Standard reference state

Quantitative details of the concepts introduced above will be given in later chapters. As a beginning, however, it is important that one begins to get a feel for the nature of toe beast one is to confront as a first step into toe twilight zone. 

FIGURE 2.7. For a liquid-vapor system, the interfacial region will be smooth with a narrow transition region and smooth concentration profile. 

Calculate the total reversible thermodynamic work required to produce a spray of water of droplet diameter 2000 nm from 40 liters of water at 25°C. Take the surface tension of water as 72 mN m How many water drops would be produced, theoretically, if the droplets are all of equal 

Explain why the experimentally determined work of cohesion for the cleavage of a solid crystalline material in vacuum will always be greater than that obtained by the same process in the presence of nitrogen. 

It is generally found that the surface tension of a liquid decreases with an increase in temperature. Give a qualitative explanation for that phenomenon based on the general rules of molecular motion and the spring concepts presented in the chapter. 

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The values of fH° and Ay.G° that are given in the tables represent the change in the appropriate thermodynamic quantity when one mole of the substance in its standard state is formed, isothermally at the indicated temperature, from the elements, each in its appropriate standard reference state. The standard reference state at 25°C for each element has been chosen to be the standard state that is thermodynamically stable at 25°C and 1 atm pressure. The standard reference states are indicated in the tables by the fact that the values of fH° and Ay.G° are exactly zero. 

The resolution of this paradox lies in the assumptions about standard (reference), states which are unavoidably involved in the above definitions of and /3l-l- In order to ensure that and /3l-l are dimensionless (as they have to be if their logarithms are to be used) when concentrations are expressed in units which have dimensions, it is necessary to use the ratios of the actual concentrations to the concentrations of... 

Calculate the heat of reaction at the standard reference state (1 atm, 25°C) for... 

For ions in solution the standard reference state is the hydrogen ion whose standard chemical potential at = 1 is given an arbitrary value of zero. Similarly for pure hydrogen at Phj = = 0- Thus for the... 

The complex Cu(II)2(0-BISTREN) is much more acidic than the free Cu2+ ion, by a factor of more than three log units. This is primarily due to the presence of two Cu(II) ions, because the formation constant of the Cu2(OH)+ complex is not much less than that for the Cu2(0-BISTREN) complex with hydroxide. This is not a good indication of how well two free Cu2+ ions would bind hydroxide compared to the Cu2(0-BISTREN) complex, however, since one must take into account the dilution effect operative in the chelate effect to make the comparison more realistic (90). Thus, the formation constant for the Cu2OH+ complex above applies for the standard reference state of 1 M Cu2 +. In contrast, in 10 6 M Cu2+, for example, the pH at which Cu2(OH) + would form is raised from pH 5.6 to 11.6, ignoring the fact that Cu(OH)2(s) would precipitate out long before this pH as reached. By comparison, the acidity of the Cu2(0-BISTREN) complex is not affected by dilution and would still form the hydroxide complex at pH 3.9 if present at a 10"6 M concentration. 

Since AG° can be calculated from the values of the chemical potentials of A, B, C, D, in the standard reference state (given in tables), the stoichiometric equilibrium constant Kc can be calculated. (More accurately we ought to use activities instead of concentrations to take into account the ionic strength of the solution this can be done introducing the corresponding correction factors, but in dilute solutions this correction is normally not necessary - the activities are practically equal to the concentrations and Kc is then a true thermodynamic constant). 

Another simple method that has been used for assessing the data for many families of compounds, say ML , consists in plotting AH (ML ) versus A//y°(LH), with ML and LH in either their standard reference states (their stable physical states at 298.15 K and 1 bar) or in the gas phase20. It has been observed that many21 of the above plots which involve reliable thermochemical data define excellent straight lines. This empirical linear relationship may be expressed as equation 2. 

The meaning of this observation is seen by considering Scheme 1. AH° (3) and AH0(4) are the enthalpies of hypothetical reactions of a family of compounds ML , where reactants and products are in the standard reference states and in the gas phase, respectively, and AHy are vaporization or sublimation enthalpies. 

In summary, the standard enthalpy of formation of a pure substance at 298.15 K is the enthalpy of the reaction where 1 mol of that substance in its standard state is formed from its elements in their standard reference states, all at 298.15 K. A standard reaction enthalpy can be calculated from the values of AfH° for reactants and products by using equation 2.7 (Hess s law) ... 

It is obvious from the definition of standard enthalpy of formation that these quantities do not represent the absolute enthalpic stability of compounds. They merely reflect their enthalpic stability relative to that of the chemical elements in standard reference states (to which AfH° = 0 has been arbitrarily assigned). It is thus unreasonable to state that a given substance is more stable than another just because it has a lower standard enthalpy of formation. We can only use AfH° values to make such direct comparisons when we are assessing the relative stability of isomers. 

Could we have avoided the convention of A II° = 0 for the elements in their standard reference states Although this assumption brings no trouble, because we always deal with energy or enthalpy changes, it is interesting to point out that in principle we could use Einstein s relationship E = me2 to calculate the absolute energy content of each molecule in reaction 2.2 and derive ArH° from the obtained AE. However, this would mean that each molar mass would have to be known with tremendous accuracy—well beyond what is available today. In fact, the enthalpy of reaction 2.2, -492.5 kJ mol-1 (see following discussion) leads to Am = AE/c2 of approximately -5.5 x 10-9 g mol-1. Hence, for practical purposes, Lavoisier s mass conservation law is still valid. 

