Enthalpy standard-state reaction change

The molar enthalpy of any substance depends on its state. The standard state of a liquid or solid substance is specified to be the pure substance at a fixed pressure of exactly 1 bar (100,000 Pa), which we denote by P°. The standard state for a gas is defined to be the corresponding ideal gas at pressure P°. The difference between the molar enthalpy of a real gas at 1 bar pressure and the corresponding ideal gas at 1 bar is numerically very small, but we will discuss this difference in a later chapter. If substance number i is in its standard state, its molar enthalpy is denoted by H (i). A standard-state reaction is one in which all substances are in their standard states before and after the reaction. The enthalpy change for a standard-state reaction is denoted by A 71°. The standard-state pressure was at one time defined to equal 1 atm (101,325 Pa). The difference in numerical values is small, and the formulas involving P° are the same with either choice. For highly accurate work, one must determine which standard pressure was used for an older set of data. 

The enthalpy change for 1 mol of any standard-state reaction in our restricted class is given by... 

If the products and reactants are not at their standard states, the enthalpy change for a reaction can have a different value from that of the standard-state reaction. For the reactions in our present class this difference is small. The enthalpy of an ideal gas does not depend on the pressure, and the enthalpies of real gases are nearly constant for moderate pressure changes. The effect on the enthalpy of pure solids and liquids due to moderate changes in pressures is also small. In a later chapter we will learn how to calculate these effects, but unless there is some need for great accuracy we will use the value of the standard-state enthalpy change at another pressure. 

Since the elements are in their standard states, the enthalpy change for the reaction is equal to the standard enthalpy of COj less the standard enthalpies of C and Oj, which are zero in each instance. Thus,... 

The heal of reaction (see Section 4.4) is defined as tlie enthalpy change of a system undergoing chemical reaction. If the retictants and products are at tlie same temperature and in their standard states, tlie heat of reaction is temied tlie standard lieat of reaction. For engineering purposes, the standard state of a chemical may be taken as tlie pure chemical at I atm pressure. Heat of reaction data for many reactions is available in tlie literature. ... 

Standard Heat of Reaction. This is the standard enthalpy change accompanying a chemical reaction under the assumptions that the reactants and products exist in their standard states of aggregation at the same T and P, and stoichiometric amounts of reactants take part in the reaction to completion at constant P. With P = 1 atm and T = 25°C as the standard state, AH (T,P) can be written as... 

The first ACH° is AfH for C02 at 298.15 K, since elements in their naturally occurring state are combining to give C02(g). This combustion reaction is the standard state enthalpy of formation if we carry it out at p = 1 bar and make small corrections to change the C02(g) to the ideal gas condition. 

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. 

In order to have a consistent basis for comparing different reactions and to permit the tabulation of thermochemical data for various reaction systems, it is convenient to define enthalpy and Gibbs free energy changes for standard reaction conditions. These conditions involve the use of stoichiometric amounts of the various reactants (each in its standard state at some temperature T). The reaction proceeds by some unspecified path to end up with complete conversion of reactants to the various products (each in its standard state at the same temperature T). 

The effect of pressure on AG° and AH0 depends on the choice of standard states employed. When the standard state of each component of the reaction system is taken at 1 atm pressure, whether the species in question is a gas, liquid, or solid, the values of AG° and AH0 refer to a process that starts and ends at 1 atm. For this choice of standard states, the values of AG° and AH0 are independent of the system pressure at which the reaction is actually carried out. It is important to note in this connection that we are calculating the enthalpy change for a hypothetical process, not for the actual process as it occurs in nature. This choice of standard states at 1 atm pressure is the convention that is customarily adopted in the analysis of chemical reaction equilibria. 

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 enthalpy that accompanies a change of physical state at standard conditions is called the standard enthalpy of transition and is denoted A trsH°. Enthalpy changes accompanying chemical reactions at standard conditions are in general termed standard enthalpies of reaction and denoted A r H0. Two simple examples are given in Table 1.3. In general, from the first law, the standard enthalpy of a reaction is given by... 

The standard enthalpy of formation, A fH, of a compound at 0 K reflects the strength of the chemical bonds in the compound relative to those in the constituent elements in their standard state. The standard enthalpy of formation of a binary oxide such as CaO is thus the enthalpy change of the reaction... 

Enthalpy changes of processes depend only on the end states. Normally the enthalpy change of reaction is known at some standard temperature, Tb = 298 K for instance. The simplest formulation of the heat balance, accordingly, is to consider the reaction to occur at this temperature, to transfer whatever heat is required and to raise the enthalpy of the reaction products to their final values. 

