Infinite dilution enthalpy solution

FIG. 2-29 Enthalpy-concentration diagram for aqueous sodium hydroxide at 1 atm. Reference states enthalpy of liquid water at 32 F and vapor pressure is zero partial molal enthalpy of infinitely dilute NaOH solution at 64 F and 1 atm is zero. [McCahe, Trans. Am. Inst. Chem. Eng., 31, 129(1935).]... 

The net retention volume and the specific retention volume, defined in Table 1.1, are important parameters for determining physicochemical constants from gas chromatographic data [9,10,32]. The free energy, enthalpy, and. entropy of nixing or solution, and the infinite dilution solute activity coefficients can be determined from retention measurements. Measurements are usually made at infinite dilution (Henry s law region) in which the value of the activity coefficient (also the gas-liquid partition coefficient) can be assumed to have a constant value. At infinite dilution the solute molecules are not sufficiently close to exert any mutual attractions, and the environment of each may be considered to consist entirely of solvent molecules. The activity... 

The physical state of each substance is indicated in the column headed State as crystalline solid (c), liquid (liq), gaseous (g), or amorphous (amorp). Solutions in water are listed as aqueous (aq). Solutions in water are designated as aqueous, and the concentration of the solution is expressed in terms of the number of moles of solvent associated with 1 mol of the solute. If no concentration is indicated, the solution is assumed to be dilute. The standard state for a solute in aqueous solution is taken as the hypothetical ideal solution of unit molality (indicated as std state, m = 1). In this state the partial molal enthalpy and the heat capacity of the solute are the same as in the infinitely dilute real solution (aq. m). 

The standard change of enthalpy for the formation of sodium chloride in an infinitely dilute aqueous solution is thus given by the sum of the standard changes of enthalpy for the last two changes of state. Therefore,... 

Because both Kl and Ks are the constants determining the thermodynamic equlibria at infinite dilution of solute in the gas phase the differential heat of sorption q may be identified with differential enthalpy for isothermal transfer of 1 mole of solute from the reference standard gas phase to an adsorbed or diluted state, —AH [2,3]. Then... 

From thermodynamic tables, the enthalpy of formation of H" in an infinitely dilute aqueous solution is zero by definition the same quantity for Na" " from tabulated data is -240.1 kJmol On the basis of these results, the enthalpy associated with reaction (3.3.5) is 686.7 kJmol This result agrees within experimental error with that obtained by comparing the heats of formation of infinitely dilute aqueous solutions of NaCl and HCl. 

The enthalpy of vaporization of solid sulfur is 278.8 kJ mol h The enthalpy of formation of H" " in the gas phase is 1536.2kJmol h The enthalpy of formation of in an infinitely dilute aqueous solution is 33.1kJmol The enthalpy of solvation of is defined by the process... 

Infinite Dilution Enthalpies of Solution for Some Ionic Compounds ... 

The value of A//sat can differ from the infinite dilution enthalpy of solution AH defined in Section 7.6 for two reasons ... 

Many ionic properties show extremal behaviour for salts that consist of ions of roughly equal sizes. Let us consider the heat of solution iLsol> which is particularly easy to discuss since it corresponds to the enthalpy difference between a salt crystal and the infinitely dilute salt solution. For a given cation, let us say sodium, the heat of solution shows a maximum in between sodium chloride and sodium fluoride. For the slightly larger potassium ion, the maximum has moved to potassium iodide, while for rubidium the maximum is not observed for any halide ion, as shown in Fig. 1. Since the heat of solution Ffsol is related to the lattice enthalpy Hi tt and the ionic hydration enthalpy Ffhyd via... 

We can generalize this result by stating that extrapolating enthalpy changes in solution to infinite dilution gives the enthalpy change AHa for the process5... 

Thus, with a Henry s law standard state, H° is the enthalpy in an infinitely dilute solution. For mixtures, in which we choose a Raoult s law standard state for the solvent and a Henry s law standard state for the solute, we can... 

