Useful Work and Gibbs Energy

dissipates in the thermostat (environment). The useful work special tools provide the extraction of the thermal energy of the thermostat (environment) and the transformation of thermal energy into work at the process of the restoration of the chemical equilibrium. The volume of the useful work is in reversible conditions, to the change in Gibbs function. A spatial separation of reactor and tools can lead to a substantial increase in the energy produced. The direct conversion of the Gibbs energy into useful work does not exist. The concepts of free and bound energy become unnecessary.


Introduction
Devices for performing chemical reactions are widely used to produce heat and work. Heat, in turn, produces work, e.g., in the form of electric energy in the so-called heat engines. It is the well-known fact that the efficiency of heat engines is restricted by Carnot principle. Therefore, it is generally recognized that heat cannot be fully converted to work. The efficiency of electric energy production due to the burning of fossil fuel of various kinds varies from 30 to 50 %.
On the other hand, there are galvanic and fuel cells whose efficiency can reach theoretically unity if it implies the ratio between the electric energy produced and the value of a change in Gibbs energy during chemical reactions occurring in a cell. These devices operate at constant temperature and pressure. It is concluded then that the devices, similar to a galvanic cell, cannot work at constant and uniform temperature according to the principle of heat engine. These devices assumed to operate only due to the direct transformation of chemical reaction energy, described by a change in the Gibbs energy, into work [1]. This viewpoint causes, however, numerous contradictions. The goal of this work is to analyze in detail the mechanism of useful work and heat production in chemical systems functioning at constant temperature and pressure.

Fundamental functions
In this Section, the fundamental functions of thermodynamics will be characterized, as the fundamental functions play the important role in the description of the process of the energy transformation. This notion includes four functions, i.e., internal energy, enthalpy, Helmholtz energy, and Gibbs energy. All of them are the state functions of energy dimension. It is generally believed that the value with energy dimension describes energy but this is by no means always the case. Below, the fundamental functions will elucidate whether these are energy values or not. , U q w    (1) where q is the heat, entering the system, and w is the total work performed on the system by the surroundings. Usually, the total work is given as the sum of two terms: expansion work ( ) p V   and so-called useful work If the process occurs at constant volume, the expansion work is absent and w describes the useful work. In the case of reversible process [3] .
Thus, eq. (1) is of the form in the case of reversible process Useful Work and Gibbs Energy 31 where A  is the change in Helmholtz energy at constant temperature and volume. Since the term "energy" means the capacity of the system to perform work, from eq. (4) it is formally concluded that A is the energy (but in this case eq. (4) can have the second explanation -A is the numerical characteristic of work and not the work itself). Further, from eq. (4) it was concluded that only the part of internal energy U minus TS can be used to produce work. Therefore, the TS quantity was called "bound energy" and (U -TS) -"free energy". The meaning of these notions will be considered in more detail using the Gibbs energy as an example because it is more often used in chemical applications.

Gibbs energy
According to IUPAC [2], "Gibbs energy (function), , is the enthalpy minus the product of thermodynamic temperature and entropy. It was formerly called free energy or free enthalpy". The reasons for the appearance of the term "Gibbs energy" are similar to those discussed when considering the Helmholtz energy except for the fact that the Gibbs energy describes the reversible useful work performed at constant temperature and pressure. This is readily observed by substituting eq. (3) and eq. (2) into eq. (1) with regard where G  is the change in Gibbs energy at constant temperature and pressure in the reversible process.
Unfortunately, the word "energy" as defined by IUPAC for a Gibbs energy (and also for a Helmholtz energy), causes great confusion. The Gibbs energy G = H -TS consists of two terms, the enthalpy and the entropy one. The origin of both of the terms is quite different despite the same dimension. The enthalpy, considered above, is not energy.
Consider now the problem of TS nature. In the case of the reversible process T S q   , but in the case of the irreversible process T S q   and additional contributions to T S  can arise without change in energy. For example, it is well known the increase of the entropy in the process of ideal gas expansion in vacuum without heat consumption (q = 0). Let us consider another example. Let the ideal gas-phase system involves a spontaneous process of the monomolecular transformation of substance A into B. As suggested a change in enthalpy tends to zero in this reaction. Thus, the internal energy, temperature, pressure, and volume will not undergo changes in this process. However, the entropy will increase due to the entropy of the mixing, because the entropy is a function of state. The value of the TS product will increase accordingly. However, the energy and even the bound energy cannot arise from nothing, whereas the entropy, being a function of state, can increase thus reflecting a change in system state without any changes in the internal system energy. Therefore, the TS term is not the energy, which also implies the absence of the term "bound" energy.
Since neither enthalpy nor TS are the energy quantities, the difference between them cannot represent energy. Thus, G cannot represent energy precisely in terms of this notion. Note that in the irreversible process, occurring at constant temperature and pressure, the Gibbs energy decreases and thus, is not conserved. This is readily demonstrated by e.g., the aforementioned example of a monomolecular transformation of substance A into B. Thus, conservation, as the most important criterion for energy quantity, fails for the Gibbs energy. It is concluded then that the Gibbs energy is not energy [4] but a function of state. In this regard, the Gibbs energy does not differ from heat capacity. The notions of the non-existing in reality quantities of "free energy" and "bound energy" cause only confusion and are, at present, obsolete [5].
Nevertheless, the notions that the Gibbs energy is the energy and thus, obeys conservation laws, prove to be long-lived, which causes erroneous interpretation of a number of processes some of which are of paramount importance.
Let us consider now the reaction of adenosine triphosphate (ATP) hydrolysis in water solution which is of great concern in biochemistry ATP + H2O = ADP + Pi.
Under the standard conditions [6]  The heat of 4 kcalmol -1 is actually released into solution due to hydrolysis. Unfortunately, it is then assumed that the Gibbs energy is conserved which makes his difference in o r H  and o r G  of 3 кcalmol -1 be located on the degrees of freedom of product molecules. However, in this connection, the product molecules could appear in the non-equilibrium excited states and transfer this energy to solvent molecules which would result in the emission of 7 kcalmol -1 rather than 4 kcalmol -1 which contradicts the experiment. There are no additional 3 кcalmol -1 on the degrees of freedom of AТР and Pi because the Gibbs energy is not conserved.

