Standard enthalpy defined

The values of the thermodynamic properties of the pure substances given in these tables are, for the substances in their standard states, defined as follows For a pure solid or liquid, the standard state is the substance in the condensed phase under a pressure of 1 atm (101 325 Pa). For a gas, the standard state is the hypothetical ideal gas at unit fugacity, in which state the enthalpy is that of the real gas at the same temperature and at zero pressure. 

Enthalpy of Formation The ideal gas standard enthalpy (heat) of formation (AHJoqs) of chemical compound is the increment of enthalpy associated with the reaction of forming that compound in the ideal gas state from the constituent elements in their standard states, defined as the existing phase at a temperature of 298.15 K and one atmosphere (101.3 kPa). Sources for data are Refs. 15, 23, 24, 104, 115, and 116. The most accurate, but again complicated, estimation method is that of Benson et al. " A compromise between complexity and accuracy is based on the additive atomic group-contribution scheme of Joback his original units of kcal/mol have been converted to kj/mol by the conversion 1 kcal/mol = 4.1868 kJ/moL... 

When the partial pressure of each gaseous reagent is 1 bar and the concentration of each species in solution is 1 M, the conditions are defined to be standard. Under these conditions, the enthalpy change in a formation reaction is the standard enthalpy of formation (A... 

For the thermodynamic factors Stull takes into account the decomposition temperature . This is defined as the temperature reached by the decomposition compounds of the particular substance when the latter decomposes into these constituent elements. It is therefore calculated using the standard enthalpy of formation of the compound. 

The standard enthalpy of formation AH°f of a compound is defined as the enthalpy change when one mol of the compound is formed from its constituent elements in the standard state. The enthalpy of formation of the elements is taken as zero. The standard heat of any reaction can be calculated from the heats of formation —AH of the products and reactants if these are available or can be estimated. 

We define the standard enthalpy of formation AH as the enthalpy change involved in forming 1 mol of a compound from its elements, each element existing in its standard form. Both T and p need to be specified, because both variables influence the magnitude of AH. Most books and tables cite AH at standard pressure p and at a temperature of 298 K. Table 3.1 cites a few representative values of AH. ... 

This enthalpy has a special name we call it the enthalpy of combustion, and define it as the change in enthalpy accompanying the burning of methane, and symbolize it as A77(CombUstion) or just AHc.ln fact, we rarely perform calculations with AHc but with the standard enthalpy of combustion AH, where the plimsoll symbol implies s.t.p. conditions. 

The bond-dissociation energy is defined as the standard enthalpy change of the reaction in which the bond is broken R X - R —X. 

The proton affinity of any species A in the gas phase, abbreviated by PA(A), is defined as the negative of the standard enthalpy of reaction 4.25 at 298.15 K. The minus sign ensures that proton affinities always have positive values. 

Consider a molecule AB, where A and B can be atoms or groups of atoms. The A-B bond dissociation enthalpy, represented by DH (A-B), is defined as the standard enthalpy of the gas-phase reaction where the only event is the cleavage of that bond at a given temperature ... 

The so-called Laidler scheme was developed as a tool to estimate standard enthalpies of formation of organic compounds [90], It relies on the bond-additivity concept, that is, it assumes that the standard enthalpy of atomization of a given molecule in the gas phase (Aat//°, defined as the standard enthalpy of the reaction where all the chemical bonds are cleaved, yielding the gaseous ground-state atoms) can be evaluated by adding the relevant bond enthalpy terms. For instance, in the case of phenol, its standard enthalpy of atomization, or simply its enthalpy of atomization, refers to reaction 5.28 at 298.15 K ... 

Let us return to the thermal decomposition of Fe(CO)(l,3-C4H6)2. Once the calibration constant is known, the enthalpy of the net process 9.10 can be calculated as the product of s and the area (A + B). The next step is to correct this value to 298.15 K by using heat capacity data. This exercise is, however, complicated by the cyclobutadiene polymerization. Brown et al. analyzed the reaction products by mass spectrometry and found several oligomers, in particular the dimer (C4H6)2 and the trimer (C4H6)3 [163]. With such a mixture, it is difficult to ascribe the observed enthalpy change to a well-defined chemical reaction. This is discussed in the paper by Brown and colleagues, who were nevertheless able to recommend a value for the standard enthalpy of formation of the iron-olefin... 

Taking methane, CH4, as a reference compound, its standard enthalpy of formation is defined by the reaction ... 

Some elements exist in more than one form under standard conditions. For example, carbon can exist as either graphite or diamond, as shown in Figure 5.16. Graphite is defined as the standard state of carbon. Therefore, the standard enthalpy of formation of graphite carbon is 0 kj/mol. The standard enthalpy of formation of diamond is 1.9 kj/mol. Another example is oxygen, 02(g). Oxygen also exists in the form of ozone,... 

