Enthalpy absolute values

Our immediate goal is an expression for AHj and we must remember that this is the difference in the enthalpies of the solution and the pure components. We need not worry about the absolute values of the enthalpies of the individual states. 

The specific enthalpy (or total heat) of the mixture can be taken from 0 K (- 273.15°C) or from any convenient arbitrary zero. Since most air-conditioning processes take place above the freezing point of water, and we are concerned mostly with differences rather than absolute values, this is commonly taken as 0°C, dry air. For conditions of 25°C, saturated, the specific enthalpy of the mixture, per kilogram of dry air, is... 

The enthalpy of a substance, like its volume, is a state property. A sample of one gram of liquid water at 25.00°C and 1 atm has a fixed enthalpy, H. In practice, no attempt is made to determine absolute values of enthalpy. Instead, scientists deal with changes in enthalpy, which are readily determined. For the process... 

We described methods for obtaining values for V,-, Cpi, and S but did not apply the methods to //, and G, (or w), since absolute values of Gm and Hm cannot be obtained. We did describe a procedure for obtaining the volume difference V,— Vf using equations (5.40). (5.41) and (5.42),r where V is the volume of the pure substance, and indicated that equations of the same form can be used to obtain //, - Hf. We will return to this method later in this chapter as we describe ways for measuring relative partial molar enthalpies. 

We cannot obtain values for H since we cannot obtain absolute values for H or H. To overcome this problem, we define a quantity d>L, which we call the relative apparent molar enthalpy, by the equation... 

If AH% is negative, with an absolute value smaller than that of A//f, then the quantity of A// -I- Ais a negative number. In such a case the rate constant for the small reaction will have an apparent negative activation enthalpy (energy). That is, the rate will decrease with increasing temperature. 

There was a clear linear correlation between (a + (l)-values and the differences in activation enthalpies. The absolute value of the activation enthalpy difference went through a minimum, meaning that at medium angle sum there was no distinct preference of one or the other o-QM type, whereas at extreme angle sums —either very large or very small ones—one of the o-QM types is largely preferred over the other one. 

Like enthalpy, the absolute value of G for a substance cannot be measured, and only changes in G are meaningful. For a process occurring at constant temperature, the change in free energy from Equation 6.3 is ... 

Thermodynamics deals with processes and reactions and is rarely concerned with the absolute values of the internal energy or enthalpy of a system, for example, only with the changes in these quantities. Hence the energy changes must be well defined. It is often convenient to choose a reference state as an arbitrary zero. Often the reference state of a condensed element/compound is chosen to be at a pressure of 1 bar and in the most stable polymorph of that element/compound at the... 

Larger differences are observed when comparing the enthalpy of formation of the different halides of a given alkali metal. The enthalpy of formation of gaseous halide ions is exothermic since the exothermic electron gain enthalpy in absolute value is larger than the endothermic dissociation enthalpy. Furthermore, the enthalpy of formation of gaseous halide ions becomes less favourable with... 

The reaction enthalpy of the hydride transfer step usually has a low absolute value. Whether hydride transfer is exo- or endothermic depends on the stability (evidenced by the heat of formation) of the involved carbenium ions. Branched carbenium ions are more stable than linear ones. Longer carbenium ions are more stable than shorter ones. Replacement of a long-chain carbenium ion by... 

The inconvenience of the convention Af//°(H+, ao) = 0 is, of course, that it does not provide absolute values of the ion hydration enthalpies—only relative numbers can be evaluated. In other words, it tells nothing about the real size of the difference between the energetics of gas-phase and solution ions. Yet given the uncertainty that still affects the value of Af/7°(H+, ao) [50], the convention is a sensible option. 

Apparently, there is not much advantage in using bond enthalpy contributions to discuss bonding energetics in a series of similar complexes. As already stated, we could have selected any value for Z)//,°(Cr-CO) + DH (Cr-CO) + Z)//j (Cr-CO) and then derived chromium-arene bond dissociation enthalpies in Cr(CO)3(arene) compounds, all based on the same anchor. The trend would not be affected by our choice. Nevertheless, besides emphasizing that the absolute values so obtained should not be regarded as bond dissociation enthalpies, the bond enthalpy contribution concept attempts to consider a pertinent issue in molecular energetics the transferability of bond enthalpies. 

It is also evident from the definition [Equation (4.3)] that absolute values of H are unknown because absolute values of U cannot be obtained from classic thermodynamics alone. Therefore, from an operational point of view, it is possible only to consider changes in enthalpy AH. Such changes can be defined readily by the expression... 

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. 

If the retention enthalpies of the two sites differ, curvature may be observed in the plots. Moreover, if the enthalpies are opposite in sign, a minimum will occur in the van t Hoff plot at a temperature where the ratio of the retention foctors for the two mechanisms equals the absolute value of the reciprocal of the ratio of the corresponding enthalpies. Most frequently, however, less dramatic curvature would be expected. Such behavior may be anticipated in the RPC of amines with- arge nonpolar moieties which could be retained by silmiophilic interactions with surface silanols and by solvophobic interactions with nonpolar ligates of a reversed phase with low surface coverage. Recently an lihalysis of this behavior has been reported 93). 

This treatment illustrates the inherent difficulty of the problem. Any cycle of this type will allow the calculation of sums of enthalpies of hydration of cations and anions, but it will not allow the estimation of the separate quantities. There are two ways of dealing with the matter. One is to use the conventional reference zero that the enthalpy of hydration of the proton is zero, i.e. Ahyti// (H+, g) = 0. The second approach is to estimate an absolute value for A Z/tH h, g) that may be used to estimate the absolute values for enthalpies of hydration of any other ions. Both are exemplified in the text, but only the second is of general use in the study of the hydration of ions and the discussion of the factors that determine the values of enthalpies of hydration of individual ions. 

The estimated conventional values for the enthalpies of hydration of the Group 1 cations are very positive and give the wrong impression about the interaction of the gaseous ions with liquid water. This is because of the convention for the hydrated proton. The absolute values for the enthalpies of hydration for gaseous cations are given by the equation (rearranged equation 2.16) ... 

When an absolute value for the enthalpy of hydration of the proton is used in equation (2.22) it would have the effect of making the absolute enthalpies of hydration of the halide ions considerably less negative than the conventional values. 

The Absolute Value for the Standard Molar Enthalpy of Hydration of the Proton ... 

From the values for the conventional enthalpies of hydration of the Group 1 cations (Table 2.4) and those of the halide ions (Table 2.5), it is clear that they differ enormously. This leads to the quest for absolute values, which can be compared on a more equal basis. Equations (2.17) and (2.22) connect the conventional and absolute values of cations and anions respectively, and an approximate value for Ahyd//TH +, g) may be obtained by comparing the conventional values of the enthalpies of hydration of the Group I cations and the Group 17 halide anions by using equation (2.16) modified for singly charged cations ... 

This would allow the estimation of the value of Ahyd// (H +, g) only if the terms representing the absolute values for the enthalpies of hydration of the two ions cancel out, so that ... 

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