin-reductin reactins int electric wrk. Hwever, using VHEB as an example, It is clear that the energy f chemical reactins is first cnverted int the thermal energy f thermstat (envirnment) and then the thermal energy is extracted frm the thermstat and transfrmed int wrk by means f special devices. It is assumed then that in galvanic cells, useful wrk is prduced via the mechanism similar t the VHEB ne [12, 13]. The r G value is used t calculate electric wrk which des nt, hwever, mean that the electric wrk is perfrmed at the expense f the Gibbs energy, all the mre it was shwn that the Gibbs energy is nt energy. The electric wrk f a galvanic cell results frm the electrdes discharged. Electric charging f electrdes is caused by chemical reactins in electrdes. The mechanism f electric energy prductin in galvanic cells will be slved by analyzing the behavir f ne in. But it des nt dente that thermdynamics will be applied t a real single in: thermdynamic parameters f ne in imply the averaged parameters f many ins A galvanic cell Fr simplicity a Daniell cell will be cnsidered, cnsisting f zinc ( 1) and cpper ( 2) electrdes (Fig. 3). The activity f salts in slutins is dented by а1 and а2, respectively. Let the cell with an pen, external circuit be in equilibrium. Clse nw the external circuit fr the mment and tw electrns will transfer frm the zinc t the cpper electrde. The balance f the cell is distrted. Cnsider nw the establishment f equilibrium n the zinc electrde (Fig 3). T this end, the zinc in must leave a metallic plate and escape int the bulk. The disslving f zinc ins is described by the change in a Gibbs functin rg1 rg1 RT a1 ln, (16)

13 40 Thermdynamics Fundamentals and Its Applicatin in Science where rg1 is a standard change in the Gibbs functin upn disslving. The in penetrates further int slutin with executin f the wrk ( w 1g) in the electric field sl 1g Met1 1, w nf (17) where n is the number f electrns, participating in the reactins, F is the Faraday cnstant, and sl Met1 1 is the difference in ptentials f slutin and metal. The wrk described in equatin (17), is the electric wrk spent t charge an electrde. It is perfrmed at the extractin f the thermal energy f slutin due t the absence f ther energy surces in the system. Since in equilibrium, the chemical ptential f ins in slutin equals the chemical ptential f metal, it is pssible t derive the equatin fr electrchemical equilibrium sl rg1 RT a1 nf Met1 1 ln 0, (18) which readily gives the expressin fr bth the wrk perfrmed n the first electrde and its galvanic ptential [3] sl 1g Met1 1 r 1 1 w nf G RTln a, (19) sl rg1 RT a1 Met1 1 ln. (20) nf nf The latter is the ptential fr a half-cell. Thus, the apprach, based n the cnsideratin f the behavir f ne in, prvides a cmmn expressin fr electrde ptential. Figure 3. Establishment f equilibrium n the electrdes

14 Useful Wrk and Gibbs Energy 41 The change in electrde enthalpy invlves disslutin enthalpy and thermal energy cnsumptin upn in transprt int slutin. The equatin fr disslutin enthalpy is readily btained frm eq. (16) ln a, 2 1 rh1 rh1 RT (21) where rh1 is a standard change in enthalpy during in disslving. The ttal change in the enthalpy f the first electrde ( H1,thermstat ) is the sum f the expressins r H 1 and wg1 2 ln a1 H1,thermstat rh1 wg1 rs1 RTln a1 RT rs1, (22) where rs1 is a standard change in entrpy upn in disslving and r S 1 is the change in entrpy upn in disslving n the first electrde which amunts t ln a1 rs1 rs1 Rln a1 RT. (23) As fllws frm eq. (22), the change in enthalpy, related t the first electrde, is independent f the prcesses, ccurring n the secnd ne. Therefre, studying either release r absrptin f heat n a separate electrde, ne may calculate the change in entrpy due t the escape f the ins f the same type int the bulk. A crrespnding expressin fr the secnd electrde is f the same frm but index "1" shuld be substituted by index "2": rg2 rg2 RT a2 ln, (24) sl 2g Met2 2 r 2 ln 2 w nf G RT a (25) sl rg2 RTlna2 Met2 2. (26) nf nf ln a 2 2 rh2 rh2 RT ln a2 rs2 rs2 Rln a2 RT,, (27) (28) 2 ln a2 H2,thermstat rh2 w2g rs2 RTln a2 RT rs2. In the peratin f the galvanic cell, the prcesses n the secnd electrde are ppsitely directed which shuld be taken int accunt in cnsideratin f the thermdynamic cell parameters. (29)

