Molar reaction enthalpy

The molar reaction enthalpy ArH of the oxidation consists of work and heat. The second law of thermodynamics applied on reversible processes yields... 

Assessing the thermal risks of the process means answering the six questions in the cooling failure scenario (see Section 3.3.1). The overall energy potential of the reaction is calculated from the molar reaction enthalpy of 200 kj moT1. The concentration to be used is that of the final reaction mass (2molkg 1), since the reactant B must be added to allow the reaction ... 

The activation energy of an endothermic step is necessarily at least as high as the molar reaction enthalpy, AH° (see Figure 2.2 in Section 2.2), and a step with very high activation energy is apt to be quite slow. Accordingly, a pathway with one or more highly endothermic steps is suspect if there are alternatives without these. 

Ds, Dp Effective diffusion coefficient of substrate and product, respectively AHr Molar reaction enthalpy... 

The disadvantage of the first approach is the requirement to know the quantities involved in the energy balance (e.g. molar reaction enthalpy, fluid heat capacity etc.). This disadvantage is eliminated by approaches based on calibration of the micro calorimeter. Moreover, calibration can compensate for small systematic errors produced by the micro calorimetric equipment, as well. In the second approach, however, the post-column analysis of reactant concentrations by an... 

However, during calorimetric experiments, if we assume that each step is characterized by a molar reaction enthalpy value AH, which has the dimension of a molar heat Qi, then ... 

The quantity refered to as the volumetric heat of reacton k is unconventionally defined from a thermodynamic viewpoint. The dimensions [kJ T ] are given for practical reasons. Strictly speaking, a (molar) reaction enthalpy has... 

Table 16. Molar reaction enthalpies for selected processes [328], [329]...

Equation 11.2.5 gives an expression for the total differential of the enthalpy with T, p, and as the independent variables. The coefficient of df in this equation is called the molar reaction enthalpy, or molar enthalpy of reaction, Af// ... 

That is, the molar reaction enthalpy is the rate at which the enthalpy changes with the advancement as the reaction proceeds in the forward direction at constant T and p. 

CHAPTER 11 liEACTIONS AND OTHER CHEMICAL PROCESSES 11.3 MOLAR REACTION ENTHALPY... 

During a process in a closed system at constant pressure with expansion work only, the enthalpy change equals the energy transferred across the boundary in the form of heat dH = dq (Eq. 5.3.7). Thus for the molar reaction enthalpy AfH = (dH/d )r,p, which refers to a process not just at constant pressure but also at constant temperature, we can write... 

A standard molar reaction enthalpy, ArH°, is the same as the molar integral reaction enthalpy A//ni(rxn) for the reaction taking place under standard state conditions (each reactant and product at unit activity) at constant temperature (page 318). 

AfH, of a substance is the enthalpy change per amount of substance produced in the formation reaction of the substance in its standard state. Thus, the standard molar enthalpy of formation of gaseous methyl bromide at 298.15 K is the molar reaction enthalpy of the reaction... 

A principle called Hess s law can be used to calculate the standard molar enthalpy of formation of a substance at a given temperature from standard molar reaction enthalpies at the same temperature, and to calculate a standard molar reaction enthalpy from tabulated values of standard molar enthalpies of formation. The principle is an application of the fact that enthalpy is a state function. Therefore, AH for a given change of the state of the... 

For example, the following combustion reactions can be carried out experimentally in a bomb calorimeter (Sec. 11.5.2), yielding the values shown below of standard molar reaction enthalpies (at T = 298.15 K, p = p° = bar) ... 

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... 

The standard molar reaction enthalpy at 298.15 K for this reaction is known, from reaction calorimetry, to have the value A H° = —167.08 kJmoP. The standard states of the gaseous H2 and CI2 are, of course, the pure gases acting ideally at pressure p°, and the standard state of each of the aqueous ions is the ion at the standard molality and standard pressure, acting as if its activity coefficient on a molality basis were 1. From Eq. 11.3.3, we equate the value of ArH° to the sum... 

Most reactions cause a change in the composition of one or more phases, in which case A//m(rxn) is not the same as the molar differential reaction enthalpy, Af/f = dH/d )r,p, unless the phase or phases can be treated as ideal mixtures (see Sec. 11.2.2). Corrections, usually small, are needed to obtain the standard molar reaction enthalpy Ar f ° from Ai/m(rxn). 

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). 

Use values of Af/f ° and AfG° in Appendix H to evaluate the standard molar reaction enthalpy and the thermodynamic equilibrium constant at 298.15 K for the oxidation of nitrogen to form aqueous nitric acid ... 

For some of the derivations in this chapter, we will need an expression for the rate at which the ratio jit / T varies with temperature in a phase of fixed composition maintained at constant pressure. This expression leads, among other things, to an important relation between the temperature dependence of an equilibrium constant and the standard molar reaction enthalpy. 

Equations 12.1.13and 12.1.14 are two forms of the van t Hoff equation. They allow us to evaluate the standard molar reaction enthalpy of a reaction by a noncalorimetric method from the temperature dependence of In AT. For example, we can plot In K versus /T then according to Eq. 12.1.14, the slope of the curve at any value of l/T is equal to -AtH /R at the corresponding temperature T. 

Some of the most useful experimentally-derived data for thermodynamic calculations are values of standard molar reaction enthalpies, standard molar reaction Gibbs energies, and standard molar reaction entropies. The values of these quantities for a given reaction are related, as we know (Eq. 11.8.21), by... 

For a homogeneous reaction in which the reactants and products are solutes in a solution, write a rigorous relation between the standard molar reaction enthalpy and the temperature dependence of the thermodynamic equilibrium constant, with solute standard states based on concentration. 

The reaction can be assumed to go to completion, and the amount of KCl was in slight excess, so the amount of AgCl formed was equal to the initial amount of AgNOj. After correction for the enthalpies of diluting the solutes in the initial and final solutions to infinite dilution, the standard molar reaction enthalpy at 298.15 K was found to be Ar // ° = —43.042 kJ mol . The same workers used solution calorimetry to obtain the molar enthalpy of solution at infinite dilution of crystalline AgNOs at298.15K Asoi,b// = 22.727kJmor ... 

Equation 14.3.16 also allows us to evaluate the standard molar reaction enthalpy by substitution in Eq. 12.1.13 on page 368 ... 

ArH (Molar) reaction enthalpy (heat of reaction for constant pressure) according to the stoichiometric equation J mol ... 

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