Differential heat

The heat evolved will now be a differential heat of adsorption, equal at constant volume to Qd or per mole, to qd - AI2, where Ae2 is the change in partial molar energy. It follows that... 

The integral heat of adsorption Qi may be measured calorimetrically by determining directly the heat evolution when the desired amount of adsorbate is admitted to the clean solid surface. Alternatively, it may be more convenient to measure the heat of immersion of the solid in pure liquid adsorbate. Immersion of clean solid gives the integral heat of adsorption at P = Pq, that is, Qi(Po) or qi(Po), whereas immersion of solid previously equilibrated with adsorbate at pressure P gives the difference [qi(Po) heat evolved as small increments of adsorbate are added [123]. 

Fig. XVn-21. (a) Differential heat of adsorption of N2 on Graphon, except for Oand , which were determined calorimetrically. (From Ref. 89.) (b) Differential heat of adsorption of N2 on carbon black (Spheron 6) at 78.5 K (From Ref. 124).

Differential heats of adsorption generally decrease steadily with increasing amount adsorbed and, in the case of physical adsorption tend to approach the heat of liquefaction of the adsorbate as P approaches P. Some illustrative data... 

It is not surprising, in view of the material of the preceding section, that the heat of chemisorption often varies from the degree of surface coverage. It is convenient to consider two types of explanation (actual systems involving some combination of the two). First, the surface may be heterogeneous, so that a site energy distribution is involved (Section XVII-14). As an example, the variation of the calorimetric differential heat of adsorption of H2 on ZnO is shown in Fig. 

Fig. XVIII-11. Calorimetric differential heat of adsorption of H2 on ZnO. Dashed line differential heat of desorption. (From Ref. 104.)...

Fig. 2.25 The differential heat of adsorption of argon on carbon blacks at 78 K, before and after graphitizalion.. Spheron O, Graphon. , and El denote molar heat of sublimation and of evaporation respectively.

Fig. 4.6 Plat of the net differential heat of adsorption q — qj against the relative adsorption n/no.j, where H(,.2 is the adsorption at p/p° = 0-2. (A) active carbon (B) carbon black. (After Dubinin.)...

Differential heats of adsorption for several gases on a sample of a polar adsorbent (natural 2eohte chaba2ite) are shown as a function of the quantities adsorbed in Figure 5 (4). Consideration of the electrical properties of the adsorbates, included in Table 2, allows the correct prediction of the relative order of adsorption selectivity ... 

Fig. 5. Differential heats of sorption in nature chaba2ite (4). A = N2 B = Ar Q = O2 <) = CO = CO2. See Table 2 for polarizabiUty, dipole moment, and quadmpole moment values for the gases. Volume adsorbed is expressed as cm of adsorbate as Hquid. To convert kj to kcal, divide by 4.184.

At low adsorbate loadings, the differential heat of adsorption decreases with increasing adsorbate loadings. This is direct evidence that the adsorbent surface is energetically heterogeneous, ie, some adsorption sites interact more strongly with the adsorbate molecules. These sites are filled first so that adsorption of additional molecules involves progressively lower heats of adsorption. 

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). 

At low relative humidities, adsorption is due to interaction of water with accessible hydroxyl groups. These are present on the lignin and on the carbohydrates ia the noncrystalline or poorly crystalline regions. The high differential heat of adsorption by dry wood, - 1.09 kJ/g (469 Btu/lb) water. 

At high relative humidities, adsorption is befleved to occur in response to a tendency for cellulose chains and lignin to disperse (solution tendency). Complete dispersion (dissolution) is prevented because of the strong interchain or interpolymer bonding at certain sites or regions. The differential heats of adsorption are much smaller than at low relative humidities. 

The latent heats at 25 C are 7656 kcal/kmol for acetone and 10,490 kcal/kmol for water, and the differential heat of solution of acetone vapor in pure water is given as 2500 kcal/kmol. The specific heat of air is 7.0 kcal/(kmol-K). 

The vertical temperature gradient (the lapse rate) is usually not monitored by routine meteorological observation, and it, too, must be approximated from estimates of solar insolation, solar angle, and differential heating due to uneven cloud cover. For purposes of diffusion analyses, the lapse rate is usually approximated by a constant. 

When an agitated bateh eontaining M of fluid with speeifie heat e and initial temperature t is heated using an isothermal eondensing heating medium Tj, the bateh temperature tj at any time 6 ean be derived by the differential heat balanee. For an unsteady state operation as shown in Figure 7-27, the total number of heat transferred is q, and per unit time 6 is ... 

The various terms appearing in these equations are self-evident. The differential heat release, dkidt, data are computed from differential scanning calorimetry (DSC). A typical DSC isotherm for a polyurethane reactive system appears in Fig. 11. Energetic composite processing is normally conducted under isothermal conditions so that Eq. (15) is more applicable. 

Spalling the break-up of a surface through the operation of internal stresses, often caused by differential heating or cooling. 

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 ... 

Differential Heats of Adsorption—corresponding with heats of evaporation ( 178), and evolved or absorbed when one equili-... 

Equations (2.47) to (2,49) can be solved for the respective differential heat element, and substitutions can be made into equation (2.46) to yield... 

In differential scanning calorimetry (DSC), higher precision can be obtained and heat capacities can be measured. The apparatus is similar to that for a DTA analysis, with the primary difference being that the sample and reference are in separate heat sinks that are heated by individual heaters (see the following illustration). The temperatures of the two samples are kept the same by differential heating. Even slight... 

Figure 7.5. Sticking coefficients along with differential heats of adsorption as measured by microcalorimetry for ethylene and acetylene on Rh(lOO). [Adapted from R. Kose, W.A. Brown and D.A. King, Chem. Rhys. Lett. 311 (1999) 109.]...

B) at the indicated stages, and the PGl, PG2, and total PG activities were determined by differential heat inactivation. Each time point is the average of at least two separate extractions assayed in duplicate. The developmental stages are MG, mature green Br, breaker stage, (time of first external color development) and +2, +5, +7, and +10 are days after breaker. 

Nagoe, M. Morimoto, T. (1969). Differential heat of adsorption and entropy of water absorbed on zinc oxide surface. Journal of Physical Chemistry, 73, 3809-14. 

To run adsorption storage systems efficiently the appropriate adsorbent has to be used. The right choice is possible on the basis of the measured adsorption equilibrium. The adsorption equilibrium of water vapor and different adsorbents (zeolites and silica gels) was experimentally found [3,4], The differential heat of adsorption (AHd) was calculated from the equilibrium data. 

B. Differential Heats of Interaction between a Reactant and Preadsorbed Species. Reaction Mechanisms. 246... 

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