Enthalpy other than standard-state

The activation parameters from transition state theory are thermodynamic functions of state. To emphasize that, they are sometimes designated A H (or AH%) and A. 3 4 These values are the standard changes in enthalpy or entropy accompanying the transformation of one mole of the reactants, each at a concentration of 1 M, to one mole of the transition state, also at 1 M. A reference state of 1 mole per liter pertains because the rate constants are expressed with concentrations on the molar scale. Were some other unit of concentration used, say the millimolar scale, values of AS would be different for other than a first-order rate constant. 

The standard entropy difference between the reactant(s) of a reaction and the activated complex of the transition state, at the same temperature and pressure. Entropy of activation is symbolized by either A5 or and is equal to (A// - AG )IT where A// is the enthalpy of activation, AG is the Gibbs free energy of activation, and T is the absolute temperature (provided that all rate constants other than first-order are expressed in temperature-independent concentration units such as molarity). Technically, this quantity is the entropy of activation at constant pressure, and from this value, the entropy of activation at constant volume can be deduced. See Transition-State Theory (Thermodynamics) Gibbs Free Energy of Activation Enthalpy of Activation Volume of Activation Entropy and Enthalpy of Activation (Enzymatic)... 

The equilibrium constant depends on the temperature at which a reaction takes place, but at any given temperature, it is independent of pressure. If the standard enthalpies of the reactants and products of a reaction are known, the equilibrium constant for the reaction at a temperature other than that of the standard state may be calculated using the van t Hoff equation, i.e. 

A single reference temperature Tr must be defined, at which the standard-state enthalpy H°(Tr) of the elements (in their most stable form) are all defined to be zero, H°(Tr) = 0. This reference temperture is taken to be Tr = 298.15 K. The enthalpy of an element at a temperature other than Tr is nonzero, in general, that is, H°(T Tr) 0 (for an element). 

The standard enthalpy of formation, A H (also represented by A or simply H ). of a substance at a given temperature is by definition, the enthalpy change when I mole of the substance in its standard state is formed, isothermally, at the indicated temperature from the elements, each in its standard stale. Usual units are kiloealories/mole. For all elements in their stable form at 25 C (298.15 K), the enthalpy of formation is zero If solid substances have more than one crystalline form, the most stable one is taken as the standard state, and the others have slightly different enthalpies. This convention about zero enthalpy is arbitrary hut universally accepted, and it may be compared to the arbitrary choice of zero lor terrestrial altitudes. The combination of enthalpies of formation, enthalpies of transition, and heat capacities makes possible the calculation of the enthalpy of a substance, in a given state at a given temperature, relative to a commonly accepted reference. 

In thermodynamic data tables (standard enthalpies or Gibbs energies of formation and standard molar entropies) which relate to compounds other than ions in a solution, the common convention that is applied involves setting the values of standard enthalpy and standard Gibbs energy of formation (or chemical potential) equal to OJmor for all simple pure elements in their stable physical state at the temperature in question. The data therefore refer to the formation of substances from simple elements. 

The above equation is a logical development of equation (2.7). Both equations include a reference temperature which is often 0°C, sometimes 25°C. It is important to know the value of this reference temperature, particularly if data are being collected from more than one source. Above it was stated that enthalpy represents the energy content of a stream. It will now be appreciated that it represents the energy content of a stream, with respect to some standard state that is taken to have zero enthalpy. Today enthalpy and other relevant data... 

The sea level reference point for all enthalpy expressions is called the standard enthalpy of formation (MIf). Substances ate said to be in the standard state at 1 atm, hence the term standard enthalpy. The superscript represents standard-state conditions (1 atm), and the subscript f stands for formation. By convention, the standard enthalpy of formation of any element in its most stable form is zero. Take the element oxygen as an example. Molecular oxygen (O2) is more stable than the other allotropic form of oxygen, ozone (O3), at 1 atm and 25°C. Thus, we can write = 0, but... 

The values of some standard enthalpies of formation at 25°C are given in Table 1.8, and a longer list is given in the Resource section. Tlie standard enthalpies of formation of elements in their reference states are zero by definition (because their formation is the null reaction element element). Note, however, that the standard enthalpy of formation of an element in a state other than its reference state is not zero ... 

Enthalpies of formation, such as those in Table 6.1, have been tabulated for standard states at certain temperatures, and that allows us to predict other reaction enthalpies at the same temperatures. At other than those temperatures, heat capacities are used to calculate a reaction enthalpy. When H is expressed as a function of T and P, the differential enthalpy for an individual reactant or product, i, is... 

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