Solution process enthalpy change

We can consider the solution process as having three components, each with an associated enthalpy change Solute particles separate from one another (AHsoiute)> solvent particles separate from one another ( Hgolventh solute and solvent particles mix (AHj ). The overall enthalpy change, AHsoln> is... 

The overall enthalpy change upon solution formation may be either positive or negative. Solution formation is favored both by a negative enthalpy change (exothermic process) and by a positive entropy change (the increase in disorder) of the system. 

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

In this process, the original solution is diluted by the addition of pure solvent, and hence, the enthalpy change is called an integral enthalpy of dilution. 

Solution In this example, it is assumed that we add a solute to a large enough volume of solution so that the composition of the mixture does not change. The enthalpy change for this process is referred to as a differential enthalpy of solution. We can represent this process by... 

From the nature of apparent properties, we note that the apparent molar enthalpy assigns all of the enthalpy change in forming a mixture to the solute. The result, as shown in equation (7.79), is that all we need to do to calculate AH for a solution process is find the difference in oL between the products and reactants. Thus, to solve Example 7.2 using apparent molar enthalpies, we would write... 

To show how we can calculate relative apparent molar enthalpies from enthalpies of dilution, consider as an example, a process in which we start with a HC1 solution of molality m = 18.50 mol-kg-1 and dilute it to a concentration of m = 11.10 mol-kg-1. The initial solution contains 3 moles of H20 per mole of HC1 (A = 3) while the final solution has A = 5. The enthalpy change for that process is measured. Then the m = 11.10 mol-kg-1 solution is diluted to one with m = 4.63 mol-kg-1 and its enthalpy of dilution measured. The series continues as illustrated below,... 

Arrecognizes that in the infinitely dilute solution HC1 is already completely separated into ions so that no enthalpy change is involved in the ionization process. 

Potassium nitrate dissolves readily in water, and its enthalpy of solution is +34.9 kj-niol. (a) Does the enthalpy of solution favor the dissolving process (b) Is the entropy change of the system likely to be positive or negative when the salt dissolves (c) Is the entropy change of the system primarily a result of changes in positional disorder or thermal disorder ... 

In the second hypothetical step, we imagine the gaseous ions plunging into water and forming the final solution. The molar enthalpy of this step is called the enthalpy of hydration, AHhvd, of the compound (Table 8.7). Enthalpies of hydration are negative and comparable in value to the lattice enthalpies of the compounds. For sodium chloride, for instance, the enthalpy of hydration, the molar enthalpy change for the process... 

When we include the data, the limiting enthalpy of solution of sodium chloride, the enthalpy change for the process... 

The entry where the row labeled Na+ intersects the column labeled Cl, for instance, is the enthalpy change, -784 kj-mol, for the process Na+(g) + Cl (g) —> Na (aq) + Cl(aq) the values here apply only when the resulting solution is very dilute. 

In addition to chemical reactions, the isokinetic relationship can be applied to various physical processes accompanied by enthalpy change. Correlations of this kind were found between enthalpies and entropies of solution (20, 83-92), vaporization (86, 91), sublimation (93, 94), desorption (95), and diffusion (96, 97) and between the two parameters characterizing the temperature dependence of thermochromic transitions (98). A kind of isokinetic relationship was claimed even for enthalpy and entropy of pure substances when relative values referred to those at 298° K are used (99). Enthalpies and entropies of intermolecular interaction were correlated for solutions, pure liquids, and crystals (6). Quite generally, for any temperature-dependent physical quantity, the activation parameters can be computed in a formal way, and correlations between them have been observed for dielectric absorption (100) and resistance of semiconductors (101-105) or fluidity (40, 106). On the other hand, the isokinetic relationship seems to hold in reactions of widely different kinds, starting from elementary processes in the gas phase (107) and including recombination reactions in the solid phase (108), polymerization reactions (109), and inorganic complex formation (110-112), up to such biochemical reactions as denaturation of proteins (113) and even such biological processes as hemolysis of erythrocytes (114). 

When ammonium nitrate, NH jNOj, dissolves in water, it absorbs heat. Consequently, its standard enthalpy of solution must be positive. This means that the entropy change caused by ammonium nitrate going from solid to solution must increase for the process to proceed spontaneously. This is exactly what one would expect based on the concept of entropy as a measure of randomness or disorder. 

Solid ammonium nitrate is an orderly, crystalline substance, a state considerably less random than a solution of ions in water. In this case, the positive entropy change outweighs the enthalpy change. That is TAS > AH. The Gibbs free energy change is negative, so the process will proceed spontaneously. 

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 overall enthalpy change of the insertion process contains contributions from four bonds (M-CO, M-COR, M-R and CO-R). As there is no significant difference between (Mn-R) and Zs(Mn-COR) then, at least in the case of manganese and hydrocarbon groups, R, the dominant factor will be the difference between T (Mn-CO) and E R-COX) [for R = CH3, E = 339 kJ mop1 (X = H), 370 kJ mol"1 (X = Cl) (Ref.23 )] which suggests that the insertion reaction is thermodynamically favoured with respect to decarbonylation. Kinetic studies of the carbonyl insertion reaction in solution have shown87) that the enthalpy of activation is 62 kj mol-1 for inser-... 

Table III gives values of the changes in Gibbs energy, enthalpy, entropy, and heat capacity of the solution process as calculated from the equations of Table I. Figure 1 shows the recommended noble gas mole fraction solubilities at unit gas partial pressure (atm) as a function of temperature. The temperature of minimum solubility is marked.

In order for mixing and solution to occur, it is essential that the change in free energy, AG, which is the driving force in the solution process, decrease to below zero. A/f and AG are equal to the change in enthalpy and change in entropy, and for constant temperature the relationship is the classical Gibbs equation ... 

This value will be compared with a calculation using data of heat capacities and heat of solution. From Perry s Chemical Engineers Handbook (1984), the heat solution of the heptahydrate is -39.2 Btu/lb and its heat capacity is 0.36 Btu/(lb)(°F). The enthalpy change of the cooling and crystallization process is... 

Those heal effects can be easily calculated when the enthalpies of formation and the enthalpy-temperature relations are available for the substances considered. Usually, the heat of reaction is defined as the heat evolved by the process, and it is equal to the enthalpy change but opposite in sign, while heats of fusion or vaporization always refer to ihe heat adsorbed, and for heals of solution the usage varies. In order to avoid any confusion, it is recommended to express heat effects of chemical process by reporting the enthalpy change. AH. 

Now we bring the two steps of the dissolving process together and calculate the energy for the overall change. As we see from Fig. 8.23, the limiting enthalpy of solution of sodium chloride, the enthalpy change for the process... 

Is it possible for a spontaneous process to absorb heat Use the Enthalpy of Solution activity (eChapter 17.2) to find a solution process that confirms your answer. What entropy change must accompany this process ... 

An important thermochemical quantity associated with the formation and stability of an ion in aqueous solution is its hydration enthalpy A//h yd, the enthalpy change under standard conditions for the process ... 

---