THE REACTION QUOTIENT

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The reaction quotient has the szmt 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 for any specified mixture of reactants and products with that of Kc for a reaction under given conditions to decide whether the forward or the reverse reaction must occur to a greater extent to establish equilibrium. 

We can think of the reaction quotient, Q, as a measure of the progress of the reaction. When the mixture contains only reactants, the concentrations in the numerator are zero, so Q = 0. As the reaction proceeds to the right, the product concentrations (numerator) increase and the reactant concentrations (denominator) decrease, so Q would increase to an infinitely large value when all reactants have been consumed and only products remain. The value of is a particular value of Q that represents equilibrium mixtures for the reaction. 

What is the concentration of PCl3(g) in the system described in Model 1  

Verify that the reaction occurring in the box described above is at equilibrium. 

A needle is inserted into the box described in Model 1 and an additional 0.0600 moles of PCI3 are injected into the reaction mixture. 

At the instant of injection (before any chemical reaction takes place)  

Predict which of the following will happen to the moles of PCI5 after injection of the 0.0600 moles of PCI3. 

The first term on the right in the second equality is the standard reaction Gibbs energy, AjG  

Because the standard states refer to the pure materials, the standard chemical potentials in this expression are the standard molar Gibbs energies of the (pure) species. Therefore, eqn 4.4a is the same as 

We consider this important quantity in more detail shortly. At this stage, therefore, we know that 

To make further progress, we rearrange the remaining terms on the right as follows  

To simplify the appearance of this expression still further, we introduce the (dimensionless) reaction quotient, Q, for reaction C  

The equilibrium constant describes only equilibrium conditions. For reactions not at equilibrium, a similar equation gives information about the reaction  

The equilibrium constant depends upon temperature only. Don t confuse Che equilibrium constant with equilibrium. 

Don t use solids or pure liquids such as water in the law of mass action, 

Use the reaction quotient Q to predict, the direction in which a reaction will proceed. 

Since reactions always move toward equilibrium, Q will always change toward K. Thus we can compare Q and K for a reaction at any given moment, and learn in which direction the reaction will proceed. 

There are times when you will be given information about the reactants and products when they have not reached equilibrium. Under these conditions, a value known as the reaction 

The value of Q can be helpful in determining the direction of a reaction in a nonequilibrium state. For instance, if the value of Q is greater than K, it means that the equation is top-heavy or that there are too many products (or not enough reactants). In this case, the reaction will have to proceed to the left to lower Q toward the value of K. If Q is smaller than K, there are too many reactants and not enough products, which means the reaction will need to shift to the right to reach equilibrium. If Q and K are equal to one another, the reaction is at equilibrium. 

In the reaction shown above, the value of Kc at 500°C is 6.0 X 10-2. At some point during the reaction, the concentrations of each material were measured. At this point, the concentrations of each substance were [N2] = 1.0 X 10 5 M, [H2] = 1.5 X 10-3 M, and [NH3] = 1.5 X 10-3 M. Calculate the value of Q, and determine the direction that the reaction was most likely to proceed when the measurements were taken. 

Answer To solve this problem, you need to begin by determining the value of Q using 

The value of Q is nearly 9 orders of magnitude larger than K. Therefore, the only way that equilibrium will be reached is if the reaction proceeds toward the left. That will decrease the numerator, increase the denominator, and decrease the value of Q. 

There are times when you will be given information about the reactants and products when they have not reached equilibrium. Under these conditions, a value known as the reaction quotient can be calculated. The value of the reaction quotient, Q, when compared to the equilibrium constant, will indicate the direction the reaction is proceeding. The reaction quotient is calculated using the same expression as K, but the concentrations of the reactants and products are not equilibrium values. For the reaction 

The equilibrium constant, K, is determined by the concentrations of reactants and products at equilibrium for a constant temperature. Therefore, of a reaction is always constant at a definite temperature. However, the value for reaction quotient Q is not constant. It is determined by the instantaneous concentrations of reactants and products. The reaction quotient expression is written as the same as expression for a reaction. For example, for the reaction  

Comparison of a reaction quotient and values gives several ideas about the condition of an equilibrium reaction. 

The equilibrium constant of a given reaction is 8 at a given temperature. 

The system is not at equilibrium. The reaction must proceed from reactants towards products to reach equilibrium. 

2 moles of each of CO2, H2, CO and H2O are put into a 1 L container at a specific temperature. According to following reaction, 

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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—... 

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. 

Decomposition of N2 O4 causes Q to increase A G becomes less negative, and eventually the reaction quotient reaches a value that makes A G = 0. 

A change in the amount of any substance that appears in the reaction quotient displaces the system from its equilibrium position. As an example, consider an industrial reactor containing a mixture of methane, hydrogen, steam, and carbon monoxide at equilibrium ... 

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. 

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

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