Free energy nonstandard conditions

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. 

D) AG° represents the free energy at standard conditions 25°C and 1 atm pressure. AG represents the free energy at nonstandard conditions. In this problem, we have the nonstandard condition of 100°C. In order to solve for the free energy of this reaction, you must use the following equation ... 

What is the mathematical relationship necessary to adjust the Gibbs free energy to nonstandard conditions. 

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 ... 

From thermodynamic principles, chemists have demonstrated that the free energy change at nonstandard conditions, Ac , is related to the free energy change imder standard conditions, Ac °, by... 

The sign of the standard free-energy change AG° tells the direction of spontaneous reaction when both reactants and products are present at standard-state conditions. In actual reactions, however, the composition of the reaction mixture seldom corresponds to standard-state pressures and concentrations. Moreover, the partial pressures and concentrations change as a reaction proceeds. How, then, do we calculate the free-energy change AG for a reaction when the reactants and products are present at nonstandard-state pressures and concentrations ... 

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. 

What is the relationship between the free-energy change under nonstandard-state conditions, AG, the free-energy change under standard-state conditions, AG°, and the reaction quotient, Q ... 

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. 

Two ways of predicting reaction direction are from the vaiue of AG and from the relation of Q to K. These variabies represent different aspects of the same phenomenon and are reiated to each other by AG = RT in Q/K. When Q = K, the system can reiease no more free energy. Beginning with Q at the standard state, the free energy change is AG°, and it is reiated to the equiiibrium constant by AG° = -RT In K. For nonstandard conditions, AG has two components AG° and RT in Q. Any nonequilibrium mixture of reactants and products moves spontaneousiy (AG < 0) toward the equiiibrium mixture. A product-favored reaction has K > 1 and, thus, AG° < 0. 

Expressing the free energy change for nonstandard initial conditions (673) ... 

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

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. 

The extent to which a given salt dissolves in water at a particular temperature also depends on the standard free energy change between products and reactants, AG°, for that temperature. For the dissolving of PbCl2 at constant temperature and pressure, including nonstandard conditions, the following equations are valid. 

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... 

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