Conclusions
Thus, among the four quantities, that claims to be called energy quantity, only the internal energy deserves this name. The other functions, i.e., enthalpy Н, Helmholtz energy A, and Gibbs energy G are the parts of a mathematical apparatus for calculating various quantities, such as useful work, equilibrium constants, etc. This also means that the useful work is only calculated by using functions A and G, but cannot arise from the change in either the Helmholtz or the Gibbs energy. The physical nature of the work performed should be considered separately. Since the Helmholtz energy and the Gibbs energy are not energies, then, to avoid misunderstanding, it is better to exclude the word "energy" from the name of corresponding functions and to use the second variant of the name of these functions according to IUPAC: a Helmholtz function and a Gibbs function [7].

Direct conversion of chemical reaction energy to useful work
This Section is devoted to the discussion of the generally accepted theory of the direct conversion of energy [1,8] produced by chemical reaction to useful work. For simplicity, hereafter exergonic r ( 0) G   and exothermic r ( 0) H   reactions will be considered.
The useful work of the chemical reaction occurring at constant temperature and pressure in the reversible conditions can be calculated through the change in the Gibbs function (5). When the interest is the useful work performed by the system in the environment From eq. (6) it follows formally that the useful work of the reversible system in the environment is the sum of the enthalpy member The second case of r 0 S   is also of interest. In this case useful r w H    and the system must evolve the part of reaction heat to the environment. Why cannot the system use the total reaction heat for useful work production if this energy is at its disposal? Why can the system transfer energy of volume r T S  and neither more or less to the environment?
The third case is r 0 H   . Here the system can use only the thermal energy of the environment to produce useful work.
In the fourth case r 0 S   and the system performs work formally due to the reaction heat r ( ) H  without exchanging thermal energy with the environment. But it is not the case.
As mentioned in the Introduction, at present, it is generally accepted that the high efficiency of reversible devices is inconsistent with the notions that heat can be used to produce work and that such devices realize the direct conversion of chemical system energy into work. But below it will be shown that in all the cases, the useful work results from the heat of volume r G  dragged from the environment.

A mechanism of useful work production -A Van't Hoff Equilibrium Box
In this Section, it will demonstrate the mechanism of producing useful reversible work which involves no notions of the direct conversion of reaction energy into useful work. To this end, let us consider a Van't Hoff equilibrium box (VHEB) [9 -11]. A thermodynamic system must provide realization of the reversible process. This means that all changes in the system are infinitely slow at infinitely minor deviation from equilibrium.
It is assumed that in the system the following reaction occurs where A i are the reagents and B j are the products. The reaction takes place in the reactor (Fig. 1) where the reagents and products are in equilibrium. The chemical process is afforded by reservoirs with reagents and products contained in the system. For simplicity, the reagents and products are assumed to be in standard states. The system should have instruments to transport both the reagents from standard vessels to reactor and the products from reactor to standard vessels. In addition, the system should have tools to perform work, because the reversible process must be followed by reversible work production. The instruments and tools for performing work can be used together. The reactor, transporting instruments, and tools for performing work can be placed either separately or together. To provide constant and uniform temperature, it is necessary to locate the system, including reactor, standard vessels, transporting instruments, and tools in a thermostat, which can also imply the environment of constant temperature. Let us consider reversible chemical process in a closed system (Fig. 1). The realization of the reversible chemical process consists in reversible transformation of the reagents to products via chemical reaction. Let us consider the closed system.

