Chemical Engineering Thermodynamics Lecturer: Zhenxi Jiang (Ph.D. U.K.)

Chemical Engineering Thermodynamics Lecturer: Zhenxi Jiang (Ph.D. U.K.) School of Chemical Engineering

Chapter 12Solution Thermodynamics: Application

12.4 Heat Effects of Mixing Processes The heat of mixing, defined in accord with Eq. (12.29), is: (12.39) It gives the enthalpy change when pure species are mixed at constant T and P to form one mole (or a unit mass) of solution. Data are most commonly available for binary systems, for which Eq. (12.39) solved for H becomes: H =x1H1+x2H2 + ΔH (12.40)

12.4 Heat Effects of Mixing Processes This equation provides for the calculation of the enthalpies of binary mixtures from enthalpy data for pure species 1 and 2 and from the heats of mixing. Treatment is here restricted to binary systems.

12.4 Heat Effects of Mixing Processes Data for heats of mixing are usually available for a very limited number of temperatures. If the heat capacities of the pure species and of the mixture are known, heats of mixing are calculated for other temperatures by a method analogous to the calculation of standard heats of reaction at elevated temperatures from the value at 25°C.

12.4 Heat Effects of Mixing Processes Heats of mixing are similar in many respects to heats of reaction. When a chemical reaction occurs, the energy of the products is different from the energy of the reactants at the same T and P because of the chemical rearrangement of the constituent atoms.

12.4 Heat Effects of Mixing Processes When a mixture is formed, a similar energy change occurs because interactions between the force fields of like and unlike molecules are different. These energy changes are generally much smaller than those associated with chemical bonds; thus heats of mixing are generally much smaller than heats of reaction.

12.4 Heat Effects of Mixing Processes Heat of Solution When solids or gases are dissolved in liquids, the heat effect is called a heat of solution, and is based on the dissolution of 1 mol of solute. If species 1 is the solute, then x1is the moles of solute per mole of solution. Becauseis the heat effect per mole of solution, H/x1is the heat effect per mole of solute. Thus, where is the heat of solution on the basis of a mole of solute ～

12.4 Heat Effects of Mixing Processes Solution processes are conveniently represented by physical-change equations analogous to chemical-reaction equations. When 1 mol of LiCl(s) is mixed with 12 mol of H2O, the process is represented by: LiCl (s) + 12H20 (l) → LiCl (12H20) The designation LiCl (12H20) represents a solution of 1 mol of LiCl dissolved in 12 mol of H2O.

12.4 Heat Effects of Mixing Processes The heat of solution for this process at 25°C and 1 bar is = - 33,614 J. This means that the enthalpy of 1 mol of LiCl in 12 mol of H2O is 33,614 J less than the combined enthalpies of 1 mol of pure LiCl (s) and 12 mol of pure H2O(J). Equations for physical changes such as this are readily combined with equations for chemical reactions. This is illustrated in the following example, which incorporates the dissolution process just described.

12.4 Heat Effects of Mixing Processes Example 12.4 Calculate the heat of formation of LiCI in 12 mol of H20 at 25°C. Solution 12.4 The process implied by the problem statement results in the formation from its constituent elements of 1 mol of LiCl in solution in 12 mol of H2O. The equation representing this process is obtained as follows:

12.4 Heat Effects of Mixing Processes

12.4 Heat Effects of Mixing Processes The first reaction describes a chemical change resulting in the formation of LiCl(s) from its elements, and the enthalpy change accompanying this reaction is the standard heat of formation of LiCl(s) at 25°C.

12.4 Heat Effects of Mixing Processes The second reaction represents the physical change resulting in the dissolution of 1 mol of LiCl(s) in 12 mol of H20(l), and the enthalpy change is a heat of solution. The overall enthalpy change, -442,224 J, is the heat of formation of LiCl in 12 mol of H20. This figure does not include the heat of formation of the H20.

12.4 Heat Effects of Mixing Processes Often heats of solution are not reported directly but must be determined from heats of formation by the reverse of the calculation just illustrated. Typical are data for the heats of formation of 1 mol of LiCI:

12.4 Heat Effects of Mixing Processes Heats of solution are readily calculated from these data. The reaction representing the dissolution of 1 mol of LiCl(s) in 5 mol of H20(l) is obtained as follows:

12.4 Heat Effects of Mixing Processes This calculation can be carried out for each quantity of H2O for which data are given. The results are then conveniently represented graphically by a plot of , the heat of solution per mole of solute, vs. , the moles of solvent per mole of solute. The composition variable, , is related to x1:

12.4 Heat Effects of Mixing Processes whence The following equations therefore relate, the heat of mixing based on 1 mol of solution, and, , the heat of solution based on 1 mol of solute: or

12.4 Heat Effects of Mixing Processes Figure 12.14 shows plots of vs. for LiCl(s) and HCl(g) dissolved in water at 25°C. Data in this form are readily applied to the solution of practical problems.

12.4 Heat Effects of Mixing Processes Because water of hydration in solids is an integral part of a chemical compound, the heat of formation of a hydrated salt includes the heat of formation of the water of hydration. The dissolution of 1 mol of LiCl2H2O(s) in 8 mol of H2O produces a solution containing 1 mol LiCl in 10 mol of H2O, represented by LiCl(10H2O). The equations which sum to give this process are:

12.4 Heat Effects of Mixing Processes Heats of Solution

12.4 Heat Effects of Mixing Processes Example 12.5 A single-effect evaporator operating at atmospheric pressure concentrates a 15% (by weight) LiCl solution to 40%. The feed enters the evaporator at the rate of 2 kg s-1 at 25°C. The normal boiling point of a 40% LiCl solution is about 132°C, and its specific heat is estimated as 2.72 kJ kg-1 °C-1. What is the heat-transfer rate in the evaporator?

