Free energy change reaction quotient

Recall from Chapter j 4 that the free energy change for a chemical process, A G, Is a signpost for spontaneity. Equation relates A G to concentrations through the reaction quotient Q ... 

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. 

For the reaction aA + bB cC + t/D, the equilibrium constant is K = [C]l[D], /[A]"(B), Solute concentrations should be expressed in moles per liter gas concentrations should be in bars and the concentrations of pure solids, liquids, and solvents are omitted. If the direction of a reaction is changed. K = UK. If two reactions are added. A", = K, K-,. The equilibrium constant can be calculated from the free-energy change for a chemical reaction K = e AcrlRT. The equation AG = AH — TAS summarizes the observations that a reaction is favored if it liberates heat (exothermic, negative AH) or increases disorder (positive AS). Le Chatelier s principle predicts the effect on a chemical reaction when reactants or products are added or temperature is changed. The reaction quotient, Q, tells how a system must change to reach equilibrium. 

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 ... 

Equation (16-7) is a remarkable statement. It implies that Qeq, the value of the reaction quotient under equilibrium conditions, depends only on thermodynamic quantities that are constant in the reaction (the temperature, and the standard free-energy change for the reaction at that temperature), and is independent of the actual starting concentrations of reactants or products. For this reason, Qeq is usually denoted the equilibrium constant, K, and (16-7) is rewritten as... 

The free energy change (AG) of a chemical reaction is related to its reaction quotient (Q, ratio of products to reactants) by... 

When the reaction quotient furnishes the minimum value of the free energy change for the reaction, which is zero (i.e., AG = 0), the reaction is in equilibrium and Q = K, where K is the equilibrium constant. Equation (1.133) becomes ... 

The maximum energy available, w is —AG, the actual free energy change of the reaction. The standard change, AG , is found to be +12.08, using the thermodynamic data in Appendix C. The reaction quotient for the conditions given is = Mn02 H /... 

In real-world applications, concentrations and pressnres are rarely conveniently fixed at their standard state values. It is thus necessary to understand how concentration and pressnre affect the cell voltage by applying the thermodynamic principles of Chapter 14 to electrochemical cells. In Chapter 14, we showed that the free energy change is related to the reaction quotient Q through... 

The change in Gibbs free energy (AG), which occurs as a system proceeds toward equilibrium, can be expressed as the sum of two terms. The first term is the standard free energy change (A G°), which is fixed for any given reaction. AG° can be calculated from the stoichiometry of the reaction (i.e., how many moles of one compound react with how many moles of another compound) and the standard free energies of the chemicals involved. The second term contains the reaction quotient (Q), which depends on the concentrations of chemicals present. The fact that AG can be expressed in terms of the concentrations of all chemicals present in a system makes it possible to determine in which direction a chemical reaction will proceed and to predict its final composition when it reaches equilibrium. 

The standard free energy change is related to the reaction s equilibrium constant, Keq, the value of the reaction quotient at equilibrium when the forward and reverse reaction rates are equal. 

Relationship between free-energy change and standard free-energy change and reaction quotient. 

Strategy From the information given we see that neither the reactants nor prodncts are at their standard state of 1 atm. We use Equation (18.13) of the text to calculate the free-energy change nnder non-standard-state conditions. Note that the partial pressures are expressed as dimensioidess quantities in the reaction quotient Qp. 

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. 

Here we have divided both sides of the equation by nF to isolate the cell potential in the equation. This equation also resembles the Nernst equation (Equation 13.4), and it is easy to see how it arises. At equilibrium, the free energy change is zero and the reaction quotient, Q, is equal to the equilibrium constant, K. 

Under nonstandard conditicxis, 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° = —RTlnKfy. Thus, the standard free-energy change is directly related to the equilibrium constant for the reaction. This rdationship can be used to explain the temperature dependence of equilibrium constants. 

Reaction spontaneity (AG < 0) depends on two factors the free energy change at standard conditions, AG", and the size of the reaction quotient, Q. No matter what the starting conditions, any process is spontaneous until Q = K (AG = 0). (Section 20.4)... 

The Nernst equation was named after the German chemist Walther Nernst who established very useful relations between the energy and the potential of a cell to the concentrations of participating ions and other chemical species. Equation (4.8) can be derived from the equation linking free energy changes to the reaction quotient... 

The free energy change associated with the hydrolysis or synthesis of each of the two pyrophosphate bonds of ATP amounts, imder near-physiological conditions (pH 7.0 to 7.4 0.005 M inorganic phosphate ATP/ADP = 10), to about 14 Kcal. On the assumption that the free energy of any secondary reaction of ATP is not utilized in the resynthesis of ATP, the quotient... 

The Nernst equation, named after the German chemist Walther Nernst, can be derived from the equation linking free energy changes to the reaction quotient ... 

The free-energy change (AG) is determined using the standard free-energy change (AG°) and the reaction quotient Q). 

Notice that at standard state conditions, all activities are unity, the value of the quotient within the parentheses in Equahon 5.39 is 1, and with those conditions, the AG of the reaction is properly the AGi, the standard state value for the free energy change of the reaction. 

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