Gibbs free energy, standard calculation

The Gibbs free energies are calculated using standard thermodynamic tables which are easily usable by machine since they give the data in the form of polynomial coefficients. The data are sometimes limited to 6000 K and it is therefore necessary to make extrapolations or to carry out calculations of partition functions from spectroscopic data In the latter case, which is certainly more reliable, one can determine standard thermodynamic functions with the aid of the classical formulae of statistical thermodynamics. The results may then be fitted to polynomials so that they match the tabulated data . Furthermore the calculation of partition functions is necessary for spectroscopic diagnostics and for the calculations of reaction rate parameters. 

Having calculated the standai d values AyW and S" foi the participants in a chemical reaction, the obvious next step is to calculate the standard Gibbs free energy change of reaction A G and the equilibrium constant from... 

Standard molar enthalpies of formation, AfH°m, and standard molar Gibbs free energies of formation, Af(7, are useful, since they can be used to calculate ArH° and ArG°. The relationships are... 

EXAMPLE 7.14 Calculating a standard Gibbs free energy of formation from enthalpy and entropy data... 

Calculate the standard Gibbs free energy of formation of HI(g) at 25°C from its standard molar entropy and standard enthalpy of formation. 

STRATEGY We write the chemical equation for the formation of HI(g) and calculate the standard Gibbs free energy of reaction from AG° = AH° — TAS°. It is best to write the equation with a stoichiometric coefficient of 1 for the compound of interest, because then AG° = AGf°. The standard enthalpy of formation is found in Appendix 2A. The standard reaction entropy is found as shown in Example 7.9, by using the data from Table 7.3 or Appendix 2A. 

J 12 Calculate the standard Gibbs free energy of reaction from standard Gibbs free energies of formation (Example 7.15). 

Use the standard Gibbs free energies of formation in Appendix 2A to calculate AG° for each of the following reactions at 25°C. Comment on the spontaneity of each reaction under standard conditions at 25°C. 

Calculate the standard reaction entropy, enthalpy, and Gibbs free energy for each of the following reactions from data found in Appendix 2A ... 

The vapor pressure of chlorine dioxide, Cl02, is 155 Torr at —22.75°C and 485 Torr at ().()0°C. Calculate (a) the standard enthalpy of vaporization (b) the standard entropy of vaporization (c) the standard Gibbs free energy of vaporization (d) the normal boiling point of C102. 

What Do We Need to Know Already The concepts of chemical equilibrium are related to those of physical equilibrium (Sections 8.1-8.3). Because chemical equilibrium depends on the thermodynamics of chemical reactions, we need to know about the Gibbs free energy of reaction (Section 7.13) and standard enthalpies of formation (Section 6.18). Ghemical equilibrium calculations require a thorough knowledge of molar concentration (Section G), reaction stoichiometry (Section L), and the gas laws (Ghapter 4). 

STRATEGY Calculate the reaction quotient and substitute it and the standard Gibbs free energy of reaction into Eq. 5. If AGr < 0, the forward reaction is spontaneous at the given composition. If AGr > 0, the reverse reaction is spontaneous at the given composition. If AGr = 0, there is no tendency to react in either direction the reaction is at equilibrium. At 298.15 K, RT = 2.479 kJ-moF h... 

Example 9.4 deals with a system at equilibrium, but suppose the reaction mixture has arbitrary concentrations. How can we tell whether it will have a tendency to form more products or to decompose into reactants To answer this question, we first need the equilibrium constant. We may have to determine it experimentally or calculate it from standard Gibbs free energy data. Then we calculate the reaction quotient, Q, from the actual composition of the reaction mixture, as described in Section 9.3. To predict whether a particular mixture of reactants and products will rend to produce more products or more reactants, we compare Q with K ... 

We are free to choose either K or Kc to report the equilibrium constant of a reaction. However, it is important to remember that calculations of an equilibrium constant from thermodynamic tables of data (standard Gibbs free energies of formation, for instance) and Eq. 8 give K, not Kc. In some cases, we need to know Kc after we have calculated K from thermodynamic data, and so we need to be able to convert between these two constants. 

Calculate an equilibrium constant from a standard Gibbs free energy (Example 9.3). 

Predict the standard cell emf and calculate the standard reaction Gibbs free energy for galvanic cells having the following cell reactions ... 

The standard potential of the AI3+/A1 couple is —1.66 V. Calculate the standard Gibbs free energy of formation for Al +(aq). Account for any differences between the standard Gibbs free energy of formation of Tl,+(aq) (see Exercise 14.65) and that of Al +(aq). 

Once the standard states for the various species have been established, one can proceed to calculate a number of standard energy changes for processes involving a change from reactants, all in their respective standard states, to products, all in their respective standard states. For example, the Gibbs free energy change for this process is... 

As equation 2.4.8 indicates, the equilibrium constant for a reaction is determined by the temperature and the standard Gibbs free energy change (AG°) for the process. The latter quantity in turn depends on temperature, the definitions of the standard states of the various components, and the stoichiometric coefficients of these species. Consequently, in assigning a numerical value to an equilibrium constant, one must be careful to specify the three parameters mentioned above in order to give meaning to this value. Once one has thus specified the point of reference, this value may be used to calculate the equilibrium composition of the mixture in the manner described in Sections 2.6 to 2.9. 

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