Elements standard molar enthalpy

The standard molar enthalpy of formation of a compound, AH , is equal to the enthalpy change when one mole of the compound is formed at a constant pressure of 1 atm and a fixed temperature, ordinarily 25°C, from the elements in their stable states at that pressure and temperature. From the equations... 

A/Tf, the standard molar enthalpy of formation of a substance, is the enthalpy change for a reaction in which 1 mole of the substance in a specific state is formed from its elements in their standard states. 

The standard molar enthalpy of formation, A// , is the amount of heat absorbed when 1 mole of the substance is produced from its elements in their standard states. At 25°C, A// of liquid water is -285.8 kJ/mol and A// of water vapor is -241.8 kJ/mol. This means that more heat is released when liquid water is formed from its elements, then when gaseous water is formed from its elements. So, the formation reaction of liquid water is... 

The standard molar enthalpy of formation, AH, of elements in their standard states is zero. From the tabulated values of standard molar enthalpies in Appendix K, we can identify the standard states of elements. 

In Investigation 5-B, you used the reaction of oxygen with hydrogen to form water. Reactions like this one are known as formation reactions. In a formation reaction, a substance is formed from elements in their standard states. The enthalpy change of a formation reaction is called the standard molar enthalpy of formation, AH°f. The standard molar enthalpy of formation is the quantity of energy that is absorbed or released when one mole of a compound is formed directly from its elements in their standard states. 

Some standard molar enthalpies of formation are listed in Table 5.3. Notice that the standard enthalpies of formation of most compounds are negative. Thus, most compounds are more stable than the elements they are made from. 

Enthalpy of Formation. Tables of enthalpies of reaction generally list the enthalpies of formation of various compounds in their standard states from the elements in their standard states at the specified temperature. Thus, if the standard molar enthalpy of formation, Af//, of CO2 at 25°C is given as —393.509 kJ mol , the following equation is implied ... 

Besides equilibriumconstants, additional thermodynamic data were included, if available, although little emphasis was put on their completeness. The data for primary master species comprise the standard molar thermodynamic properties of formation from the elements (AfG standard molar Gibbs energy of formation AfH°m standard molar enthalpy of formation ApSm- standard molar entropy of formation), the standard molar entropy (5m), the standard molar isobaric heat capacity (Cp.m), the coefficients Afa, Afb, and Afc for the temperature-dependent molar isobaric heat capacity equation... 

The conventional thermodynamic standard state values of the Gibbs energy of formation and standard enthalpy of formation of elements in their standard states are A(G — 0 and ArH = 0. Conventional values of the standard molar Gibbs energy of formation and standard molar enthalpy of formation of the hydrated proton are ArC (H +, aq) = 0 and Ar// (H +, aq) = 0. In addition, the standard molar entropy of the hydrated proton is taken as zero 5 (H+, aq) = 0. This convention produces negative standard entropies for some ions. 

The enthalpies of formation of aqueous ions may be estimated in the manner described, but they are all dependent on the assumption of the reference zero that the enthalpy of formation of the hydrated proton is zero. In order to study the effects of the interactions between water and ions, it is helpful to estimate values for the enthalpies of hydration of individual ions, and to compare the results with ionic radii and ionic charges. The standard molar enthalpy of hydration of an ion is defined as the enthalpy change occurring when one mole of the gaseous ion at 100 kPa (1 bar) pressure is hydrated and forms a standard 1 mol dm-3 aqueous solution, i.e. the enthalpy changes for the reactions Mr + (g) — M + (aq) for cations, X (g) — Xr-(aq) for monatomic anions, and XOj (g) —< XO (aq) for oxoanions. M represents an atom of an electropositive element, e.g. Cs or Ca, and X represents an atom of an electronegative element, e.g. Cl or S. 

Since the chosen pressure of 1 bar represents the selected standard state, we designate the standard molar enthalpy of pure i at temperature T by the symbol = 0. However, the asterisk is ordinarily omitted, it being understood that element i is in its pure state. One must be careful in the application of this rule for example, the stable configuration of carbon at room temperature and ambient pressure is graphite, not diamond. In the same vein, sulfur under these conditions is stable in the rhombic habit, and Sn, in the white rather than the grey crystalline state. As another example, Br2 at P = 1 bar and 300 K is a liquid, while as a participant in reactions at 500 K Br2 is in the gaseous state. 

The factors of 2 multiply 5° for NO2 and O2 because 2 mol of each appears in the chemical equation. Note that standard molar entropies, unlike standard molar enthalpies of formation AH°, are not zero for elements at 25°C. The negative A5° results because this is the entropy change of the system only. The surroundings must undergo a positive entropy change in such a way that A5jot — 0-... 