Closed system
The process of reversible work production includes six stages.
Step 1. A small amount of substance Ai is removed from the vessel with reagent Ai in the standard state upon reversible process. Gaseous substances can be removed from a standard vessel and put into a portable cylinder with pistons [11]; solid or liquid substances are placed in lock chambers.
Then, the change in the Gibbs function and the work are zero because a minor portion of substance Ai is in the same standard state as the residual reagent.
Step 2. Reagent Ai is transformed reversibly from the standard into the equilibrium state in the reactor. For example, for ideal gas, the gas pressure will vary from a standard value to the equilibrium partial value in the reactor. In this stage, the reversible work 2i w is produced and The work 2i w can be done only due to thermostat heat because there are no other energy sources in the system (reaction is in the equilibrium). This work depends on the difference in the physical states of reagent Ai in the initial and equilibrium states. All reagents Ai participate in all stages in quantities proportional to i  . For ideal gas, the useful work is 2 , e q , s t ln( / ), where ,eq i p is the equilibrium pressure of i-th gas in the reactor, and ,st i p is the pressure of i-th gas in a standard vessel. For gaseous components, e.g., the process of reversible gas expansion (compression) in a portable cylinder for producing the maximum useful work, must proceed to the value ,eq i p . If expansion (compression) stops at ,eq i i p p  , then the inlet of gas into the reactor causes irreversible gas expansion and thus, the useful work will be less than the maximum one. When due to expansion (compression) the final pressure is less than ,eq i p , then the inlet of gas into the reactor causes the irreversible inlet of the i-th gas from an equilibrium mixture in the reactor to the portable cylinder, which also leads to a decrease in useful work. The solid and liquid substances can be transported by lock chambers. The pressure above either solid or liquid substances is varied from 1 bar to the value of the total equilibrium pressure in the reactor. The pressure is created using a minor portion of equilibrium reaction mixture.
The thermostat enthalpy varies as follows: Step 3. Reagent Ai is reversibly introduced into the reactor. Gaseous components are introduced into the reactor through semipermeable membranes using portable cylinders [11]; the solid or liquid ones -by means of lock chambers. Hence, 3 3 0, 0 The useful work production and the change in thermostat enthalpy 2 The same procedure is used to bring products from the standard vessels to reactor.
Step 4. An equivalent amount of product BJ is reversibly removed from the reactor. After this step is 4 4 0, 0 Step 5. Product BJ, removed from the reactor, is reversibly transformed from the equilibrium state into the standard one to perform work 5 j w . The change in the Gibbs function is not zero, where dragged Q is the heat dragged by tools.
For the reversible process, the maximal useful work is numerically equal to r G  , eq. (5) and, hence, the heat dragged by tools from thermostat in the volume The process has resulted in the useful work of the reaction, r G  , but the reaction did not occur yet. To put it otherwise, reaction work was performed without reaction. Only the thermal energy of the thermostat (environment) may be the source of work. This means that the process of useful work production and the reaction itself may be temporally and spatially separated. Thus, eq. (6) numerically connects reaction parameters and the magnitude of the work. However, no reaction energy is needed to produce the work. There is no need to subdivide energy sources into reaction source ( r H  ) and thermal because there is only one energy source: the thermal energy of thermostat (environment). Thus, the mixture in the reactor is moved off balance to be restored later. As a result, the reaction heat is emitted into the thermostat. Indeed, because of the elementary chemical act in the reactor, the energy released concentrates at the degrees of freedom of the product molecules. As the reactor temperature is constant, this energy is dissipated in the reactor and transferred to the thermostat which causes a r H  change in thermostat enthalpy. The total change in thermostat enthalpy is The cycle is over. Equations (12,13) can be used to calculate the total change in thermostat enthalpy thermostat r r The change in thermostat enthalpy is controlled only by reaction entropy [11].

