Constant-pressure processes enthalpy change calculations

To calculate the heat duty it must be remembered that the pressure drop through the choke is instantaneous. That is, no heat is absorbed or lost, but there is a temperature change. This is an adiabatic expansion of the gas w ith no change in enthalpy. Flow through the coils is a constant pressure process, except for the small amount of pressure drop due to friction. Thus, the change in enthalpy of the gas is equal to the heat absorbed. 

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... 

Calculating enthalpy (or energy) change for a constant-pressure process. 

The subscript P on q indicates that the process occurs at constant pressure. Thus, the change in enthalpy equals the heat qp gained or lost at constant pressure. Because qp is something we can either measure or readily calculate and because so many physical and chemical changes of interest to us occur at constant pressure, enthalpy is a more useful function for most reactions than is internal energy. In addition, for most reactions the difference in AH and AE is small because P A V is small. 

The practical utility of the heat capacities is twofold. First, they allow us to calculate heat in constant-volume and constant-pressure processes. This is useful in energy balances. Second, they allow us to calculate changes in internal energy and enthalpy. This allows us to calculate these properties using equations rather than tables, or to obtain their values in states that are not found in tables. There is a limitation, however. Equation (. 17) maybe used only between two states of the same volume, and eg. f. iQ ) only between two states of the same pressure. The general calculation of properties between any two states will be discussed in Chanter r. 

The coffee-cup calorimeter shown in Figure 6.12 is a coustant-pressure calorimeter. The heat of the reaction is calculated from the temperature change caused by the reaction, and since this is a constant-pressure process, the heat can be directly related to the enthalpy change. A//. Research VCTsions of a constant-pressure calorimeter arc available, and these are used when gases are not involved. 

This calculation shows that reaction energies and reaction enthalpies are usually about the same, even when reactions Involve gases. For this reason, chemists often use A 5 reaction nd A reaction interchangeably. Because many everyday processes occur at constant pressure, thermodynamic tables usually give values for enthalpy changes. Nevertheless, bear In mind that these are different thermodynamic quantities. For processes with modest AE values and significant volume changes, A " and A H can differ substantially. 

Because the free-energy change for any process at constant temperature and pressure is AG = AH — TAS, we can calculate the standard free-energy change AG° for a reaction from the standard enthalpy change AH0 and the standard entropy change AS°. Consider again the Haber synthesis of ammonia ... 

The enthalpy change associated with a chemical reaction or phase change at constant pressure and temperature can be calculated from the enthalpy of each species involved in the process. When species A undergoes the phase transformation from a to p,... 

The enthalpy change for this polymerization is AWp = —6.5 Real mor. The polymerization reaction in this problem is finished at a fixed steam pressure (1 atm). The equilibrium concentration of H2O in the polymer melt varies with temperature and steam pressure in this case. Tlte enthalpy of vaporization of H2O is about 8 Real mol . Compare the limiting values of number average molecular weight of the polyamide produced at 280 and 250°C final polymerization temperatures. Hint Recall that the variation of an equilibrium constant K with temperature is given by r/(ln K)/d /T) = —AH/R, where AH is the enthalpy change of the particular process and R is the universal gas constant. Calculate Ki and the equilibrium concentration of H2O in the melt at 250°C and use Eq.(10-8).]... 

A well-insulated ice-water bath at 0.0°C contains 20 g ice. Throughout this experiment, the bath is maintained at the constant pressure of 1 atm. When a piece of nickel at 100°C is dropped into the bath, 10.0 g of the ice melts. Calculate the total entropy change for the thermodynamic universe of this process. (Specific heats at constant P nickel, 0.46 J g water, 4.18 J g ice, 2.09 J g. Enthalpy of fusion of ice, 334JK-ig-h)... 

Hess s law states that the heat changes of successive processes are additive if they are carried out at the same temperature and at constant pressure. This property follows from the fact that the enthalpy is a function of state and thus is a function only of the initial and final states of a system. Hess s law is extremely useful in thermochemistry since it permits the calculation of the heat change of a reaction difficult to perform from a series of reactions which are more easily carried out. 

For processes that involve phase transformation, the general approach is to use the ideal-solution equation for the enthalpy of the liquid and treat the vapor phase as an ideal-gas mixture. This reduces the problem to a calculation of the enthalpies of pure liquid and pure vapor components. If the calculation involves states near the phase boundary, hypothetical states maybe involved, whose properties must be calculated by extrapolation from known real states. As an example, consider the constant-pressure heating of a solution that contains 30% acetonitrile in nitromethane, at 1 bar. This is shown by the line LVon the Txy graph in Figure 11-1. The enthalpy change for this process is... 

A simpler device than the constant-volume calorimeter is the constant-pressure calorimeter, which is used to determine the heat changes for noncombustion reactions. A crude constant-pressure calorimeter can be constructed from two Styrofoam coffee cups, as shown in Figure 6.9. This device measures the heat effects of a variety of reactions, such as acid-base neutralization, as well as the heat of solution and heat of dilution. Because the pressure is constant, the heat change for the process is equal to the enthalpy change MI). As in the case of a constant-volume calorimeter, we treat the calorimeter as an isolated system. Furthermore, we neglect the small heat capacity of the coffee cups in our calculations. Table 6.3 lists some reactions that have been studied with the constant-pressure calorimeter. 

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