The standard molar enthalpy of formation, AHf, listed in Appendix K is zero for almost all elements. A few entries are not zero explain why, and give two examples. 

Af//° the standard molar enthalpy of formation from the elements in their reference states (kJ-mol )... 

The problem this creates is that we do not want to have to tabulate an enthalpy change for every process or chemical reaction which might become of interest to us - there are too many. We would like to be able to associate an enthalpy with every substance - solids, liquids, gases, and solutes - for some standard conditions, so that having tabulated these, we could then easily calculate an enthalpy change between any such substances under those standard conditions. After that, we could deal with the changes introduced by impurities and other nonstandard conditions. The method developed to allow this is to determine, for every pure compound, the difference between the enthalpy of the compound and the sum of the enthalpies of the elements, each in its most stable state, which make up the compound. This quantity is called the standard molar enthalpy of formation from the elements. For aqueous ions, the quantity determined is a little more complicated (Chapter 15), but the principle is the same. It is this enthalpy quantity which is invariably tabulated in compilations of data. 

The reference point for all enthalpy expressions is called the standard molar enthalpy of formation (AHf) which is defined as the heat change that results when 1 mole of a compound in its standard state is formed from its elements in their standard states. The standard state of a liquid or solid substance is its most thermodynamically stable pure form at 1 bar pressure. The standard state for gases is similar, except that standard state gases are assumed to obey the ideal gas law exactly. The standard state for solutes dissolved in solution will be discussed in Chapter 10. In the notation AHf, the superscript represents standard-state conditions (1 bar), and the subscript f stands for formation. Although the standard state does not specify a temperature, we will assume, unless otherwise stated, AH° values are measured at 25°C. 

Plan We can use standard enthalpies of formation to calculate AH for the reaction. We can then use Le ChateUer s principle to determine what effect temperature will have on the equilibrium constant. Recall that the standard enthalpy change for a reaction is given by the sum of the standard molar enthalpies of formation of the products, each multipUed by its coefficient in the balanced chemical equation, less the same quantities for the reactants. At 25 C, AHj for NH3( ) is —46.19 kj/mol. The AHJ values for H2(g) and N2(g) are zero by definition, because the enthalpies of formation of the elements in their normal states at 25 C are defined as zero (S tion 5.7). Because 2 mol of NH3 is formed, the total enthalpy change is... 

This value is one of the many standard molar enthalpies of formation to be foimd in compilations of thermodynamic properties of individual substances, such as the table in Appendix H. We may use the tabulated values to evaluate the standard molar reaction enthalpy AfFf ° of a reaction using a formula based on Hess s law. Imagine the reaction to take place in two steps First each reactant in its standard state changes to the constituent elements in their reference states (the reverse of a formation reaction), and then these elements form the products in their standard states. The resulting formula is... 

There is no ordinary reaction that would produce an individual ion in solution from its element or elements without producing other species as well. We can, however, prepare a consistent set of standard molar enthalpies of formation of ions by assigning a value to a single reference ion. We can use these values for ions in Eq. 11.3.3 just like values of AfH° for substances and nonionic solutes. Aqueous hydrogen ion is the usual reference ion, to which is assigned the arbitrary value... 

Bomb calorimetry is the principal means by which standard molar enthalpies of combustion of individual elements and of compounds of these elements are evaluated. From these values, using Hess s law, we can calculate the standard molar enthalpies of formation of the compounds as described in Sec. 11.3.2. From the formation values of only a few compounds, the standard molar reaction enthalpies of innumerable reactions can be calculated with Hess s law (Eq. 11.3.3 on page 320). 

Standard molar enthalpy of formation A// [X] of a compound X, at a specified temperature T, is the enthalpy of formation of the compound X from its constituent elements in their standard state. Here is an example ... 

Ions in solntions are characterized by several thermodynamic quantities, including the standard molar heat capacities (at constant pressure) and entropies. Other important qnantities are the standard molar enthalpy and Gibbs energy of formation of the ions in solntion from the elements. As said earUer, in all these measures, it is possible to deal experimentally only with entire electrolytes or with such sums or differences of ions that are nentral. The assignment of absolute values to individual ions requires the splitting of the electrolyte values by some extra thermodynamic assumption that cannot be proved or disproved within the framework of thermodynamics. 

In much the same fashion as the AH° was tabulated, the standard molar entropies (S°) of elements and compounds are tabulated. This is the entropy associated with 1 mol of a substance in its standard state. Unlike the enthalpies, the entropies of elements are not zero. For a reaction, it is possible to calculate the standard entropy change in the same fashion as the enthalpies of reaction ... 

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