Chemical equilibrium reaction quotient

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

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. 

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. 

This reaction quotient is a fraction. The numerator is the product of the chemical species on the right hand side of the equilibrium arrow, each one raised to the power of that species coefficient in the balanced chemical equation. The denominator is the product of the chemical species on the left hand side of the equilibrium arrow, each one raised to the power of that species coefficient in the balanced chemical equation. It is called Qc, in this case, since molar concentrations are being used. If this was a gas phase reaction, gas pressures could be used and it would become a Qp. 

In this section, you learned that the expression for the reaction quotient is the same as the expression for the equilibrium constant. The concentrations that are used to solve these expressions may be different, however. When Qc is less than Kc, the reaction proceeds to form more products. When Qc is greater than Kc, the reaction proceeds to form more reactants. These changes continue until Qc is equal to Kc. Le Chatelier s principle describes this tendency of a chemical system to return to equilibrium after a change moves it from equilibrium. The industrial process for manufacturing ammonia illustrates how chemical engineers apply Le Chatelier s principle to provide the most economical yield of a valuable chemical product. 

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. 

When the reactants and products of a given chemical reaction are mixed, it is useful to know whether the mixture is at equilibrium and, if it is not, in which direction the system will shift to reach equilibrium. If the concentration of one of the reactants or products is zero, the system will shift in the direction that produces the missing component. However, if all the initial concentrations are not zero, it is more difficult to determine the direction of the move toward equilibrium. To determine the shift in such cases, we use the reaction quotient (Q). The reaction quotient is obtained by applying the law of mass action, but using initial concentrations instead of equilibrium concentrations. For example, for the synthesis of ammonia,... 

The change in Gibbs free energy (AG), which occurs as a system proceeds toward equilibrium, can be expressed as the sum of two terms. The first term is the standard free energy change (A G°), which is fixed for any given reaction. AG° can be calculated from the stoichiometry of the reaction (i.e., how many moles of one compound react with how many moles of another compound) and the standard free energies of the chemicals involved. The second term contains the reaction quotient (Q), which depends on the concentrations of chemicals present. The fact that AG can be expressed in terms of the concentrations of all chemicals present in a system makes it possible to determine in which direction a chemical reaction will proceed and to predict its final composition when it reaches equilibrium. 

For the moment, consider only reactions involving chemicals dissolved in water. The preceding equations can be combined with the definition of the reaction quotient, Eq. [1-10], to define an equilibrium constant, K, that applies to the final expected chemical composition of the system ... 

In spite of the outlined above formulation of chemical equilibrium problem in terms of rigorous thermodynamics (equilibrium constants defined as quotients of activities) which is well known and does not pose any special difficulty when it is compared with formulation in terms of conditional equilibrium constants (defined as quotients of concentrations), the former approach is not very popular, and many equilibrium constants of surface reactions reported in published papers were defined in terms of concentrations. Even praise of use of concentrations rather than activities in modeling of adsorption can be found in recent literature. Many publications do not address this question explicit, and then it is difficult to figure out how the equilibrium constants of surface species were defined K, or Accordingly, the equilibrium constants of surface species reported in tables of Chapter 4 constitute a mixture of constants defined in different ways (K, or The details regarding the definition of equilibrium constants can be found (but not always) in the original publications. 

An important quantity to describe the state of the chemical reaction (4.102) is the reaction quotient Q. In contrast to Eq. (4.87), the concentrations are not expressed as an equilibrium (when the reaction reaches an equilibrium the condition Q = K... 

We refer to this ratio as the reaction quotient, Q. Product concentrations appear in the numerator of the expression, and reactants appear in the denominator. Each concentration is raised to a power corresponding to the stoichiometric coefficient of that species in the balanced chemical equation for the equilihrium. At equilih-rium, however, this ratio becomes the equilibrium expression, and the corresponding value of Q is called the equilibrium constant, K. 

