## Gibbs energy for chemical reactions

Earlier we showed how to find the enthalpy for phase changes and chemical reactions by manipulating values taken from standard tables. In this section we

3 The unit electronvolt (eV) is the energy an electron has after being accelerated across a potential difference of

1 volt. This is the preferred unit in atomic and nuclear physics. The binding energy of an electron in the ground state of a hydrogen atom is 13.6 eV.

will work with the Gibbs energy, which is useful in determining the feasibility of a chemical reaction and the abundances of species in chemical equilibrium situations. Using enthalpy to determine whether a reaction will proceed is limited, since enthalpy depends on entropy S and pressure p as well as the concentrations of the various species present. If we are to examine whether a reaction will proceed, we will find it hard to hold the entropy constant, especially in nature. On the other hand, the Gibbs energy is useful when the temperature and pressure are held constant. This is often the case in the atmosphere when the reaction occurs between trace gases at a certain altitude (pressure) and the temperature is constant because the reagents are buffered thermally by the surrounding background gas molecules.

The standard Gibbs energy is introduced similarly to the standard enthalpy of the reaction. The standard Gibbs energy of a chemical compound, AG , is the change of the Gibbs energy when 1 mol of a compound is formed (the overbar is an indication of 1 mol being considered). Conventionally, the standard Gibbs energy of compounds in their most stable form is taken to be zero. The superscript o indicates the standard state, which is at 1 atm and 25 °C.

For the general chemical reaction the standard Gibbs energy is the difference between the Gibbs energies of products and reactants:

AG° = [c AG°(C) + d AG°(D)] - [a AG°(A) + b AG°(B)]. (8.25)

In Chapter 4 we learned that if temperature and pressure are held constant, then as the system tends spontaneously to its equilibrium, its Gibbs energy will decrease to a minimum. Applying this equilibrium criterion to chemical systems, we conclude that if AG° of the reaction is negative, the reactants in their standard state are are converted to the products in their standard state. If, on the other hand, AG is positive, then an additional source of energy is needed for the reaction to proceed.

Example 8.5 Calculate the standard Gibbs energy of formation at 25 °C and 1 atm for the reaction:

Can it proceed spontaneously?

Table 8.2 Standard Gibbs energy for selected compounds (AG in units kJmol-1), all values relate to the standard conditions 298 K and 1 atm of pressure

Answer: The standard Gibbs energy of this reaction (Table 8.2)

AG° = AG°(NO2) + AG°(OH) — AG° (HO2) — G°(NO)

= (51.3 + 34.23 — 18.41 — 86.6) kJmol-1 = —19.5 kJ mol-1.

Since AG° is negative, the reaction (8.26) can proceed spontaneously. Note that there is no information about how long the reaction will take to complete. □

Example 8.6 Suppose we are looking for some effective mechanism of OH production in the atmosphere. We suggest that the recombination of H2O and O2 can work as a source for OH:

Before we start the laboratory experiments to check our idea, we can calculate the Gibbs energy of this reaction:

After substituting the numbers from Table 8.2, we get AG° = 281.3 kJ mol—1. The positive value of standard Gibbs energy means that the suggested mechanism for OH formation is thermodynamically impossible in the atmosphere. □

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