Enthalpy change of a reaction

The enthalpy change of a reaction, denoted by AHo, is the heat absorbed when reactants are completely converted to products at a fixed temperature and at a reference, or standard, pressure. For the purpose of defining AHo, the reactants are unmixed and pure, as are the products. With reference to Eq (9.5), if a moles of A and b moles of B are converted entirely to c moles of C and d moles of D, the enthalpy change is:

AHo = Ho (products) - Ho(reactants) = (dh^ + ch^ - (ahoA + bh^ (9.6)

where ho is the molar enthalpy of pure species i. The superscript o indicates that the enthalpies of the pure species are evaluated at the reference pressure, which is arbitrarily set at 1 atm (actually 1 bar, which is 1.01 atm). A pure substance at this pressure is said to be in its standard state. As a practical matter, the effect of pressure on AHo is small; the enthalpies of ideal gases are pressure-independent (Sect. 2.4) and those of solids and liquids are only weakly pressure-dependent. However, the entropy of an ideal gas is highly pressure-dependent, and adherence to the standard-pressure convention is essential for proper specification of the entropy analog of AHo.

Because the enthalpy change is equal to the heat exchanged with the surroundings in a constant-pressure process, AHo is also called the heat of reaction. If the reaction releases heat (AHo negative), it is called exothermic. If heat is absorbed (AHo positive), the reaction is endothermic. The reactions given by Eqs (9.1) and (9.4) are exothermic. Dissociation reactions such as N2(g) = 2N(g) are endothermic, since energy (or enthalpy) is required to break the N-N bond.

Contrary to the effect of pressure, the molar enthalpy of a pure substance is strongly temperature dependent. However, because AHo is the difference between the molar enthalpies of product and reactants, it varies much less strongly with temperature. Because enthalpy is not a property with an absolute value, a reference temperature must be chosen for the calculation of the individual ho values of the participants in the reaction. By convention, the molar enthalpies are those at 298 K (and 1 atm pressure). However, AHo, being the difference in molar enthalpies, does not depend on the choice of the reference temperature. This reference temperature is selected in part because the vast majority of chemical reactions of practical interest take place at room temperature or higher.

At the reference temperature and pressure, each substance taking part in the reaction is assumed to exist in its normal state. Thus, O2 is gaseous, water is liquid, and aluminum is solid., The molar enthalpy at temperatures T (but still at 1 atm) is given by Eqs (3.19) and (3.20) for solids and liquids, respectively, and for gases, by:

where Cp is the heat capacity at constant pressure. This equation is valid as long as the substance remains in its normal (i.e., 298 K, 1 atm) state at T. The reference temperature is arbitrary, but must be the same for all participants in the reaction.


Example: Oxidation reaction of metal M according to Eq (9.3) takes place at a temperature T above the melting point of M but below the melting point of MO2. Using Tref = 298 K and neglecting the difference between the heat capacities of solid and liquid M, the enthalpy change of the reaction is:

AHo = hMo2,298 + CPMO2 (T -298) - [hO,,298 + Cpo2 (T -298)]- [h°M,S298 + cpm(t -298)+ AhM,M] = AH298 + ACp(T - 298) + AhM,M

AH for the reaction given by Eq (9.5) is obtained by substituting h., hn from Eq (9.7) into

The second term on the right of this equation is usually small compared to the first and third terms. In this case, AHo is independent of temperature.

Example: Alternate method of calculating AHo for reaction (9.3) when M = Zr.

Values of h° for reactants and product at two temperatures are shown below (in kcal/mole)

T, K



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Getting Started With Solar

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