Reaction Quotient Q and Equilibrium Constant

Chemical potential is related to concentration through activity a  

The activity of a species depends on its chemical nature. Here are a few simple guidelines to help you calculate the activity for various species depending on their state  

For an ideal gas, , = Pi/p°, where p,- is the partial pressure of the gas and is the standard-state pressure (1 atm). For example, the activity of oxygen in air at 1 atm is approximately 0.21. The activity of oxygen in air pressurized to 2 atm would be 0.42. Since we accept p° = 1 atm, we are often lazy and write a, = recognizing that Pi is a unitless gas partial pressure. 

For a nonideal gas, , = YiiPi/p°), where fi is an activity coefficient describing the departure from ideality (0 /, 1). 

For pure components, a, = 1. For example, the activity of gold in a chunk of pure gold is 1. The activity of platinum in a platinum electrode is 1. The activity of liquid water is usually taken as 1. 

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Reaction Quotient, Q and Equilibrium Constant, K Relationship Between AG°and Kp/po... 

Explain the important distinctions between each pair of terms (a) reaction that goes to completion and reversible reaction (b) and (c) reaction quotient (Q) and equilibrium constant expression (K) (d) homogeneous and heterogeneous reaction. 

Understand the relationships among Gibbs free energy, chemical potential, reaction quotients (Q), the equilibrium constant, and the saturation index SI). 

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. 

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 ... 

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 ... 

The sign of AG allows us to predict reaction direction, but you already know that it is not the only way to do so. In Chapter 17, we predicted direction by comparing the values of the reaction quotient (Q) and the equilibrium constant (K). Recall that... 

The relationship between reaction quotient Q and the equilibrium constant K. 

But how does this response offset the applied stress When we began our discussion of the equihbrium constant in Section 12.3, we first defined the reaction quotient, Q, and then considered the equilibrium constant as a special case of this ratio. Thus at equihbrium, we have the relationship, Q = K But if we change the concentrations fi-om their equilibrium values, Q will no longer be equal to K Immediately following an increase in the concentration of a reactant, as in Figure 12.7, Q must become smaller than K. So to establish a new equilibrium, the value of the ratio must increase. Thus the system must respond by increasing the con-... 

The effects of concentration changes on equilibrium can be rationalized by considering the reaction quotient, Q, and comparing it to the equilibrium constant, K. 

Thus, we can use the reaction quotient (Q) and the equilibrium constant (K) as guides to help us understand reaction equilibria. For reactions that are not at equilibrium, we can compare Q versus K to determine the direction a reaction should proceed in order to restore its equilibrium. The key points of our discussion of Q and K are summarized in Table 2.2. 

The subscript eq on Q emphasizes that the equation, as written, applies only if the system has reached equilibrium. If we rearrange the expression above for In we get In Qeq = — ArG°/ RT. For a given reaction at a particular temperature, AfG° has a specific value, as demonstrated by Example 13-7. Therefore, In and also have certain fixed values once the reaction and the temperature are specified. Let s use the symbol K to represent the value of Qgq and call it the equilibrium constant. So, by definition, the equilibrium constant, K, represents the value of the reaction quotient, Q, at equilibrium. By replacing with K, we can write the equation above in the... 

Predicting the Direction of Net Chemical Change—A comparison of the reaction quotient with the equilibrium constant makes it possible to predict the direction of net change leading to equilibrium (Fig. 15-4). If Q < K, the forward reaction is favored, meaning that when equilibrium is established the amounts of products will have increased and the amounts of reactants will... 

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 9.4 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 ... 

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. 

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. 

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

Under the equilibrium condition (8.18), where the remaining terms AG°, R, and T are all constants, the reaction quotient Q must itself become a constant, which we identify as the equilibrium constant Keq ... 

We can find a value of x that satisfies this equation by trial-and-error guessing with the spreadsheet in Figure 6-9. In column A, enter the chemical species and, in column B, enter the initial concentrations. Cell B8, which we will not use, contains the value of the equilibrium constant just as a reminder. In cell B11 we guess a value for x. We know that x cannot exceed the initial concentration of IO7, so we guess x = 0.001. Cells C4 C7 give the final concentrations computed from initial concentrations and the guessed value of x. Cell Cl 1 computes the reaction quotient, Q, from the final concentrations in cells C4 C7. 

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. 

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. 

A mixture of gaseous N2, H2, and NH3, each at a partial pressure of 1 atm, reacts spontaneously at 300 K to convert some of the N2 and H2 to NH3. We can predict the direction of spontaneous reaction from the relative values of the equilibrium constant K and the reaction quotient Q (Section 13.5). Since Kp = 4.4 X 105 at 300 K and Qp = 1 for partial pressures of 1 atm, the reaction will proceed in the forward direction because Qp is less than Kp. Under these conditions, the reverse reaction is nonspontaneous. At 700 K, however, Kp = 8.8 X 10 5, and the reverse reaction is spontaneous because Qp is greater than Kp. 

We can now derive a relationship between free energy and the equilibrium constant. At equilibrium, AG for a reaction is zero and the reaction quotient Q equals the equilibrium constant K. Substituting AG = 0 and Q = K into the equation... 

An equilibrium constant, K, and the reaction quotient, Q (Frames 40,44 and 45), can both usefully be thought of qualitatively in terms of the following representation ... 

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