12.4 Heat Effects of Mixing Processes Solution 12.5 The 2 kg of 15% LiCl solution entering the evaporator each second consists of 0.30 kg LiCl and 1.70 kg H20. A material balance shows that 1.25 kg of H20 is evaporated and that 0.75 kg of 40% LiCl solution is produced. The process is represented by Fig. 12.15.

12.4 Heat Effects of Mixing Processes The energy balance for this flow process is ΔHt = Q, where ΔHt is the total enthalpy of the product streams minus the total enthalpy of the feed stream. Thus the problem reduces to finding ΔHtfrom available data.

12.4 Heat Effects of Mixing Processes Because enthalpy is a state function, the calculational path for is immaterial and is selected for convenience and without reference to the actual path followed in the evaporator. The data available are heats of solution of LiCl in H20 at 25°C (Fig. 12.14), and the calculational path, shown in Fig. 12.16, allows their direct use.

12.4 Heat Effects of Mixing Processes The enthalpy changes for the individual steps shown in Fig. 12.16 must add to give the total enthalpy change: The individual enthalpy changes are determined as follows.

12.4 Heat Effects of Mixing Processes Heats of Solution

12.4 Heat Effects of Mixing Processes Enthalpy/Concentration Diagrams The enthalpy/concentration (Hx) diagram is a useful way to represent enthalpy data for binary solutions. It plots enthalpy as a function of composition (mole fraction or mass fraction of one species) with temperature as parameter. The pressure is a constant and is usually l(atm). Figure 12.17 shows a partial diagram for the H2SO4/H2O system, where enthalpy values here are for a unit mass of solution. Equation (12.40) is therefore directly applicable:

12.4 Heat Effects of Mixing Processes Enthalpy/Concentration Diagrams (12.40) Values of H for the solution depend not only on heats of mixing, but also on enthalpies H1and H2of the pure species. Once these are known for a given T and P, H is fixed for all solutions at the same T and P, because has a unique and measurable value for each composition.

12.4 Heat Effects of Mixing Processes Absolute enthalpies are unknown, and arbitrary zero points are chosen for the enthalpies of the pure species. Thus, the basis of an enthalpy/concentration diagram is H1= 0 for some specified state of species 1 and H2 =0 for some specified state of species 2. The same temperature need not be selected for these states for both species.

12.4 Heat Effects of Mixing Processes In the case of the H2S04( 1)/H2O(2) diagram shown in Fig. 12.17, H2 =0 for pure liquid H20 at the triple point [32(°F)], and H1= 0 for pure liquid H2S04 at 25°C [77(°F)]. In this case the 32(°F) isotherm terminates at H = 0 at the pure- H2O edge of the diagram, and the 77(°F) isotherm terminates at H = 0 at the pure-H2S04 edge of the diagram. The advantage of taking H = 0 for pure liquid water at its triple point is that this is the base of the steam tables. Enthalpy values from the steam tables can then be used in conjunction with values taken from the enthalpy/concentration diagram. Were some other base used for the diagram, one would have to apply a correction to the steam-table values to put them on the same basis as the diagram.

12.4 Heat Effects of Mixing Processes Enthalpy/Concentration Diagrams

12.4 Heat Effects of Mixing Processes For an ideal solution, isotherms on an enthalpy/concentration diagram are straight lines connecting the enthalpy of pure species 2 at =0 with the enthalpy of pure species 1 at = 1, as illustrated for a single isotherm in Fig. 12.18 by the dashed line. The solid curve represents an isotherm for a real solution. Also shown is a tangent line from which partial enthalpies maybe determined in accord with Eqs, (11.15) and (11.16). Equations (11.82) and (12.40) combine to give ; is therefore the vertical distance between the curve and the dashed line of Fig. 12.18.

12.4 Heat Effects of Mixing Processes Here, the actual isotherm lies below the ideal-solution isotherm, and H is everywhere negative. This means that heat is evolved whenever the pure species at the given temperature are mixed to form a solution at the same temperature. Such a system is exothermic. The H2SO4/H2O system is an example. An endothermic system is one for which the heats of solution are positive; in this case heat is absorbed to keep the temperature constant. An example is the methanol/benzene system.

12.4 Heat Effects of Mixing Processes One useful feature of an enthalpy/concentration diagram is that all solutions formed by adiabatic mixing of two other solutions are represented by points lying on a straight line connecting the points that represent the initial solutions. This is shown as follows.

12.4 Heat Effects of Mixing Processes Let the superscripts a and b denote two initial binary solutions, consisting of na and nb moles respectively. Let superscript c denote the final solution obtained by simple mixing of solutions a and b in an adiabatic process, either batch "mixing at constant P or steady-flow mixing with no shaft work or change in potential or kinetic energy. In either case, Ht = Q = 0, and the total energy balance is:

12.4 Heat Effects of Mixing Processes Our purpose now is to show that the three points c, a, and b represented by (Hc, x1c), (Ha, x1a), and (Hb, x1b) lie along a straight line on an Hx diagram. The equation for a straight line in these coordinates is:

12.4 Heat Effects of Mixing Processes H = m x1 + k (B) If this line passes through points a and b, Ha = m x1a + k and Hb = m x1b + k Each of these equations may be subtracted from the general equation, Eq. (B): H – Ha = m (x1 - x1a) H - Hb = m (x1-x1b)

Chemical Engineering Thermodynamics Lecturer: Zhenxi Jiang (Ph.D. U.K.)