The main principles of reversible device functioning in useful work production
This consideration demonstrates the main characteristics of the reversible process of useful work production at constant temperature and pressure in closed systems: 1. The useful work arises from the stage of the reversible transport of reagents from reservoir to reactor and from the stage of the reversible transport of products from the reactor. 2. The only energy source of useful work is the thermal energy of thermostat (or environment). 3. The heat released by chemical reactions is dissipated to the thermostat; the reaction heat is infinitely small in comparison with the volume of the thermostat thermal energy; therefore no reaction heat is really needed to produce work. 4. Although the useful work is produced by the cooling of one body (thermostat), the second law of thermodynamics is not violated, because the process is followed by a change in the amount of reagents and products. 5. The useful work is produced by heat exchange with thermostat (environment) according to the scheme reaction heat → thermal thermostat energy → useful work (scheme I) 6. The maximal useful work is equal the heat dragged by tools from thermostat. 7. Useful work depends on the difference in the concentrations of standard and equilibrium states of reagents and products. Therefore, the amount of extracted energy can be calculated via the change in the Gibbs function.
8. There is no direct conversion of the Gibbs energy into useful work. Gibbs energy is equal numerically the thermal energy dragged by systems from the environment for doing work.

The energy limit of chemical reactions -Open systems
Usually, the total energy which can be produced by chemical system, is r H  . However, this holds for closed systems only. For open systems, the case is quite different [11].
The open system is depicted in Fig. 2. As compared with the closed one (Fig. 1), the open system consists of two thermostats: the first one contains a reactor and the second one contains standard vessels with substances A and B and tools. The second thermostat can be replaced by the environment. In the process, steps 1, 2, 5, and 6 occur in the second thermostat (environment); steps 3 and 4 take place in the first one. Thus, the heat is released in the first thermostat only and the work is performed by thermal energy of the second thermostat (environment). The processes of heat and work production are spatially separated! The energy potential of the open system obeys the equation In the case of coal burning, it is possible to obtain the double total energy [11]. Thus, understanding the mechanism of useful work production in the reversible process allows us to predict an increase in the energy potential of chemical reactions in the open system.
It is worth noting that the open system under study is not a heat pump. The heat pump consumes energy to transfer heat from a cold body to the warm one. The open system studied does not consume external energy and produces heat due to chemical reactions in one thermostat and performs work by extraction of thermal energy from the second one.

Conclusions
The chemical reaction heat is always released in the reversible chemical processes and passes to the environment independent of the fact whether the system produces work or not, whether it is closed or open. The discussed mechanism of useful work production in the reversible systems did not use such notions as "free energy", "bound energy", "direct Gibbs energy conversion". The useful work arises only due to the heat exchange with a thermal basin in the process, described by the scheme I. The total energy of chemical system can be high and equal to r r H G    .

The mechanism of electric work production in a galvanic cell
The current theory of galvanic cells [1,3,8] is based on a direct transformation of the energy ( r G  ) of oxidation-reduction reactions into electric work. However, using VHEB as an example, It is clear that the energy of chemical reactions is first converted into the thermal energy of thermostat (environment) and then the thermal energy is extracted from the thermostat and transformed into work by means of special devices. It is assumed then that in galvanic cells, useful work is produced via the mechanism similar to the VHEB one [12,13]. The r G  value is used to calculate electric work which does not, however, mean that the electric work is performed at the expense of the Gibbs energy, all the more it was shown that the Gibbs energy is not energy. The electric work of a galvanic cell results from the electrodes discharged. Electric charging of electrodes is caused by chemical reactions in electrodes.
The mechanism of electric energy production in galvanic cells will be solved by analyzing the behavior of one ion. But it does not denote that thermodynamics will be applied to a real single ion: thermodynamic parameters of one ion imply the averaged parameters of many ions.

A galvanic cell
For simplicity a Daniell cell will be considered, consisting of zinc (№1) and copper (№2) electrodes (Fig. 3). The activity of salts in solutions is denoted by а1 and а2 , respectively. Let the cell with an open, external circuit be in equilibrium. Close now the external circuit for the moment and two electrons will transfer from the zinc to the copper electrode. The balance of the cell is distorted. Consider now the establishment of equilibrium on the zinc electrode (Fig 3). To this end, the zinc ion must leave a metallic plate and escape into the bulk. The dissolving of zinc ions is described by the change in a Gibbs function which readily gives the expression for both the work performed on the first electrode and its galvanic potential [3]  The latter is the potential for a half-cell. Thus, the approach, based on the consideration of the behavior of one ion, provides a common expression for electrode potential. dissipates in the thermostat (environment). The useful work is produced by special tools that provide the extraction of the thermal energy of the thermostat (environment) and the transformation of thermal energy into work at the process of the restoration of the chemical equilibrium. The volume of the useful work is equal, in reversible conditions, to the change in Gibbs function. A spatial separation of reactor and tools can lead to a substantial increase in the energy produced. The direct conversion of the Gibbs energy into useful work does not exist. The concepts of free and bound energy become unnecessary.