The energy equivalent of the calorimeter, e, and the enthalpy of the isothermal calorimetric process, A//icp, were derived from equations 8.2 and 8.4, respectively. The standard enthalpy of reaction 8.5 was computed as Ar//°(8.5) = AZ/icp/n, where n is the amount of substance of Mo(ri5-C5H5)2(C2H4) used in the experiment. The data in table 8.1 lead to a mean value Ar//°(8.5) = — 186.0 2.1 kJ mol-1, where the uncertainty is twice the standard deviation of the mean (section 2.6). This value was used to calculate the enthalpy of reaction (8.6), where all reactants and products are in their standard reference states, at 298.15 K, from... 

The activity a a of a component A in solution may be found by considering component A as the solvent. Then its activity at any mole fraction is the ratio of the partial pressure of the vapor of A in the solution to the vapor pressure of pure A If B is the solute, its standard reference state is taken as a hypothetical B with properties which it possesses at infinite dilution,... 

As suggested by Amis [99,100], ifthe standard reference state of dielectric constant is taken as inLnity ... 

The following reaction describes the formation of a compound from the constituent elements in their most stable forms at 1 atm, 25°C, the standard reference states. 

Table 6-2 lists some values of AH° at 25 °C. Note the absence of entries for H2(g), I2(s), and C(graphite), and all other elements in their standard reference states. By definition AH/ = 0 for all elements in their most stable states. By a special convention, AH° = 0 for H+(aq). 

Physical property data for many of the key components used in the simulation for the ethanol-from-lignocellulose process are not available in the standard ASPEN-Plus property databases (11). Indeed, many of the properties necessary to successfully simulate this process are not available in the standard biomass literature. The physical properties required by ASPEN-Plus are calculated from fundamental properties such as liquid, vapor, and solid enthalpies and density. In general, because of the need to distill ethanol and to handle dissolved gases, the standard nonrandom two-liquid (NRTL) or renon route is used. This route, which includes the NRTL liquid activity coefficient model, Henry s law for the dissolved gases, and Redlich-Kwong-Soave equation of state for the vapor phase, is used to calculate properties for components in the liquid and vapor phases. It also uses the ideal gas at 25°C as the standard reference state, thus requiring the heat of formation at these conditions. 

For a general compound, CaHbOcNd then the standard enthalpy of formation for the compound, Af//"(CaHbOcNd, s), is the enthalpy change taking place when 1 mole of the compound CaI IbOcNd is formed from its elements all in their standard reference states (i.e. defined as the form these elements take at the temperature of interest1, (see Note 11.1) (usually 25 °C = 298 K) and (curiously) at a pressure of 101.325 Pa (i.e. 1 atm) (see Note 11.1). The superscript ° refers to the standard... 

The standard state means that for each state a reference state of the aggregate exists. For gases, the thermodynamic standard reference state is taken to the ideal gaseous state at one atmosphere pressure at each temperature. The ideal gaseous state is the case of isolated molecules which gives no interactions and which obey the equation of state of a perfect gas. The standard reference state for pure liquids and solids at a given temperature is the real state of the liquid or solid substance at a pressure of 1 atmosphere. 

As already indicated, an activity of 1 is defined in different ways for the solute and the solvent. To describe liquid properties, such as the dielectric constant, the heat of vaporization, and the boiling point, the most convenient standard state is that of the pure solvent. For a solvent, aSoivent equals ysoiventAgoivent so the activity is 1 when the mole fraction Nso v nt is 1 (ysoivent = 1 for pure solvent). Specifically, the properties of a solvent are fully expressed when no solute is present. Thus the standard reference state for water is pure water at atmospheric pressure and at the temperature and gravitational level of the system under consideration. 

We take, as a standard reference state, the state of the bulk liquid methane of the same temperature T in equilibrium with a vapor of fugacity fs. For supercritical temperatures, we assumed extrapolated effective values of fugacity... 

Knowledge of trends of thermochemical data found for other elements may help to show that, in fact, the values for the trialkyl species in Table 1 are unreasonable. A method that seems to be a generally valid approach is to assess the data for families of compounds, say ML , by plotting AH/(ML ) versus Af//(LH), either with ML and LH in their standard reference states (i.e. in their stable physical states at 298.15 K... 

Enthalpy changes are relative quantities, so it is important to relate each substance to an interconsistent base. This is done by referring each enthalpy of formation to the chemical elements in their standard reference states. By convention, the enthalpy of formation of an element in its standard reference state is zero at all temperatures. 

Is zero by definition for the adopted standard reference state of Achesson spectroscopic graphite, i.e. artificial... 

H(298.15 K, 10 bar)-H (298.15 K)]. The enthalpy increment is taken from the recent equation of state formulation of Haar et al. (2) which yields enthalpy data at any temperature and pressure referenced to the triple point of water. The values of A H, a G and log K in this table refer to formation of HgO at p=10 bar from Hg and Og in their standard reference states (ideal gas at a pressure of 1 bar). 

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