15 42 Thermdynamics Fundamentals and Its Applicatin in Science Equatins (20) and (26) allw t get the Nernst equatin fr the ptential f the cell [3] sl sl rg RT a1 Met2 2 Met1 1 nf nf a2 E ln, (30) where E the cell ptential, rg rg1 rg2. The electric wrk f the galvanic cell ( w el ) results frm the transfrmatin f the ptential energy f the charged electrdes int electric energy. The ptential energy arises frm the thermal energy f bth f the electrdes upn ins transprt int slutin and equals a w w w G RTln w. (31) 1 el 1g 2g r useful a2 The change in thermstat enthalpy is f the frm Hthermstat H1,thermstat H2,thermstat r S, (32) which is in fair agreement with similar expressin, described by eq. (14), fr the VHEB. The detailed equatin fr Hthermstat can be get after substitutin crrespnding expressins (22) and (29) int (32) 2 lna2 ln a1 Hthermstat ( rs1 rs2 ) RT ln( a2 / a1) RT ( ). (33) The sum f eqs. (31) and (33) gives the ttal energy (electric wrk + heat), prduced by the galvanic cell 2 lna2 lna1 wel Hthermstat rh RT ( ). Frm eq.(34) it fllws that the ttal energy prduced by the galvanic cell is equal t the heat emitted by xidatin-reductin reactin. Thus, the apprach, based n the analysis f the behavir f ne in gives the same results as the present-day thery. Hwever, it uses nt a mysterius, direct transfrmatin f the chemical energy ( r G ) int electric wrk, but the cncept f chemical energy cnversin int the thermal ne, and then, the thermal energy f thermstat (envirnment) is cnverted int the ptential energy f charged electrdes [12, 13]. The electric energy f the galvanic cell arises accrding t the scheme: (34) reactin heat thermal thermstat energy ptential energy f charged electrdes electric energy. Thus, in varius systems with unifrm temperature, useful wrk is prduced by the same mechanism thrugh the exchange f thermal energy with thermstat (envirnment). N direct cnversin f chemical energy int useful wrk is bserved. Unfrtunately, in the

16 Useful Wrk and Gibbs Energy 43 galvanic cell, the prcesses f heat release and useful wrk prductin cannt be spatially separated, because bth f them ccur in a duble layer. Therefre, galvanic cells are unprmising in prductin f a duble amunt f energy A cncentratin cell Cnsider nw a cncentratin cell, cnsisting f tw electrdes, e.g., the zinc nes f different slutin activity. Standard changes in the Gibbs functin, enthalpy, and entrpy fr the cncentratin cell tend t zer due t the same chemical nature f bth f the electrdes. By definitin, it has been cnsidered that a2 a1. Frm eq. (31) it fllws w RTln( a / a ) w, (35) el 2 1 useful which is a usual expressin fr the electric energy f the cncentratin cell. Frm eq. (34) it fllws 2 lna2 lna1 wel Hthermstat RT ( ). Fr the system in which the activities are temperature-independent, the electric energy arises frm the thermal thermstat energy (envirnment) which is in fair agreement with cnventinal cncepts. (36) w el H thermstat w useful, (37) 6. Useful wrk f the systems with cncentratin gradient An ideal system with cncentratin gradient has n ptential energy because the mixing des nt result in heat release and H 0. Nevertheless, the system with cncentratin gradient can be used, as any nn-equilibrium system, t prduce useful wrk if this system is supplied with special tls fr extracting heat frm the envirnment with a simultaneus transfrmatin f the extracted thermal energy int wrk upn the system appraches t the equilibrium. The vlume f useful wrk is equal t the vlume f the heat extracted frm the envirnment w useful H (38) thermstat The useful wrk f the system with a cncentratin gradient w useful beys expressins (35) and (38). The cncentratin cell is a gd example f such a system. 7. General cnclusins Any nn-equilibrium state can serve as an energy surce. The thermstat (envirnment) is an active participant f the prcess f reversible useful wrk prductin in devices perating at cnstant temperature. The heat released by chemical reactins, always

17 44 Thermdynamics Fundamentals and Its Applicatin in Science dissipates in the thermstat (envirnment). The useful wrk is prduced by special tls that prvide the extractin f the thermal energy f the thermstat (envirnment) and the transfrmatin f thermal energy int wrk at the prcess f the restratin f the chemical equilibrium. The vlume f the useful wrk is equal, in reversible cnditins, t the change in Gibbs functin. A spatial separatin f reactr and tls can lead t a substantial increase in the energy prduced. The direct cnversin f the Gibbs energy int useful wrk des nt exist. The cncepts f free and bund energy becme unnecessary. Authr details Niklai Bazhin Institute f Chemical Kinetics and Cmbustin, Nvsibirsk State University, Institutskaya 3, Nvsibirsk, Russia 8. References [1] Denbigh K (1971) The Principles f Chemical Equilibrium, 3rd ed., The University Press: Cambridge, 494 p. [2] IUPAC Green Bk (1996) Quantities, Units and Symbls in Physical Chemistry 48 p. [3] Atkins P (2001) The Elements f Physical Chemistry, 3rd ed., Oxfrd University Press, Oxfrd,.549 p. [4] Lwer S. (2010) Chemistry. Available virtualtextbk.html [5] Gkcen NA, Reddy RG (1996) Thermdynamics, Secnd editin, Springer, 416 p. [6] Haynie DN (2008), Bilgical Thermdynamics, 2 nd ed., Cambridge University Press, 422 p. [7] Haywd RW (1980) Equilibrium Thermdynamics fr Engineers and Scientists, J. Wiley, N.Y., 456 p. [8] Adam NK (1956) Physical Chemistry, Oxfrd, Clarendn Press, 658 p. [9] Physical Chemistry (1980) Gerasimv YaI, Ed., Chimiya, Мscw (in Russian), 1279 p. [10] Steiner LE (1948) Intrductin t Chemical Thermdynamic, 2nd ed.; McGraw-Hill Bk Cmpany, New Yrk, 516 p. [11] Bazhin NM, Parmn VN (2007) Cnversin f the Chemical Reactin Energy int Useful Wrk in the Van t Hff Equilibrium Bx. J. Chem. Ed. 84: [12] Bazhin NM, Parmn VN (2007) Ways f Energy Cnversin in Electrchemical Cells. Dklady Physical Chemistry 417: [13] Bazhin NM (2011) Mechanism f electric energy prductin in galvanic and cncentratin cells. J. Eng. Thermphysics 20: