Enthalpy change reverse process

FIGURE 6.23 The enthalpy change for a reverse process has the same value but the opposite sign of the enthalpy change for the forward process at the same temperature. 

We saw in Section 6.11 that the first law of thermodynamics implies that, because enthalpy is a state function, the enthalpy change for the reverse of a process is the negative of the enthalpy change of the forward process. The same relation applies to forward and reverse chemical reactions. For the reverse of reaction A, for instance, we can write... 

This important formula, which can be derived more formally from the laws of thermodynamics, applies when any change takes place at constant pressure and temperature. Notice that, for a given enthalpy change of the system (that is, a given output of heat), the entropy of the surroundings increases more if their temperature is low than if it is high (Fig. 7.16). The explanation is the sneeze in the street analogy mentioned in Section 7.2. Because AH is independent of path, Eq. 10 is applicable whether the process occurs reversibly or irreversibly. 

For example, consider a system in which metallic zinc is immersed in a solution of copper(II) ions. Copper in the solution is replaced by zinc which is dissolved and metallic copper is deposited on the zinc. The entire change of enthalpy in this process is converted to heat. If, however, this reaction is carried out by immersing a zinc rod into a solution of zinc ions and a copper rod into a solution of copper ions and the solutions are brought into contact (e.g. across a porous diaphragm, to prevent mixing), then zinc will pass into the solution of zinc ions and copper will be deposited from the solution of copper ions only when both metals are connected externally by a conductor so that there is a closed circuit. The cell can then carry out work in the external part of the circuit. In the first arrangement, reversible reaction is impossible but it becomes possible in the second, provided that the other conditions for reversibility are fulfilled. 

The enthalpy change can be found from the following two fundamental thermodynamic relationships which, in the case of ideal gases, are valid for irreversible processes as well as reversible ones ... 

The van t Hoff plots for thermal denaturation of proteins are linear in the transition region, thus allowing the enthalpy change (AHm) of unfolding at the transition temperature (Tm) to be estimated. Because of the change in free energy in (AG) = 0 at Tm (reversible process), the entropy of unfolding (ASm) at the transition midpoint can be calculated from ... 

Temperature and enthalpy are not the only conditions that determine whether a change is favourable. Consider the process shown in Figure 7.5. A closed valve links two flasks together. The left flask contains an ideal gas. The right flask is evacuated. When the valve is opened, you expect the gas to diffuse into the evacuated flask until the pressure in both flasks is equal. You do not expect to see the reverse process—with all the gas molecules ending up in one of the flasks—unless work is done on the system. 

The entropy and enthalpy changes associated with the reversible binding of the eluite by the stationary phase are defined by applying (he van t Hoff relationship to the chromatographic process as follows... 

The conversion from a tabulated value at 1.0 bar pressure to a real gas value at pressure P is, of course, the reverse of process 1-2-3, and so its enthalpy change is the negative of that given in Eq. (47). 

Since the mixing is the reverse process of separation, the changes in enthalpy and entropy are usually negative and positive, respectively. Therefore the vector appears in the second quadrant on the thermodynamic compass. 

Thus for a mechanically reversible, constant-pressure, nonflow process, the heat transferred equals the enthalpy change of the system. Comparison of the last two equations with Eqs. (2.16) and (2.17) shows that the enthalpy plays a role in constant-pressure processes analogous to the internal energy in constant-volume processes. 

Unlike work and heat, the property changes of the system for step d can be computed, since they depend solely on the initial and final states, and these are known. The internal energy and enthalpy of an ideal gas are functions of temperature only. Therefore, A Ud and Atfd are zero, because the initial and final temperatures are both 27°C. The first law applies to irreversible as well as to reversible processes, and for step d it becomes... 

The equilibrium state of any process involving an enthalpy change must be affected by temperature. The conformational transitions in proteins discussed in Section Pf,E are a case in point. The transition from the native to the denatured form in a nonaqueous solvent is usually an endothermic process, and a decrease in temperature will favor the native form. In such cases, it is possible that the disruption of the native conformation in a given protein-solvent system, which observed at room temperatures, may be reversed at sufficiently low temperatures. [On the other hand, particularly in mixed solvents, the transition from an ordered to a disordered state may be an exothemic process (Doty and Yang, 1956 Foss and Schellman, 1959), and the reverse effect of temperature may be ob-... 

Let s examine carefully the pathway we used in this example. First, the reactants were broken down into the elements in their standard states. This step involved reversing the formation reactions and thus switching the signs of the respective enthalpies of formation. The products were then constructed from these elements. This step involved formation reactions and thus enthalpies of formation. We can summarize the entire process as follows The enthalpy change for a given reaction can be calculated by subtracting the enthalpies of formation of the reactants from the enthalpies of formation of the products. Remember to multiply the enthalpies of formation by integers as required by the balanced equation. This procedure can be represented symbolically as follows ... 

This is not energetically reasonable since the enthalpy change for such a process is probably > 65 kcal.mole". Lapidus et subsequently studied deuterium and isotope effects in the oxalic acid decomposition. The deuterium effect (kiilko) was found to vary from 1.3 (400 °K) to 0.87 (435 °K), a reverse isotope effect. A similar reversal was found in the study, viz. 

Recall from Section 12.1 that a true reversible process is an idealization it is a process in which the system proceeds with infinitesimal speed through a series of equilibrium states. The external pressure therefore, can never differ by more than an infinitesimal amount from the pressure, P, of the gas itself. The heat, work, energy, and enthalpy changes for ideal gases at constant volume (called isochoric processes) and at constant pressure (isobaric processes) have already been considered. This section examines isothermal (constant temperature) and adiabatic (q = 0) processes. 

About the same value can be calculated using Eq. (4.24) if Q - = 0, because the enthalpy change for a reversible process for 1 lb of water going from 100 psia and 100 F to 1000 psia is 2.70 Btu. Make the computation yourself. However, usually the enthalpy data for liquids other than water are missing, or not of sufficient accuracy to be valid, which forces an engineer to turn to the mechanical energy balance. 

Heat supplied is identified with enthalpy change because pressure is constant (for these reversible processes at constant P, q ev = = A//). 

Note A// is the enthalpy change for the system. At constant pressure, the heat associated with the process is transferred reversibly to the surroundings. The heat capacity of the surroundings is vast, so its temperature remains constant. The process occurring in the system itself may be reversible or irreversible. 

A significant improvement to the process outlined above was the use of an expansion engine. Typically, in ASUs turbo expanders are used. An ideal turbo expander is isentropic and reversible. Illustrated in Figure 3.9, air at -150°F (172 K) and 90 psia (620 kPa) is expanded to 20 psia (138 kPa). In an isentropic expansion A-B, the expansion follows the isentrope with a net change in enthalpy. In reality the expansion will not be reversible and will follow a curve similar to A-C. The actual enthalpy change divided by the isentropic enthalpy change is a measure of the expander efficiency. 

The heat absorbed or released by a chemical reaction often has the impact of changing the temperature of the reaction vessel and of the chemicals themselves. The measurement of these heat effects is known as calorimetry. The enthalpy change of a reaction A Hrxn is equal in magnitude but has the opposite sign to the enthalpy change for the reverse reaction. If a series of reactions lead back to the initial reactants then the net energy change for the entire process is zero. 

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