Form of the Reaction Quotient

As you ll see in the upcoming discussion, the reaction quotient 2 is a collection of terms based on the balanced equation exactly as written for a given reaction. Therefore, the value of Q, which varies during the reaction, and the value of K, which is the constant value that Q attains when the system has reached equilibrium, also depend on how the balanced equation is written. 

A Word about Units for Q and K In this text (and most others), the values of Q and K are shown as unitless numbers. This is because each term in the reaction quotient represents the ratio of the measured quantity of the substance (molar concentration or pressure) to the thermodynamic standard-state quantity of the substance. Recall from Section 6.6 that these standard states are 1 Mfora substance in solution, 1 atm for gases, and the pure substance for a liquid or solid. Thus, a 

Form of Q for an Overall Reaction Notice that we ve been writing reaction quotients without knowing whether an equation represents an individual reaction step or an overall multistep reaction. We can do this because we obtain the same expression for the overall reaction as we do when we combine the expressions for the individual steps. That is, if an overall reaction is the sum of two or more reactions, the overall reaction quotient (or equilibrium constant) is the product of the reaction quotients (or equilibrium constants) for the steps  

For example, consider an overall equation for the formation of nitrogen dioxide, the toxic pollutant that contributes to photochemical smog and acid rain  

The overall reaction actually occurs in two steps with NO serving as the intermediate  

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E = E°-------------log Q The form of the reaction quotient comes from the balanced overall redox... 

When using the Nernst equation, be sure to use the correct form of the reaction quotient, products over reactants, and each concentration raised to the power the same as the coefficient in the balanced reaction. 

If we multiply a half-reaction by any factor, E° does not change. However, the factor n before the log term and the form of the reaction quotient, Q, do change. Let s write the Nemst equation for the reaction in the preceding example, multiplied by 2 ... 

How does the form of the reaction quotient compare with that of the equilibrium constant What is the difference between these two expressions ... 

The most common form of the reaction quotient shows reactant and product terms as molar concentrations, which are designated by square brackets, [ ]. In the cases you ve seen so far, K is the equilibrium constant based on concentrations, designated from now on as K. Similarly, we designate the reaction quotient based on concentrations as Q - For the general balanced equation... 

Another form of the reaction quotient that we discuss later shows gaseous reactant and product terms as pressures.)... 

Form of Q for o Forward and Reverse Reaction The form of the reaction quotient depends on the direction in which the balanced equation is written. Consider, for example, the oxidation of sulfur dioxide to sulfur trioxide. This reaction is a key step in acid rain formation and sulfuric acid production. The balanced equation is... 

Here Q is the thermod3mamic form of the reaction quotient. It has the same general appearance as the thermod3mamic equilibrium constant K, but the concentrations and partial pressures are those for a mixture at some instant, perhaps at the beginning of a reaction. You obtain AG from AG° by adding KTln Q, where In Q is the natural logarithm of Q = 2.303 log 0. 

To use the Nernst equation we need to establish EJeii and the reaction to which the cell diagram corresponds so that the form of the reaction quotient (Q) can be revealed (see Example 19-2). Once we have determined the form of the Nernst equation, we can insert the concentration of the species. 

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. 

The reaction quotient has the same form as the equilibrium constant, but it involves specific values that are not necessarily equilibrium concentrations. If they are equilibrium concentrations, then Q = K. The concept of the reaction quotient is very useful. We can compare the magnitude of Q with that of for a reaction under given conditions to decide whether... 

The particular ratio of concentration terms that we write for a given reaction is called the reaction quotient (Q). For the reaction of N2O4 to form NO2, the reaction quotient, based directly on the balanced equation as written, is... 

Plan We can use Equation 19.19 to calculate AG. Doing so requires that we calculate the value of the reaction quotient Q for the specified partial pressures, for which we use the partial-pressures form of Equation 15.23 Q = [D] [E]Y[A]"[B] - We then use a table of standard fiee energies of formation to evaluate AG". 

Comparison of the reaction quotient, Q, with the value of K p can be used to judge whether a precipitate will form when solutions are mixed or whether a slightly soluble salt will dissolve under various conditions. Precipitates form when Q > K. If two salts have sufficiently different solubilities, selective precipitation can be used to precipitate one ion while leaving the other in solution, effectively separating the two ions. 

Reaction quotient (Q) (12.3) Expression identical in form to the equilibrium constant, but in which the concentrations do not correspond to equilibrium values. Comparison of the reaction quotient to the equihbrium constant predicts the direction of spontaneous change. 

Depending on the values chosen to write the compositions of the multi-component phases, the expression of the reaction quotient may take a variety of forms, and therefore there are also different possible forms for the law of mass action. 

To gauge the progress of a reaction relative to equilibrium, we use a quantity called the reaction quotient. The definition of the reaction quotient takes the same form as the definition of the equilibrium constant, except that the reaction need not be at equilibrium. So, for the general reaction ... 

Strategy For each part, identify the compound that might precipitate and look up its K p value in Table 17.4 or Appendix 3. Determine the concentrations of each compound s constituent ions, and use them to determine the value of the reaction quotient, Q p then compare each reaction quotient with the value of the corresponding K p. If the reaction quotient is greater than K p, a precipitate wiU form. 

In Example 13-8, we apply these concepts to a system containing specified amounts of N2(g), H2(g), and NH3(g). Following this example, we discuss the general form for the reaction quotient, Q, so that we can apply equation (13.15) to any reaction. 

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. 

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 ... 

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. 

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). 

Many systems are not at equilibrium. The mass action expression, also called the reaction quotient, Q, is a measure of how far a system is from equilibrium and in what direction the system must go to get to equilibrium The reaction quotient has the same form as the equilibrium constant, K, but the concentration values put into Q are the actual values found in the system at that given moment. 

The bracketed term is the reaction quotient, expressed in terms of pressures, allowing us to rewrite the equation in a less intimidating form of Equation (4.49) ... 

At equilibrium, when the reaction stops, we give the reaction quotient the special name of equilibrium constant, and re-symbolize it with the letter K. The values of K and Q are exactly the same at equilibrium when the reaction stops. The value of Q is always smaller than K before equilibrium is reached, because some product has yet to form. In other words, before equilibrium, the top line of Equation (4.48) is artificially small and the bottom is artificially big. 

If the temperature is constant and the reaction is at equilibrium, then the ratio of the two reactions, the forward and reverse, should become a constant. This constant is the reaction quotient, Q, and has the following form ... 

Knowing the value of the solubility product constant can also allow us to predict whether or not a precipitate will form if we mix two solutions, each containing an ion component of a slightly soluble salt. We calculate the reaction quotient (many times called the ion product), which has the same form as the solubility product constant. We take into consideration the mixing of the volumes of the two solutions, and then compare this reaction quotient to the K.p. If it is greater than the Ksp then precipitation will occur until the ion concentrations reduce to the solubility level. 

Le Chatelier s principle predicts the way that an equilibrium system responds to change. For example, when the concentration of a substance in a reaction mixture is changed, Le Chatelier s principle qualitatively predicts what you can show quantitatively by evaluating the reaction quotient. If products are removed from an equilibrium system, more products must be formed to relieve the change. This is just as you would predict, because Qc will be less than Kc. 

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