Solution, integral heats

Molar entropy of an adsorbed layer perturbed by the solid surface Total enthalpy change for the immersion of an evacuated solid in a solution at a concentration at which monolayer adsorption occurs Heat of dilution of a solute from a solution Enthalpy change for the formation of an interface between an adsorbed mono-layer and solution Integral heat of adsorption of a monolayer of adsorbate vapor onto the solid surface... 

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... 

Corresponding to the integral heat and entropy of formation of the solution are the partial molar heats A//, and entropies AS, of solution of the components where... 

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 ... 

Integral Heat of Adsorption—corresponding with a heat of solution, and evolved when the gas is brought in contact with just enough adsorbent to take it up. 

FIG. 29 Integral heats of dilution for a solution of ammonium dodecane 1-sulfonate in water. 

The integral heat of mixing is, of course, the quantity directly measured in the calorimetric method However, the heat change on diluting a solution of the polymer with an additional amount of solvent may sometimes be measured in preference to the mixing of pure polymer with solvent In either case, the desired partial molar quantity AHi must be derived by a process of differentiation, either graphical or analytical. 

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. 

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.

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. 

The product FtCP, where Ft is the total molar flow rate and CP is the molar heat capacity of the flowing stream, may replace tic, in these equations, if the stream is an ideal solution. Integration of equation 21.5-8, or its equivalent, may need to take into account the dependence of mcP and FtCP on T and/or /A, and of (—AHRA) on T (see Example 15-7). However, compared to the effect of T on kA, the effect of T on (-AHRA) and cP is usually small. 

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

Henry s law is obeyed by a solute in a certain temperamre range. Prove that An2. Ani. and the integral heat of dilution are zero within this range. Do not assume that Heiuy s-law constant is independent of temperamre generally, it is not. 

For an ideal solution the heat of mixing is zero and therefore Equation (4.1) after integrating becomes ... 

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)... 

The integral heat (enthalpy) of solution A/7soln is defined as the total heat liberated (under constant-P conditions) when a solution is formed from its pure components A, B ... 

Pleshanov (P4) extends the integral heat balance method to bodies symmetric in one, two, or three dimensions, using a quadratic polynomial for the approximate temperature function. Solutions are obtained in terms of modified Bessel functions which agree well with numerical finite-difference calculations. 

Mishchenko and Dymarchuk (111) have studied the integral heats of reaction of cellulose with both water and aqueous solutions of electrolytes. A notable maximum in the integral heat of reaction occurs at approximately 2.5m. The authors visualize this sharp maximum as caused by the different behavior above and below the concentration where all the water is intimately tied up as water of hydration. Thus, assuming for calcium chloride that the hydration number is 8 for both the calcium ion and for the chloride ion, a concentration of 2.52m corresponds to complete hydration of the ions. Hence, they suggest that definite hydration numbers exist. It may well be argued, however, that heat of reaction with standard cotton cellulose is a poor probe to choose for studying the aqueous environment. The idea of fixed total hydration of the ions appears a somewhat unlikely interpretation if for no other reason than... 

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