Thermodynamics reaction quotient

The reaction quotient, Q, was introduced in Section 17-4. It involves a ratio of concentrations or pressures of products to those of reactants, each raised to the power indicated by the coefficient in the balanced equation. The Q expression that is used in the Nernst equation is the thermodynamic reaction quotient it can include both concentrations and pressures. Substituting these values into the Nernst equation at 25°C gives... 

Here Q is the thermodynamic reaction quotient. The reaction quotient has the form of the eqirihbrium constant, except that the concentrations and gas pressures are those that exist in a reaction mixture at a given instant. You can apply this equation to a... 

Predict the direction of spontaneous chemical change by using vaiues of the standard Gibbs energy of reaction (A,G°) and the thermodynamic reaction quotient (0). 

In the last step, we have made use of the fact that Aj.G° = Cfj.c + djjif) — (flMA + Vb) because, shown by equation (13.34), Aj.G° can be expressed in terms of standard chemical potentials. The quotient in the logarithmic term is the general form of the thermodynamic reaction quotient, Q. Thus, we can write the equation above in its most general form as... 

It is not difficult to establish the relationship between the cell potential, Eceii/ and the concentrations of reactants and products. We start from equation (13.15), which involves the thermodynamic reaction quotient Q. 

You may wonder why the equilibrium constant, 11, has no units. The reason is that each term in the reaction quotient represents the ratio of the measured pressure of the gas to the thermodynamic standard state of one atmosphere. Thus the quotient (f3No2)2/f>N2o4 in Experiment 1 becomes... 

We can explain these responses thermodynamically by considering the relative sizes of Q and K (Fig. 9.11). When reactants are added, the reaction quotient Q falls below K, because the reactant concentrations in the denominator of Q increase. As we have seen, when Q < K, the reaction mixture responds by forming products until Q is restored to K. Likewise, when products are added, Q rises above K, because products appear in the numerator. Then, because Q > K, the reaction mixture responds by forming reactants at the expense of products until Q = K again. It is important to understand that K is a constant that is not altered by changing concentrations. Only the value of Q changes, and always in a way that brings its value closer to that of K. 

What Do We Need to Know Already This chapter extends the thermodynamic discussion presented in Chapter 7. In particular, it builds on the concept of Gibbs free energy (Section 7.12), its relation to maximum nonexpansion work (Section 7.14), and the dependence of the reaction Gibbs free energy on the reaction quotient (Section 9.3). For a review of redox reactions, see Section K. To prepare for the quantitative treatment of electrolysis, review stoichiometry in Section L. 

At equilibrium, AG = 0 and the reaction quotient Q becomes the thermodynamic equilibrium constant, K. Hence, at equilibrium. 

We can explain these responses thermodynamically by considering the relative sizes of Q and K (Fig. 9.11). When reactants are added, the reaction quotient Q falls below K momentarily, because the reactant con-... 

Equations 27 and 28 permit a simple comparison to be made between the actual composition of a chemical system in a given state (degree of advancement) and the composition at the equilibrium state. If Q K, the affinity has a positive or negative value, indicating a thermodynamic tendency for spontaneous chemical reaction. Identifying conditions for spontaneous reaction and direction of a chemical reaction under given conditions is, of course, quite commonly applied to chemical thermodynamic principle (the inequality of the second law) in analytical chemistry, natural water chemistry, and chemical industry. Equality of Q and K indicates that the reaction is at chemical equilibrium. For each of several chemical reactions in a closed system there is a corresponding equilibrium constant, K, and reaction quotient, Q. The status of each of the independent reactions is subject to definition by Equations 26-28. 

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 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 /... 

The specific examples in Section 14.5 demonstrate that when 1C > 1 the reaction has progressed far toward products, and when K 1 the reaction has remained near reactants. The empirical discussion in Section 14.6 shows how the reaction quotient Q and the principle of Te Chatelier can predict the direction of spontaneous reaction and the response of an equilibrium state to an external perturbation. Here, we use the thermodynamic description of K from Section 14.3 to provide the thermodynamic basis for these results obtained empirically in Sections 14.5 and 14.6. We identify those thermodynamic factors that determine the magnitude of K. We also provide a thermodynamic criterion for predicting the direction in which a reaction proceeds from a given initial condition. 

