Free Energy Under Nonstandard Conditions

The set of standard conditions for which A G° values pertain is given in Table 19.2. Most chemical reactions occur under nonstandard conditions. For any chemical process, the relation-ship between the free-energy change under standard conditions, AG°, and the free-energy change under any other conditions, AG, is given by  

In this equation R is the ideal-gas constant, 8.314 1/mol-K T is the absolute temperature and Q is the reaction quotient for the reaction mixture of interest. (Section 15.6) Under standard conditions, the concentrations of all the reactants and products are equal to 1. Thus, under standard conditions Q = 1, In Q = 0, and Equation 19.19 reduces to AG = AG° under standard conditions, as it should. 

Analyze (a) We must write a chemical equation that describes the physical equilibrium between liquid and gaseous CCI4 at the normal boiling point, (b) We must determine the value of AG° for CCh, in equilibrium with its vapor at the normal boiling point (c) We must estimate the normal boiling point of CCI4, based on available thermodynamic data. 

Strictly speaking, we need the values of AH° and AS° for the CCl4(Z)-CCl4(g) equilibrium at the normal boiling point to do this calculation. However, we can estimate the boiling point by using the values of AH° and AS° for CCI4 at 298 K, which we obtain fi om Appendix C and Equations 5.31 and 19.8  

As expected, the process is endothermic (AH 0) and produces a gas, thus increasing the entropy (AS 0). We now use these values to estimate Tf, for CClj(/)  

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Thus far, we have considered only situations under standard conditions. But how do we cope with nonstandard conditions The change in Gibbs free energy under nonstandard conditions is ... 

The first term, AG°, is the change in Gibb s free energy under standard-state conditions defined as a temperature of 298 K, all gases with partial pressures of 1 atm, all solids and liquids pure, and all solutes present with 1 M concentrations. The second term, which includes the reaction quotient, Q, accounts for nonstandard-state pressures or concentrations. Eor reaction 6.1 the reaction quotient is... 

In most laboratories, electrochemistiy is practiced under nonstandard conditions. That is, concentrations of dissolved solutes often are not 1 M, and gases are not necessarily at 1 bar. Recall from Chapter 14 that ZlG changes with concentration and pressure. The equation that links A G ° with free energy changes under nonstandard conditions is Equation AG = AG° + i 7 lng Here, Q is the reaction quotient. 

Be able to calculate free energies from equilibrium constants and redox potentials and do so under nonstandard conditions using the appropriate equations involving reactant and product concentrations at the beginning of the reaction. 

Free Energy Changes Under Nonstandard Conditions (Eqs. 15.4,15.5)... 

In Section 19.5 we saw a special relationship between A G and equilibrium For a system at equilibrium, AG = 0. We have also seen how to use tabulated thermodynamic data to calculate values of the standard free-energy change, AG°. In this final section, we learn two more way s in which we can use free energy to analy ze chemical reactions using A G° to calculate A G under nonstandard conditions and relating the values of A G° and K for a reaction. 

Calculating the Free-Energy Change under Nonstandard Conditions... 

SECTIONS 19.6 AND 19.7 The values of AH and AS generally do not vary much with temperature. Therefore, the dependence of AG with temperature is governed mainly by the value of T in the expression AG = AH — TAS. The entropy term —TAS has the greater effect on the temperature dependence of AG and, hence, on the spontaneity of the process. For example, a process for which AH > 0 and As > 0, such as the melting of ice, can be nonspontaneous (AG > 0) at low temperatures and spontaneous (AG < 0) at higher temperatures. Under nonstandard conditions AG is related to AG° and the value of the reaction quotient, Q AG = AG" + RT In Q. At equilibrium (AG = 0, Q = K), AG = —RT InkT. Thus, the standard free-energy change is directly related to the equilibrium constant for the reaction. This relationship expresses the temperature dependence of equilibrium constants. 

AG = AG° + RTlnQ [19.19] Calculating free-energy change under nonstandard conditions... 

We can calculate the free energy change of a reaction under nonstandard conditions (AGrxn) from AG°xn using the relationship ... 

We can derive an exact relationship between Ectw (under nonstandard conditions) and 11 by considering the relationship between the change in free energy (AG) and the standard change in free energy (AG°) from Section 17.8 ... 

The free-energy change, AG, for a reaction under nonstandard-state conditions is given by AG = AG° + RT In Q, where Q is the reaction quotient. At equilibrium, AG = 0 and Q = K. As a result, AG° = —RT In K, which allows us to calculate the equilibrium constant from AG° and vice versa. 

Recall from Section 17.10 that AG is the free-energy change for a reaction under nonstandard-state conditions, AG° is the free-energy change under standard-state conditions, and Q is the reaction quotient. Since AG = —nFE and AG° = —nFE°, we can rewrite the equation for AG in the form... 

Free enthalpy of the formation of 1 mole of any substance imder standard conditions from atoms and up to the standard state is called standard free enthalpy (Gibbs energy) of formation. This potential is determined by way of subtle physicochemical experiments and measurements. Its values are continuously fine-tuned and published in articles, monographs and reference publications. In composite Tables the standard potential is usually provided for temperature of 298.15 K (25 °C) and denoted as AZp29s or AGp 298> its value, as a rule, is negative and has the dimension kcal mole or J mole Standard potential serves a measure of potential energy of inter-atomic or inter-molecular bonds in individual chemical compounds. Knowing its values, it is possible to determine free enthalpy of substances under any nonstandard conditions. 

Strategy From the information given we see that neither the reactant nor the product is at its standard state of 1 atm. To determine the direction of the net reaction, we need to calculate the free-energy change under nonstandard-state conditions (AG) using Equation (18.13) and the given AG° value. Note that the partial pressures are expressed as dimensionless quantities in the reaction quotient Qp because they are divided by the standard-state value of 1 atm (see p. 621 and Table 18.2). 

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