The calculations on the ammonium nitrate reaction demonstrate the immense value of tables that list the enthalpies for various substances. The values at 25° C and 1 atm are called standard enthalpies. For elements, the standard enthalpy is defined as zero. For compounds, the values are called standard enthalpies of formation because the compounds are considered to be formed from elements in their standard state. 

The most stable state of nitrogen in acidic solution is the ammonium ion, NH4(aq), which is isoelectronic with CH4 and H30+. It is a tetrahedral ion with strong N-H bonds. The mean N-H bond enthalpy in NH4(aq) is 506 kJ mol 1 (that of the O-H bonds in H30 + is 539 kJ mol" ). The enthalpy of hydration of the ammonium ion is — 345 kJ mol V This value placed into the Born equation (3.32) gives an estimate of the radius of the ammonium ion of 135 pm, a value insignificantly different from its thermochemical radius of 136 pm. The value is comparable to that estimated for the smaller H30+ ion (99 pm) from its more negative enthalpy of hydration (— 420 kJ mol -see Section 2.6.1). The proton affinity of the ammonia molecule is of interest in a comparison of its properties with those of the water molecule. The proton affinity is defined as the standard enthalpy change for the reaction ... 

The standard enthalpy of formation of an element in its most stable form is defined as 0. However, the enthalpy of formation of an element in... 

Values of AG°f at 25°C for some common substances are listed in Table 17.3, and additional values are given in Appendix B. Note that AG°f for an element in its most stable form at 25°C is defined to be zero. Thus, solid graphite has AG°f = 0 kj/mol, but diamond, a less stable form of solid carbon at 25°C, has AG°f = 2.9kJ/mol. As with standard enthalpies of formation, AH°f, a zero value of AG°f for elements in their most stable form establishes a thermochemical "sea level," or reference point, with respect to which the standard free energies of other substances are measured. We can t measure the absolute value of a substance s free energy (as we can the entropy), but that s not a problem because we are interested only in free-energy differences between reactants and products. 

Just as we can define a standard enthalpy of formation (AH°f) and a standard free energy of formation (AG°f), we can define an analogous standard entropy of formation (AS°f) as being the entropy change for formation of a substance in its standard state from its constituent elements in their standard states. Use the standard molar entropies given in Appendix B to calculate AS°f for the following substances ... 

The standard enthalpy of formation of a compound, AHf, is defined as the increment in enthalpy associated with the reaction of forming a given compound from its elements, with each substance in its thermodynamic standard state at the given temperature.2 The thermodynamic cycle for the enthalpy of formation of methane (CH4) from the standard states of carbon and hydrogen (graphite and hydrogen molecules) is shown in Figure 1. 

The superscript "o" or degree sign on AH designates a standard enthalpy change, that is, an enthalpy change when the reactants start out in standard states and the products end up in standard states. Standard states are defined as follows ... 

The standard enthalpy of formation is defined as the heat change that results when one mole of a compound is formed from its elements at a pressure of 1 atm. 

Thermo chemical tables list values of the standard enthalpy of formation, Af H° (formerly called heats of formation) the standard Gibbs energy of formation, Af G° the standard entropy, S° the heat capacity at constant pressure, C° m for substances in defined physical states (e.g. solid (s) or crystalline (c), liquid (1), aqueous (aq) or gas (g)). In much of this frame we shall be assuming that the heat capacities, C°m, are temperature independent. 

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... 

Although for solutions at infinite dilution the absolute enthalpy of hydration of a single ion is clearly defined, there is no purely thermodynamic way to separate the sum of the hydration energies of a cation and an anion into constituent parts. Hence it has been common practice to use conventional standard enthalpies of hydration related in the case of a cation Mz+ and an anion Xz to the absolute enthalpies of hydration by... 

In order to answer these questions we have carried out the analysis of total energies and standard enthalpies of formation of fullerenes per one carbon atom based on the published [2-4] and our own data. Every point of a plot for all stable fullerenes has been connected to the point of C6o fullerene. As a result, the allocated sector or "beam of stability" was formed (Fig. 1). Its top border line is defined by the lowest energies and standard enthalpies of formation of fullerenes, whereas the bottom curve defines the border of the highest values of energy and standard enthalpy of formation for all known stable isomers of fullerenes Cn. 

Eiere, Ea mini,2 stands for the activation energy at the step defining Eg (Eai is used at Ei < 82 and Ea2 at 81 > 82), and ArHj = Qads Pj means the standard enthalpy of step 3. 

The standard enthalpy of formation (AH°) of a compound is defined as the change in enthalpy that accompanies the formation of 1 mole of a cor -pound from its elements with all substances in their standard states. 

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