State functions enthalpy

Henceforth we concentrate on the use of Eqs. (l.lS.lf), (1.13.2f), (1.13.3f), (1.13.4e) as the fundamental building blocks (as applied to equilibrium processes) for all subsequent thermodynamic operations. The enormous advantage accruing to their use is that by the First Law all of these functions depend solely on the difference between the initial and the final equilibrium state. We no longer rely on the use of quantities such as heat and work that are individually path dependent. As will be shown shortly and in much of what is to follow, these functions of state may be manipulated to obtain useful information for characterizing experimental observations. One should note that the choice of the functions E, H, A, or G depends on the experimental conditions. For example, in processes where temperature and pressure are under experimental control one would select the Gibbs free energy as the appropriate function of state. Processes carried out under adiabatic and constant pressure conditions are best characterized by the enthalpy state function. 

By introducing the enthalpy state function (H) defined hy H = E + pV, where E is the system s total energy, p the pressure, and V the volume, and by using the condensed state condition (AV = 0), it follows from the first and second laws of thermodynamics that at constant pressure, AH = AQ and a change in the enthalpy equals the change in the heat (Q) released or absorbed by the system during any thermal process. 

Taking into account the definition of the free enthalpy state function, and more particularly its consequences on solid-state properties [107], it is not surprising that Ath has been already related to one of the intensive variables, such as refractive index, viscosity, etc., as recalled in the Introduction. 

Themodynamic State Functions In thermodynamics, the state functions include the internal energy, U enthalpy, H and Helmholtz and Gibbs free energies, A and G, respectively, defined as follows ... 

Thermodynamic paths are necessary to evaluate the enthalpy (or internal energy) of the fluid phase and the internal energy of the stationary phase. For gas-phase processes at low and modest pressures, the enthalpy departure function for pressure changes can be ignored and a reference state for each pure component chosen to be ideal gas at temperature and a reference state for the stationarv phase (adsorbent plus adsorbate) chosen to be adsorbate-free solid at. Thus, for the gas phase we have... 

Students often ask, What is enthalpy The answer is simple. Enthalpy is a mathematical function defined in terms of fundamental thermodynamic properties as H = U+pV. This combination occurs frequently in thermodynamic equations and it is convenient to write it as a single symbol. We will show later that it does have the useful property that in a constant pressure process in which only pressure-volume work is involved, the change in enthalpy AH is equal to the heat q that flows in or out of a system during a thermodynamic process. This equality is convenient since it provides a way to calculate q. Heat flow is not a state function and is often not easy to calculate. In the next chapter, we will make calculations that demonstrate this path dependence. On the other hand, since H is a function of extensive state variables it must also be an extensive state variable, and dH = 0. As a result, AH is the same regardless of the path or series of steps followed in getting from the initial to final state and... 

As with other state functions, the molar enthalpy defined by H... 

Because enthalpy is a state function, the enthalpy change of a system depends only on its initial and final states. Therefore, we can carry out a reaction in one step or visualize it as the sum of several steps the reaction enthalpy is the same in each case. 

The state function that allows us to keep track of energy changes at constant pressure is called the enthalpy, H ... 

Because enthalpy is a state function, the enthalpy of sublimation of a substance is the same whether the transition takes place in one step, directly from solid to gas, or in two steps, first from solid to liquid and then from liquid to gas. The enthalpy of sublimation of a substance must therefore be equal to the sum of the enthalpies of fusion and vaporization, provided that they are measured at the same temperature (Fig. 6.25) ... 

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... 

We have seen that a constant-pressure calorimeter and a constant-volume bomb calorimeter measure changes in different state functions at constant volume, the heat transfer is interpreted as A U at constant pressure, it is interpreted as AH. However, it is sometimes necessary to convert the measured value of AU into AH. For example, it is easy to measure the heat released by the combustion of glucose in a bomb calorimeter, but to use that information in assessing energy changes in metabolism, which take place at constant pressure, we need the enthalpy of reaction. 

Enthalpy is a state function therefore, the value of AH is independent of the path between given initial and final states. We saw an application of this approach in... 

FIGURE 6.32 In a Born-Haber cycle, we select a sequence of steps that starts and ends at the same point (the elements, for instance). The lattice enthalpy is the enthalpy change accompanying the reverse of the step in which the solid is formed from a gas of ions. The sum of enthalpy changes around the complete cycle is 0 because enthalpy is a state function. 

The lattice enthalpy of a solid cannot be measured directly. However, we can obtain it indirectly by combining other measurements in an application of Hess s law. This approach takes advantage of the first law of thermodynamics and, in particular, the fact that enthalpy is a state function. The procedure uses a Born-Haber cycle, a closed path of steps, one of which is the formation of a solid lattice from the gaseous ions. The enthalpy change for this step is the negative of the lattice enthalpy. Table 6.6 lists some lattice enthalpies found in this way. 

Equation defines a new state function, called enthalpy (H), that we can relate o gp H = E + P V We can use Equation to relate a change in enthalpy to changes in energy, pressure, and volume ... 

Enthalpy is a thermodynamic state function that describes heat flow at constant pressure. 

How do we determine the energy and enthalpy changes for a chemical reaction We could perform calorimetry experiments and analyze the results, but to do this for every chemical reaction would be an insurmountable task. Furthermore, it turns out to be unnecessary. Using the first law of thermodynamics and the idea of a state function, we can calculate enthalpy changes for almost any reaction using experimental values for one set of reactions, the formation reactions. 

Enthalpy is a state function, so A iiT for the overall reaction is the sum of the enthalpy changes for these two steps. 

