Integral enthalpy of solution

The enthalpy change for this process, in which we mix pure liquids, is known as an integral enthalpy of solution. 

Values of mixing processes. For example, for the integral enthalpy of solution process given in Example 7.1, we used L and L2 values to show that for the process... 

The integral enthalpies of solution, AH jj, of phosgene have been determined as a function of COCi concentration at 40 C using a caiorimetric method [391]. In benzene, toluene, 1,3-xylene or chlorobenzene, rises sharply to a maximum value of... 

Table A-22 Integral enthalpies of solution of ff2Se03(cr) in water.

For C° (Th", 298.15 K), as discussed in [2003GU1/FAN], the more recent results of [1997HOV] are preferred, as they are obtained using differential measurements, instead of integral enthalpies of solution, under conditions minimising com-plexation and hydrolysis. 

Enthalpies of mixing or intermediary enthalpies of dilution, copolymer partial enthalpies of mixing (at infinite dilution), or copolymer (first) integral enthalpies of solution... 

The (integral) enthalpy of mixing or the (integral) enthalpy of solution of a binaiy system is the amount of heat which must be supplied when mole of pure solvent A and ns mole of pure polymer B are combined to form a homogeneous mixture/solution in order to keep the total system... 

Note that because the values of and are independent of the solution composition, the molar differential and integral enthalpies of solution at infinite dilution are the same. 

An integral enthalpy of solution, Ai/(sol), is the enthalpy change for a process in which a finite amount soi of solute is transferred from a pure solute phase to a specified amount of pure solvent to form a homogeneous solution phase with the same temperature and pressure as the initial state. Division by the amount transferred gives the molar integral enthalpy of solution which this book will denote by A//m(sol,mB), where me is the molality of the solution formed ... 

The relations between A//(sol) and the molar integral and differential enthalpies of solution are illustrated in Fig. 11.9 on the next page with data for the solution of crystalline sodium acetate in water. The curve shows A//(sol) as a function of fsou with fsoi defined as the amount of solute dissolved in one kilogram of water. Thus at any point along the curve, the molality is /Mb = soi/(l kg) and the ratio A//(sol)/ soi is the molar integral enthalpy of solution A//m(sol, /mb) for the solution process that produces solution of this molality. The slope of the curve is the molar differential enthalpy of solution ... 

There is a simple relation between molar integral enthalpies of solution and dilution, as the following derivation demonstrates. Consider the following two ways of preparing a solution of molality mg from pure solvent and solute phases. Both paths are at constant T and p irn, closed system. 

Equation 11.4.10 is the desired relation. It shows how a measurement of the molar integral enthalpy change for a solution process that produces solution of a certain molality can be combined with dilution measurements in order to calculate molar integral enthalpies of solution for more dilute solutions. Experimentally, it is sometimes more convenient to carry out the dilution process than the solution process, especially when the pure solute is a gas or solid. 

Molar integral enthalpies of solution and dilution are conveniently expressed in terms of molar enthalpies of formation. The molar enthalpy of formation of a solute in solution is the enthalpy change per amount of solute for a process at constant T and p in which the solute, in a solution of a given molality, is formed from its constituent elements in their reference states. The molar enthalpy of formation of solute B in solution of molality will be denoted by Afi/(B, hib). 

The total enthalpy change is then Ai/(sol) = —nsAfH(B ) + BAf//(B,mB)- Dividing by B, we obtain the molar integral enthalpy of solution ... 

From tabulated values of molar enthalpies of formation, we can calculate molar integral enthalpies of solution with Eq. 11.4.11 and molar integral enthalpies of dilution with Eq. 11.4.12. Conversely, calorimetric measurements of these molar integral enthalpies can be combined with the value of AfH(B ) to establish the values of molar enthalpies of solute formation in solutions of various molalities. 

La can be related to molar differential and integral enthalpies of solution as follows. The enthalpy change to form a solution from amounts a and b of pure solvent and solute is given, from the additivity rule, by A//(sol) = (haHa + n H ) — (haH + We... 

The third method assumes we measure the integral enthalpy of solution A//(sol) for varying amounts soi of solute transferred at constant T and p from a pure solute phase to a fixed amount of solvent. From Eq. 11.4.5, the molar differential enthalpy of solution is given by Asoi/f = dA//(sol)/ d soi when a is held constant. We make the substitution... 

Equation 11.4.23 allows us to evaluate Lb at any molality from the dependence of on ms, with i obtained from experimental molar integral enthalpies of solution according to Eq. 11.4.22. 

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