If the reaction quotient Q is less than K, AG < 0 and the reaction will proceed spontaneously as written, from left to right. If Q > fC, then AG > 0 and the reverse reaction (right to left) will occur spontaneously until equilibrium is reached. These conditions are represented schematically in Figure 14.11. The second law of thermodynamics thus provides a very useful criterion for the direction of reaction in terms of the initial value of the reaction quotient. 

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... 

Equations such as those for the equilibrium constant, the reaction quotient and the Nemst equation are written mostly in terms of concentrations and partial pressures. This is correct only for very dilute solutions or ideal gases. In general, the amount of active material present appears to be less than the nominal amount measured in the customary units (in moles per litre, or in atmospheres). In order to retain the form of the equations used here and yet increase precision, thermodynamics replaces the concentration terms by the activity, which is an effective concentration, and the pressure by the fugacity, which is an effective pressure. Thus, the equilibrium constant for the reaction... 

Recall that for a system at equilibrium, AG = 0. This is the definition of thermodynamic equilibrium. Applying this definition to Equation 2.16 enables us to determine the precise ratio of reactant and product activities that lead to a perfect balance (equilibrium) between the reactant and product states in a chemical system. This specific value of the reaction quotient has a special name. It is known as the equilibrium... 

This equation is the link between tables of thermodynamic data (such as Table 4.2.1), which allow the evaluation of ArG°, and the equilibrium constant Kr of the reaction (sometimes also denoted as reaction quotient Qr), which is a function of the composition of the system in terms of concentration, molar fractions, and so on. The value and definition of Kr depends on the choice of the standard state and the ideality of the system, as shown subsequently for ideal and real gases, liquids, and gas-solid systems. 

The application of thermodynamics to electrochemical systems also helps us understand potentials at nonstandard conditions and gives us a relationship with the equilibrium constant and reaction quotient. However, we understand now that concentration is not necessarily the best unit to relate to the properties of a solution. Rather, activity of ions is a better unit to use. Using Debye-Hiickel theory, we have ways of calculating the activities of ions, so we can more precisely model the behavior of nonideal solutions. 

If ArG° possesses different numerical values (due to the different choices of standard states), the reaction quotient Q is endowed with a different value, but the A G value remains the same as before. There exists a very subtle compensation between ArG° and the numerical values of the activities that depend on the chosen standard states. ArG and AGgyst are the true invariants of the thermodynamic process. This subtle compensation takes its roots in the depth of the thermodynamics framework. 

When the reaction quotient for a reaction is written in terms of activities, the corresponding equilibrium constant is called the thermod5mamic equilibrium constant. Activities are dimensionless (unitless) quantities and therefore, the thermodynamic equilibrium constant is also a dimensionless quantity. The thermodynamic equilibrium constant is appropriate for use in equation (13.15). 

Gouy-Chapman, Stern, and triple layer). Methods which have been used for determining thermodynamic constants from experimental data for surface hydrolysis reactions are examined critically. One method of linear extrapolation of the logarithm of the activity quotient to zero surface charge is shown to bias the values which are obtained for the intrinsic acidity constants of the diprotic surface groups. The advantages of a simple model based on monoprotic surface groups and a Stern model of the electric double layer are discussed. The model is physically plausible, and mathematically consistent with adsorption and surface potential data. 

The possible factors involved in the biological selectivity towards metal ions have been considered by Frausto da Silva and Williams3 and by Kustin et al.4 In terms of thermodynamic selectivity a useful formalism for the uptake of any metal ion from a multimetal system is the quotient A Cm, where Km is a relative stability constant and Cm is the concentration of the metal ion. However, as these authors point out,3 a combination of both thermodynamic and kinetic properties must be considered. An appreciation of kinetic factors is often absent in this field, but must be of prime consideration in chelate exchange reactions and in the final irreversible step of metal ion insertion to form the metalloenzymes. 

One other serious criticism regarding the data on Cu speciation is the neglect of the cysteine present in blood plasma. Cu11 and cysteine undergo a facile redox reaction (Chapter 20.2). Since the reaction is irreversible, no quantitative thermodynamic quotient is available for use in the computer calculations. Another assumption often made is that the overwhelming concentration of other amino acids may prevent cysteine coordination and, as a result, stabilize the Cu11 state. Recent studies show that this assumption is totally unjustified48 and so the dilemma still has to be resolved. 

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