Heat of solution integral

Heats of solution are dependent on concentration. The integral heat of solution at any given concentration is the cumulative heat released, or absorbed, in preparing the solution from pure solvent and solute. The integral heat of solution at infinite dilution is called the standard integral heat of solution. 

The integral heat of solution can be used to calculate the heating or cooling required in the preparation of solutions, as illustrated in Example 3.5. 

A solution of NaOH in water is prepared by diluting a concentrated solution in an agitated, jacketed, vessel. The strength of the concentrated solution is 50 per cent w/w and 2500 kg of 5 per cent w/w solution is required per batch. Calculate the heat removed by the cooling water if the solution is to be discharged at a temperature of 25°C. The temperature of the solutions fed to the vessel can be taken to be 25°C. 

From a plot of the integral heats of solution versus concentration, -Atf°oln 2.22 mol/mol = 27.0 kJ/mol NaOH 42.2 mol/mol = 42.9 kJ/mol NaOH Heat liberated in the dilution per mol NaOH 

Heat transferred to cooling water, neglecting heat losses, 

In Example 3.5 the temperature of the feeds and final solution have been taken as the same as the standard temperature for the heat of solution, 25°C, to simplify the calculation. Heats of solution are analogous to heats of reaction, and examples of heat balances on processes where the temperatures are different from the standard temperature are given in the discussion of heats of reaction. Section 3.10. 

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The solubihty of the ammonium haUdes in water also increases with increasing formula weight. For ammonium chloride, the integral heat of solution to saturation is 15.7 kj /mol (3.75 kcal/mol) at saturation, the differential heat of solution is 15.2 kj /mol (3.63 kcal/mol). The solubihty of all three salts is given in Table 1 (7). 

The solubihty of ammonium sulfate in 100 g of water is 70.6 g at 0°C and 103.8 g at 100°C. It is insoluble in ethanol and acetone, does not form hydrates, and dehquesces at only about 80% relative humidity. The integral heat of solution of ammonium sulfate to saturation in water is 6.57 kj/mol (1.57... 

As M is increased in comparison with m, the heat of solution approaches a limiting value, which is evidently a special case of the differential as well as of the integral heat of solution it represents the first stage in the supposed series of small processes when the solute dissolves in initially pure solvent, and is called the heat of solution at infinite dilution ... 

If the integral heat of solution is independent of concentration, i.e., the same amount of heat is absorbed when unit mass of solute dissolves in any quantity of solute ... 

The heat absorbed when unit mass of solute is dissolved in an infinite amount of solvent is the differential heat of solution for zero concentration, Lo, and this is evidently equal to the integral heat of solution for concentration s plus the integral heat of dilution for concentration s ... 

Tables of the integral heat of solution over a range of concentration, and plots of the integral heat of solution as a function of concentration, are given in the handbooks for many of the materials for which the heat of solution is likely to be significant in process design calculations.

Mole fraction in liquid Integral heat of solution 0.005 0.01 0.015 0.02 0.03... 

Figure 4. Integral heat of solution of magnesium nitrate...

The hydration of anhydrous magnesium nitrate evolves heat, 25,730 cal/g mole Mg(NC>3)2 — Mg(NC>3)2 6H2O (II). Likewise, the dissolution of Mg(NC>3)2 or the hydrates in water or the addition of further water to these solutions also evolves heat (12,13,14,15). Figure 4 illustrates the molar integral heat of solution of Mg(NC>3)2, the value for infinite dilution being 21,575 cal/g mole. From these figures, the enthalpies of magnesium nitrate solutions may be computed. 

Figure 3.15 Plot of integral heat of solution Aifsoln(n) versus n (= moles H20/moles acid), showing the infinite-dilution limit A/fsoln(oo), the heat of dilution AHdn(ti, n2) from nx to n2, and the differential heat of solution (slope of tangent line) 8H(n ), 8H(n2) for representative concentrations...

AZ/soinC00) = Ai/Soin = integral heat of solution at infinite dilution (3.118)... 

TABLE 1.19 Standard Heats of Formation and Standard Integral Heats of Solution at Infinite Dilution (25° C, 1 atm)... 

Given in the literature are vapor pressure data for acetaldehyde and its aqueous solutions (1—3) vapor—liquid equilibria data for acetaldehyde—ethylene oxide [75-21-8] (1), acetaldehyde—methanol [67-56-1] (4), sulfur dioxide [7446-09-5]— acetaldehyde—water (5), acetaldehyde—water—methanol (6) the azeotropes of acetaldehyde—butane [106-97-8] and acetaldehyde—ethyl ether (7) solubility data for acetaldehyde—water—methane [74-82-8] (8), acetaldehyde—methane (9) densities and refractive indexes of acetaldehyde for temperatures 0—20°C (2) compressibility and viscosity at high pressure (10) thermodynamic data (11—13) pressure—enthalpy diagram for acetaldehyde (14) specific gravities of acetaldehyde—paraldehyde and acetaldehyde—acetaldol mixtures at 20/20°C vs composition (7) boiling point vs composition of acetaldehyde—water at 101.3 kPa (1 atm) and integral heat of solution of acetaldehyde in water at 11°C (7). 

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