Reaction quotients

If the general chemical reaction represented by Eq. (1.5) is not in equilibrium we can still formulate a ratio of concentrations that has the same form as Eq. (1.6). This is called the reaction quotient, Q 

Clearly, if Q = K i the reaction is in chemical equilibrium. If Q K the reaction is not in equilibrium, and it will proceed in the forward 

Exercise 1.5. If 0.80 mole of SOzIg), 0.30 mole of 02(g), and 1.4 mole of 503(g) simultaneously occupy a volume of 2 L at 10(X)K, will the mixture be in equilibrium If not, in what direction will it proceed to establish equilibrium Consider only the species 502(g), 02(g), and 503(g) in reaction 

5ince this value of Q is not equal to Kc (namely, 2.8 x 102), the initial mixture is not in equilibrium. Moreover, since Q K, Reaction (1.11) will proceed in the forward direction. 

02(g) disappear. If this change establishes chemical equilibrium we have 

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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... 

Traditional chemical kinetics uses notation that is most satisfactory in two cases all components are gases with or without an inert buffer gas, or all components are solutes in a Hquid solvent. In these cases, molar concentrations represented by brackets, are defined, which are either constant throughout the system or at least locally meaningful. The reaction quotient Z is defined as... 

The reaction quotient may be measured, at least in principle, for the reacting system at any time. If Z is observed not to change, the system is at equiUbrium, or trapped in a metastable state that serves as a local equiUbrium. In informal work, a time-independent Z is identified directiy with the equiUbrium constant... 

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... 

The form of the expression for Q, known as the reaction quotient, is the same as that for the equilibrium constant, K. The difference is that the partial pressures that appear in Q are those that apply at a particular moment, not necessarily when the system is at equilibrium. By comparing the numerical value of Q with that of K, it is possible to decide in which direction the system will move to achieve equilibrium. 

In this way, the partial pressures of products increase, while those of reactants decrease. As this happens, the reaction quotient Q increases and eventually at equilibrium becomes equal to K. 

The quantity Q that appears in this equation is the reaction quotient referred to in Chapter 12. It has the same mathematical form as the equilibrium constant, K the difference is that the terms that appear in Q are arbitrary, initial pressures or concentrations rather than equilibrium values. 

In this equation, E is the cell voltage, E° is the standard voltage, n is the number of moles of electrons exchanged in the reaction, and Q is the reaction quotient. Notice that—... 

Reaction quotient (Q) An expression with the same form as Kbut involving arbitrary rather than equilibrium partial pressures, 333-334 Reaction rate The ratio of the change in concentration of a species divided by the time interval over which the change occurs, 285 catalysis for, 305-307 collision model, 298-300 concentration and, 287-292,314q constant, 288 enzymes, 306-307 egression, 288... 

EXAMPLE 9.2 Calculating the Gibbs free energy of reaction from the reaction quotient... 

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... 

The reaction quotient, Q, has the same form as K, the equilibrium constant, except that Q uses the activities evaluated at an arbitrary stage of the reaction. The equilibrium constant is related to the standard Gibbs free energy of reaction by AG° = —RT In K. 

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 ... 

FIGURE 9.6 The relative sizes of the reaction quotient Q and the equilibrium constant K indicate the direction in which a reaction mixture tends to change. The arrows show that, when Q < K, reactants form products (left and when Q> K, products form reactants (right). There is no tendency to change once the reaction quotient has become equal to the equilibrium constant. 

SOLUTION Substitute the data, noting that 55 kPa is equivalent to 0.55 bar, in the reaction quotient. 

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. 

PHI = 0.10 bar. (a) Calculate the reaction quotient, (b) Is the reaction mixture at equilibrium (c) If not, is there a tendency to form more reactants or more products ... 

Sometimes it is important to know under what conditions a precipitate will form. For example, if we are analyzing a mixture of ions, we may want to precipitate only one type of ion to separate it from the mixture. In Section 9.5, we saw how to predict the direction in which a reaction will take place by comparing the values of J, the reaction quotient, and K, the equilibrium constant. Exactly the same techniques can be used to decide whether a precipitate is likely to form when two electrolyte solutions are mixed. In this case, the equilibrium constant is the solubility product, Ksp, and the reaction quotient is denoted Qsp. Precipitation occurs when Qsp is greater than Ksp (Fig. 11.17). 

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. 

Provided that the pressure of hydrogen is 1 bar, we can write the reaction quotient as Q = [H "]2[C1 ]2. To find the concentration of hydrogen ions, we write the Nernst equation ... 

In this context, Q is the charge supplied don t confuse it with the reaction quotient Q ... 

Calculate the reaction quotient, Q, for the cell reaction, given the measured values of the cell emf. Balance the chemical equations by using the smallest whole-number coefficients. 

Equilibrium constants are dimensionless numbers, yet the concentrations used in an equilibrium constant expression have units. To understand this, we need to explore the reaction quotient Q, introduced in Chapter 14. In Section 16-1 we explore in detail the link between Q and Keq. Here we use Q to address the issue of concentration units and the equilibrium constant. 

Although not stated explicitly, each concentration in a reaction quotient and in an equilibrium constant expression has been divided by standard concentration (1 bar for gases, 1 M for solutes) to make the equilibrium constant dimensionless. For example,... 

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