Molar integral heat

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 5. Molar integral heat of adsorption (HL — Hs) of argon on halozeolite...

Molar integral heat Qjnt Qjnt 1 3 Jmof Integral heat per mole adsorbed... 

By convention Q " is positive. The molar integral heat of adsorption is defined as the molar change in internal energy during the adsorption process (A u")... 

The molar integral heat of solution is defined as the change in enthalpy that results when 1 mole of solute (component 1) is isothermally mixed with Ni moles of solvent (component 2) and is given by... 

The molar integral heat, Q, is defined as the integral heat per mole of the adsorbate or... 

One of the problems encountered in the literature is that the data have been transformed and presented in such a way that it is difficult, if not impossible, to unscramble the presentation to obtain the original data. Luckily, some can be obtained directly, as is the case with data by Pace et al. [31,32], from original sources, such as PhD dissertations [33,34], or mathematically unwinding it as is the case with information supphed by Harkins and Jura [35]. Fig. 89 shows the molar integral heat of adsorption of water on anatase as obtained... 

Fig. 89. The dependence of the molar integral heat of adsorption with amonnt adsorbed from the data by Harkins and Jnra [35], The line is the zero parameter calculation.

Q = molar integral heat of adsorption as defined by Morrison, Los and Drain... 

The enthalpy change of mixing is often expressed in terms of the heat of solution or enthalpy change of solution. For a two-component solution, the molar integral heat of solution of component I in a solution with component 2 is defined by... 

Molar integral heat 2int = 1 mol Integral heat per mole adsorbed Isotherm calorimetry... 

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... 

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. 

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 differential heat of adsorption is related to the integral heat and to the differential molar energy of adsorption according to... 

Since Hi is equal to the partial molar heat content of the solute at infinite dilution, it follows from equation (44.8) that AFT in this case is equal to the differential heat of solution of the solid salt in the infinitely dilute solution. In dilute solution the total heat of solution usually varies in a linear manner with the molality, and so the differential heat of solution is then equal to the integral heat of solution per mole (cf. 44h). 

Fig. 9.10. Integral heat of solution as a function of mole fraction. The tangent intercepts are the partial molar heats of solution.

The increase of enthalpy that takes place when one mole of solute is dissolved in a sufficiently large volume of solution (which has a particular composition), such that there is no appreciable change in the concentration, is the molar differential heat of solution. When stating a value for this quantity, the specified concentration and temperature must also be quoted. Because the differential heat of solution is almost constant in very dilute solutions, the molar differential and integral heats of solution are equal at infinite dilution. At higher concentrations, the differential heat of solution generally decreases as the concentration increases. 

This relation can be used to define various other isochoric heat quantities such as integral and differential, molar and specific heats of reaction and the corresponding heat capacities. The most well known of these quantities is the (global or integral) heat capacity at constant volume or isochoric heat capacity, which we got to know briefly in Sect. 9.1 ... 

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