N2 O4 N2(g) + 2 02(g) N2 04(g) The pathway shown in Figure 6-19 is not how the reaction actually occurs, but enthalpy is a state function. Because the change of any state function is independent of the path of the reaction, we can use any convenient path for calculating the enthalpy change. Hess law summarizes this feature ... 

Again, it is convenient to follow the seven-step procedure to solve this problem. We are asked to find an enthalpy of formation. Because enthalpy is a state function, we can visualize the reaction as occurring through decomposition and formation reactions. Appendix D lists enthalpies of formation, and the experimental heat of combustion is provided. We can use Equation to relate the enthalpy of combustion to the standard enthalpy of formation for octane. 

There is no single criterion for the system alone that applies to all processes. However, if we restrict the conditions to constant temperature and pressure, there is a state function whose change for the system predicts spontaneity. This new state function is the free energy (G), which was introduced by the American J. Willard Gibbs and is defined by Equation G = H - T S As usual, H is enthalpy, T is absolute temperature, and S is entropy. 

Why do some reactions go virtually to completion, whereas others reach equilibrium when hardly any of the starting materials have been consumed At the molecular level, bond energies and molecular organization are the determining factors. These features correlate with the thermodynamic state functions of enthalpy and entropy. As discussed In Chapter 14, free energy (G) is the state function that combines these properties. This section establishes the connection between thermodynamics and equilibrium. 

Hess s law states that the overall change in enthalpy in a reaction is the same whether the reaction takes place in one step or through a number of intermediate steps. This law can also be regarded as a consequence of the fact that enthalpy is a state function so that the enthalpy difference between the final state (products) and the initial state (reactants) is the same, irrespective of the reaction path (sequence in which the reaction takes place). As an example, let the following reaction be considered,... 

Enthalpies are often used to describe the energetics of bond formations. For example, when an amide forms through the condensation reaction between an ester and an amine, the new C-N bond, has an enthalpy of formation of -293 kj/mole. The higher the negative value for the bond enthalpy of formation, the stronger the bond. An even more useful concept is the enthalpy of a reaction. For any reaction, we can use the fact that enthalpy is a state function. A state function is one whose value is independent of the path traveled. So, no matter how we approach a chemical reaction, the enthalpy of the reaction is always the same. The enthalpy of... 

The enthalpy of formation of a compound is a so-called thermodynamic state function, which means that the value depends only on the initial and final states of the system. When the formation of crystalline NaCl from the elements is considered, it is possible to consider the process as if it occurred in a series of steps that can be summarized in a thermochemical cycle known as a Born-Haber cycle. In this cycle, the overall heat change is the same regardless of the pathway that is followed between the initial and final states. Although the rate of a reaction depends on the pathway, the enthalpy change is a function of initial and final states only, not the pathway between them. The Born-Haber cycle for the formation of sodium chloride is shown as follows ... 

Finally, we look at indirect ways of measuring these energies. Both internal energy and enthalpy are state functions, so energy cycles may be constructed according to Hess s law we look also at Bom-Haber cycles for systems in which ionization processes occur. 

Figure 3.4 If geographical position were a thermodynamic variable, it would be a state function because it would not matter if we travelled from London to New York via Athens or simply flew direct. The net difference in position would be identical. Similarly, internal energy, enthalpy, entropy and the Gibbs function (see Chapter 4) are all state functions...

H is a state function since p, V and U are each state functions. As a state function, the enthalpy is convenient for dealing with systems in which the pressure is constant but the volume is free to change. This way, an enthalpy can be equated with the energy supplied as heat, so q = AH. 

We could not perform cycles of this type unless enthalpy was a state function. 

We obtained this value of AHr knowing the other enthalpies in the cycle, and remembering that enthalpy is a state function. Experimentally, the value of A Hr = 99 kJmol-1, so this indirect measurement with Hess s law provides relatively good data. 

We are only allowed to make a choice of route like this because enthalpy is a state function. 

We recall that enthalpy H is a state function (see Section 3.1), so the overall enthalpy change of the reaction is independent of the chemical route taken in going from start to finish. It is clear from Figure 8.28 that the initial and final energies, of the reactants and products respectively, are wholly unaffected by the presence or otherwise of a catalyst we deduce that a catalyst changes the mechanism of a reaction but does not change the enthalpy change of reaction. 

Entropy, which has the symbol S, is a thermodynamic function that is a measure of the disorder of a system. Entropy, like enthalpy, is a state function. State functions are those quantities whose changed values are determined by their initial and final values. The quantity of entropy of a system depends on the temperature and pressure of the system. The units of entropy are commonly J K1 mole-1. If S has a ° (5°),... 

To proceed, we need to relate the enthalpy of reaction 2.2 to that of reaction 2.1. As shown by the cycle in figure 2.1 and by equation 2.8, which are based on the fact that the enthalpy is a state function, this turns out to be a simple exercise. 

The state function property of the enthalpy should be kept in mind for the next move of our discussion. In figure 2.1 we have decomposed reaction 2.1 in a series of steps whose net effect must correspond to the overall reaction. This means that the correct value for Asin//(2) is the solution enthalpy of 1 mol of oxygen in the (ethanol + water) mixture described—and not the solution enthalpy of the gas in pure water. Unfortunately, solution enthalpy data in organic liquid mixtures are not abundant in the chemical literature. So, either we are lucky to find them, we have the equipment to measure them in the laboratory, or we assume that the values will be identical to the ones in the pure solvent. The validity of this assumption depends on the system under discussion and on the accuracy needed for the final result, but in the present case it seems fair. Leaving further discussion to section 2.5, we shall take Asin//(2) = -12 4 kJ mol-1 [17],... 

Figure 3.1 A reaction profile, showing how the thermodynamic and kinetic quantities are related. X can be any state function (enthalpy, Gibbs energy, entropy, volume, etc.).

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