Relative partial molar enthalpies can be used to calculate AH for various processes involving the mixing of solute, solvent, and solution. For example, Table 7.2 gives values for L and L2 for aqueous sulfuric acid solutions7 as a function of molality at 298.15 K. Also tabulated is A, the ratio of moles H2O to moles H2S(V We note from the table that L — L2 — 0 in the infinitely dilute solution. Thus, a Raoult s law standard state has been chosen for H20 and a Henry s law standard state is used for H2SO4. The value L2 = 95,281 Tmol-1 is the extrapolated relative partial molar enthalpy of pure H2SO4. It is the value for 77f- 77°. 

Finally, they measured the enthalpy of solution of C HsO in water as a function of concentration and extrapolated to infinite dilution to get a value of -5.84 kJ-mol-1 for the reaction... 

Ais obtained from the enthalpies of solution of HCl(g) in water, extrapolated to infinite dilution. 

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. 

Values for the enthalpy of solution of hydrogen in transition metals at infinite dilution shown in Figure 7.22 are more negative for the early transition metals. It should be noted that the enthalpies of solution in general are functions of the concentration of the solute. Still, the values at infinite dilution are useful when looking for systematic variations, particularly since changes with composition are often limited. 

Figure 7.22 Enthalpy of solution of hydrogen in transition metals at infinite dilution [45].

Enthalpies of Solution of Trichloride Hydrates in Water (25°C and Infinite Dilution) ... 

An extreme example of the measurement of solution enthalpies is provided by that of lanthanum trichloride in molten potassium chloride. The value reported, which refers to infinite dilution, is - 20.8 kcal mol-1 (-87.0 kJ mol-1), at 890°C (223). This value is comparable with those for dissolution in lower alcohols at normal temperatures. 

The enthalpy of solution of the ammoniate LaI3-6NH3 in liquid ammonia at 25°C is -178.5 kJ mol-1. This value is close to that at infinite dilution, for it was determined at a concentration of Lal3 in the product solution of only 1 in 18,500 (224). Comparisons of this value with those for other iodides, or for aqueous media, are complicated by the fact that the ammoniate rather than anhydrous Lal3 was used for this calori-... 

Reactive ionic compounds are therefore useless to derive hydration enthalpies (or more generally, solvation enthalpies). Fortunately, there are many alternatives. Take lithium chloride, for example, and data from the NBS Tables [ 17]. The enthalpy of solution of this solid in water, at infinite dilution, is given by... 

When Equation (10.24) is applied to the temperature dependence of In Kp, where Kp applies to an isothermal transformation, the A// that is used is the enthalpy change at zero pressure for gases and at infinite dilution for substances in solution (see Section 7.3). 

Solute. The standard state for the solute is the hypothetical unit mole fraction state (Fig. 16.2) or the hypothetical 1-molal solution (Fig. 16.4). In both cases, the standard state is obtained by extrapolation from the Henry s-Iaw line that describes behavior at infinite dilution. Thus, the partial molar enthalpy of the standard state is not that of the actual pure solute or the actual 1 -molal solution. 

For this reason, the infinitely dilute solution frequently is called the reference state for the partial molar enthalpy of both solvent and solute. 

We have pointed out that a concentration m2(o of the solute in the real solution may have an activity of 1, which is equal to the activity of the hypothetical 1-molal standard state. Also, Hm2, the partial molar enthalpy of the solute in the standard state, equals the partial molar enthalpy of the solute at infinite dilution. We might inquire whether the partial molar entropy of the solute in the standard state corresponds to the partial molar entropy in either of these two solutions. 

Absolute values of partial molar enthalpies cannot be determined, just as absolute values of enthalpies cannot be determined. Thus, it is necessary to choose some state as a reference and to express the partial molar enthalpy relative to that reference state. The most convenient choice for the reference state usually is the infinitely dilute solution. Without committing ourselves to this choice exclusively, we will nevertheless use it in most of our problems. 

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