## Standard enthalpy of formation

Consider a general chemical reaction a A + b B ^ c C + d D, (8.3)

where A and B are called the reactants, C and D are the products, and a, b, c and d are integers (sometimes rational numbers) inserted to balance the equation.

Suppose the ingredients on the left-hand side of the equation (the reactants) are placed in a closed container that is impermeable to matter crossing its bounding surface. Furthermore, let the reaction (8.3) proceed from left to right at constant pressure. If no heat is allowed to enter or leave the system during the (irreversible) process, the final temperature will be different from that before the reaction began. If the temperature of the system goes up, we say the reaction is exothermic. If the temperature goes down, it is endothermic. Chemists have found a convenient way of characterizing the energetics of such reactions. Suppose the reaction goes from left to right to completion (no reactants remaining), then the heat required to restore the system to its original temperature at constant pressure is its change in enthalpy during the irreversible process, AH.

In order to find the heat of reaction for a particular chemical process it is necessary to start with the so-called standard enthalpy of formation of the individual compounds. These are based upon the enthalpy needed to form the compound from the state of the individual atomic species most commonly found in nature. For example, the convention for the element oxygen is to start with the gaseous form O2, not O. Similarly the base state according to the convention for nitrogen is N2 and for hydrogen it is H2. For argon it is the atomic form Ar and for carbon it is C.

The standard enthalpy of chemical reaction, when reactants in their standard state are converted to products in their standard states, is equal to the difference between standard enthalpy of formation of products and reactants:

AH° = [cAH°(C) + dAH°(D)] - [aAH°(A) + bAH°(B)]

The overbar indicates that 1 mol of the substance is considered, the superscript o refers to the standard state, which is at 1 atm and 25 oC by convention (see Table 8.1). If AH° is negative, heat is released and the reaction is exothermic. Exothermic

Table 8.1 Standard enthalpies of formation for selected compounds ( AH in units ofkJmol-1 )

The symbol in parentheses after the compound indicates whether its physical state is liquid, solid or gas. All values relate to 298 K.

reactions can proceed spontaneously in the atmosphere. If the opposite is true, AH° is positive, the reaction is endothermic, and an external source of energy is needed for the reaction to proceed.

The exothermic reactions can be significant for the thermal budget of the atmosphere. The classical example is the reaction leading to the formation of ozone. The heat released in this process dominates the form of the temperature profile in the stratosphere.

Example 8.1 The main mechanism of ozone formation in the stratosphere is the recombination of atomic oxygen:

where M is a molecule in the background gas which is needed to carry off the excess momentum in a two-bodies-to-one molecular collision. Find how much heat is released by this reaction.

Answer: To find how much heat is liberated, we need to calculate the enthalpy of the reaction:

AH°= [AH0(O3) + AH°(M)] - [AH°(O) + AH°(O2) + AAH°(M)]. (8.6) Since AH° (O2) = 0,

From Table 8.1, AH° = 142.7 kJ mol-1- 249.17 kJ mol-1 = -106.4 kJ mol-1. The minus sign indicates that this is an exothermic reaction. Therefore, with the reaction of ozone formation (8.5) 106.4 kJ per mole is liberated. This liberated heat warms the stratospheric air and raises its temperature which reaches a maximum at about 50 km altitude. Note that the concentration of O in (8.5) is determined by the photodissociation of O2, O3 and other species. □

Example 8.2 Suppose we wanted to know the change in enthalpy for the reaction:

We form

= +(-110.53) + (-241.82) - (-393.51) - (0.0) (kJmol-1) = 41.16kJmol-1.

AH ° is positive, which means that this reaction is endothermic, and heat is absorbed during the process. □

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