Equilibrium constant reaction quotient

The Equilibrium Constant Reaction Quotient 13.7 Le ChStelier s Principle... 

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. 

We can write a reactant quotient at any point during the reaction, but the most meaningful point is when the reaction has reached equilibrium. At equilibrium, the reaction quotient becomes the equilibrium constant, Kc (or Kp if gas pressures are being used). We usually express this equilibrium constant simply as a number without units since it is a ratio of concentrations or pressures. In addition,... 

Remember that at equilibrium, the reaction quotient, Oc. s equal to the equilibrium constant, Kc-... 

At equilibrium, the reaction quotient has a certain (dimensionless) value called the equilibrium constant, K, of the reaction ... 

The difference between the reaction quotient and the equilibrium constant is that, at a given temperature, the equilibrium constant has only one value and it specifies the relative amounts of reactants and products at equilibrium. The reaction quotient, by contrast, depends on the current state of the reaction and has many different values as the reaction proceeds. For example, in a reaction mixture containing only reactants, the reaction quotient is zero (Qo = 0) ... 

In a closed reaction vessel at constant temperature, a reaction proceeds spontaneously toward equilibrium. At equilibrium, the reaction quotient Q attains the same constant value, K, irrespective of the starting amounts of reactants and products. 

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. 

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. 

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... 

In this generalized equation, (75), we see that again the numerator is the product of the equilibrium concentrations of the substances formed, each raised to the power equal to the number of moles of that substance in the chemical equation. The denominator is again the product of the equilibrium concentrations of the reacting substances, each raised to a power equal to the number of moles of the substance in the chemical equation. The quotient of these two remains constant. The constant K is called the equilibrium constant. This generalization is one of the most useful in all of chemistry. From the equation for any chemical reaction one can immediately write an expression, in terms of the concentrations of reactants and products, that will be constant at any given temperature. If this constant is measured (by measuring all of the concentrations in a particular equilibrium solution), then it can be used in calculations for any other equilibrium solution at that same temperature. 

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. 

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). 

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,... 

Because the reaction quotient has a smaller value than the equilibrium constant, a net reaction will occur to the right. We now set up this solution as we have others, based on the balanced chemical equation. 

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 ... 

The values in a reaction quotient, Q, or an equilibrium constant expression, K, may be in terms of what two factors ... 

The AG symbol refers to the nonstandard Gibbs free energy value, AG° is the standard value, R is the gas constant (8.314 J/mol-K), T is the temperature (K), and Q is the reaction quotient first seen in Chapter 14. At equilibrium, this equation becomes ... 

The equilibrium concentrations are inserted into the reaction quotient expression, and the equilibrium constant is calculated. 

The Relationship Between the Equilibrium Constant and the Reaction Quotient... 

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