The term that appears in the natural logarithm of Equation 2.16, which is a ratio of product and reactant activities raised to their appropriate stochiometric coefficients, has a special name. It is known as the reaction quotient Q. As we discussed in the section on dynamic equilibrium, it is important to think of all processes, including chemical reactions, as dynamic processes that can occur in both the forward and backward directions. Thus, you should think of a chemical reaction as being like a balance between the reactant and product species—and the reaction quotient is essentially a quantitative indicator of that balance. The reaction quotient indicates whether the current balance of a reaction under any arbitrary set of conditions has been skewed more toward the reactant or product side as compared to the standard-state conditions. At the standard-state condition, all of the reactants and product species are at unit activity, and thus the reaction quotient is 1. In this case, AG = AG°, which makes sense, since AG is the free energy under standard-state conditions. 

Recall that for a system at equilibrium, AG = 0. This is the definition of thermodynamic equilibrium. Applying this definition to Equation 2.16 enables us to determine the precise ratio of reactant and product activities that lead to a perfect balance (equilibrium) between the reactant and product states in a chemical system. This specific value of the reaction quotient has a special name. It is known as the equilibrium... 

When we substitute reactant and product partial pressures or concentrations into an equilibrium-constant expression, the result is known as the reaction quotient and is represented by the letter Q. The reaction quotient unU equal the equilibrium constant, Kg i, only if the system is at equilibrium Q = only at equilibrium. We have seen that when Q > Kg, substances on tire right side of tire chemical equation will react to form substances on tire left tire reaction moves from right to left in approaching equilibrium. Conversely, if Q < Kgq, tire reaction will achieve equilibrium by forming more products it moves from left to right. These relationships are summarized in Figure 15.10 . 

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... 

A chemical reaction proceeding toward equilibrium is a spontaneous change. Recall that we can predict the net direction of the reaction—its spontaneous direction— by comparing the reaction quotient (0 with the equilibrium constant (K). But why is there a drive to attain equilibrium And what determines the value of the equilibrium constant And, most importantly, can we predict the direction of a spontaneous change in cases that are not as obvious as burning gasoline or falling books ... 

Chemical equilibrium can be characterized by the equilibrium constant K. In the expression for the concentration of products is in the numerator and the concentration of reactants is in the denominator. Pure liquids and solids are ignored in writing the equilibrium-constant expression. When Kc is very large, the equilibrium mixture is mostly products, and when Kc is very small, the equilibrium mixture is mostly reactants. The reaction quotient takes the form of the equilibrium-constant expression. If you substitute the concentrations of substances in a reaction mixture into Q, you... 

You can derive the equation relating AG° to the equilibrium constant K from the preceding equation. In the previous section, you saw that as a chemical reaction approaches equilibrium, the free energy decreases and continues to decrease until equilibrium is reached. At equilibrium, the free energy ceases to change then AG = 0. Also, the reaction quotient Q becomes equal to the equilibrimn constant K. If you substitute AG = 0 and Q = K into the preceding equation, you obtain... 

As we have stressed earlier, Le Chatelier s principle provides a very useful descriptive tool that helps us predict the outcome of a change in conditions on a chemical equilibrium. Flowever, it does not provide an explanation for these effects. Use of the reaction quotient, Q, can give an insight into why changing the concentration of a component of an equilibrium mixture gives rise to the effect it does. Take the following reaction as an example ... 

In the mid-nineteenth century, Cato Guldberg and Peter Waage studied the equilibrium mixtures of a wide variety of chemical reactions. They observed that at a constant temperature in an equilibrium mixture of reactants and products regardless of the initial concentrations, the reaction quotient has a constant value. The reaction quotient (QJ is a fraction with product concentrations in the numerator and reactant concentrations in the denominator—with each concentration raised to a power equal to the corresponding stoichiometric coefficient in the balanced chemical equation. For the general reaction. 

Chemical equilibrium is defined in terms of a minimum of Gibbs energy with respect to the extent of a reaction. Because the Gibbs energy is related to the chemical potential, we can use equations involving chemical potential to derive some equations that relate to equilibrium and nonequilibrium conditions of a chemical process. In these expressions, a reaction quotient appears, which is a construction involving the reactants and products of the reaction. For gas-phase reactions, the reaction... 

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