Standard state, for molecules, 24 687—688 Standard state enthalpy change for methanol synthesis, 25 305 Standard-state heat, 24 688 Standard-state heat of reaction, 24 688 Standards-writing organizations, 15 760 Standard Test Conditions (STC), 23 38 Standard test methods, 15 747—748 Standpipe pressure profiles, 11 818 Standpipes, in circulating fluidized beds, 11 817-819 Stand-retting, 11 606 Stannane, 13 613, 24 813... 

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 ... 

Enthalpies of reaction can also be calculated from individual enthalpies of formation (or heats of formation), AHf, for the reactants and products. Because the temperature, pressure, and state of the substance will cause these enthalpies to vary, it is common to use a standard state convention. For gases, the standard state is 1 atm pressure. For a substance in an aqueous solution, the standard state is 1 molar concentration. And for a pure substance (compound or element), the standard state is the most stable form at 1 atm pressure and 25°C. A degree symbol to the right of the H indicates a standard state, AH°. The standard enthalpy of formation of a substance (AHf) is the change in enthalpy when 1 mol of the substance is formed from its elements when all substances are in their standard states. These values are then tabulated and can be used in determining A//°rxn. 

In the bomb process, reactants at the initial pressure pi and temperature 7 are converted to products at the final pressure pf and temperature Tf. The primary goal of a combustion calorimetric experiment, however, is to obtain the change of internal energy, Ac//°(7r), associated with the reaction under study, with all reactants and products in their standard states pi = pf = O.IMPa) and under isothermal conditions at a reference temperature 7r (usually 298.15 K). Once AC//°(298.15K) is known, it is possible to derive the standard enthalpy of combustion, AC77°(298.15K), and subsequently calculate the standard enthalpy of formation of the compound of interest from the known standard enthalpies of formation of the products and other reactants. 

The experiments are usually carried out at atmospheric pressure and the initial goal is the determination of the enthalpy change associated with the calorimetric process under isothermal conditions, AT/icp, usually at the reference temperature of 298.15 K. This involves (1) the determination of the corresponding adiabatic temperature change, ATad, from the temperature-time curve just mentioned, by using one of the methods discussed in section 7.1 (2) the determination of the energy equivalent of the calorimeter in a separate experiment. The obtained AT/icp value in conjunction with tabulated data or auxiliary calorimetric results is then used to calculate the enthalpy of an hypothetical reaction with all reactants and products in their standard states, Ar77°, at the chosen reference temperature. This is the equivalent of the Washburn corrections in combustion calorimetry... 

The enthalpy change of a chemical reaction is known as the enthalpy of reaction, AHrxn- The enthalpy of reaction is dependent on conditions such as temperature and pressure. Therefore, chemists often talk about the standard enthalpy of reaction, AH°rxn - the enthalpy change of a chemical reaction that occurs at SATP (25 C and 100 kPa). Often, Alf n is written simply as AW°, The symbol is called nought. It refers to a property of a substance at a standard state or under standard conditions. You may see the enthalpy of reaction referred to as the heat of reaction in other chemistry books. 

H2(g) -I- - -02(g) — H20( ) ah = —285.8 kj/mol Notice that equations (2) and (3) occur in aqueous solution. You can use a coffee-cup calorimeter to determine the enthalpy changes for these reactions. Equation (4) represents the formation of water directly from its elements in their standard state. 

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 States. The enthalpy change of a reaction depends on the states of the substances involved. Thus, in the formation of water,... 

However, to estimate the standard enthalpy of formation, it is necessary to add two reactions to Equation (4.46), because, by definition, the standard enthalpy of formation refers to the formation of the compound in its standard state from the elements in their standard states. Therefore we introduce the following enthalpy changes to convert the elements from their standard states to the gaseous atoms at 298 K ... 

B) The formation of hydrogen sulfide from hydrogen gas and sulfur conforms to the definition of both standard enthalpy of reaction and standard enthalpy of formation since the heat change that is measured is for the formation of one mole of compound from the elements in their standard state. In Choice (D), diamond is not the stable aUotrope of carbon—it is graphite. 

Figure 2-8 The equilibrium constant of Reaction 2-79 as a function of temperature in InK versus lOOO/T plot. The rough straight line means that the standard state enthalpy change of Reaction 2-79 is constant. Solid circles are 1-atm data from Zhang et al. (1997a) and open circles are 500-MPa data from Zhang (unpublished data).

Because Ef= lE, b = AH, where AH is the standard state enthalpy change of the reaction, we have. 

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