System at Equilibrium Predictions

Evaluating the quadratic formula always yields two roots. One root (the answer) has physical meaning. The other root, though mathematically correct, is extraneous that is, it has no physical meaning. The value of x is defined as the number of moles of A per liter that react and the number of moles of B per liter that react. No more B can be consumed than was initially present (0.100 Ad), sox = 0.309 is the extraneous root. Thus, x = 0.099 is the root that has physical meaning. The equilibrium concentrations are 

You can put the calculated equilibrium concentrations into the expression for Q to check to see that Q= Kc (within rounding error), as was shown at the end of Example 17-6. 

Solving Quadratic Equations— Which Root Shall We Use  

Quadratic equations can be rearranged into standard form. 

This formula gives two roots, both of which are mathematically correct. A foolproof way to determine which root of the equation has physical meaning is to substitute the value of the variable into the expressions for the equilibrium concentrations. For the extraneous root, one or more of these substitutions will lead to a negative concentration, which is physically impossible (there cannot be less than none of a substance present ). The correct root will give all positive concentrations. In Example 17-7, substitution of the extraneous root X = 0.309 would give [A] = (0.300 — 0.309) M = —0.009 M and [B] = (0.100 - 0.309) Ad = -0.209 Ad. Either of these concentration values would be impossible, so we would know that 0.309 is an extraneous root. You should apply this test to subsequent calculations that involve solving a quadratic equation. 

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Basic Concepts 17-2 The Equilibrium Constant 17-3 Variation of with the Form of the Balanced Equation 17-4 The Reaction Quotient 17-5 Uses of the Equilibrium Constant, Kc 17-6 Disturbing a System at Equilibrium Predictions... 

The sign of AG can be used to predict the direction in which a reaction moves to reach its equilibrium position. A reaction is always thermodynamically favored when enthalpy decreases and entropy increases. Substituting the inequalities AH < 0 and AS > 0 into equation 6.2 shows that AG is negative when a reaction is thermodynamically favored. When AG is positive, the reaction is unfavorable as written (although the reverse reaction is favorable). Systems at equilibrium have a AG of zero. 

Le Chatelier s principle provides a means for predicting how systems at equilibrium respond to a change in conditions. When a stress is applied to an equilibrium by adding a reactant or product, by adding a reagent that reacts with one of the reactants or products, or by changing the volume, the system responds by moving in the direction that relieves the stress. 

This distinction between the conditions in a chemical system at equilibrium and the rate at which these conditions are attained is very important in chemistry. By arguments that we shall consider a chemist can decide with confidence whether equilibrium favors reactants or products or neither. He cannot predict, however, how rapidly the system will approach the equilibrium conditions. That is a matter of reaction rates, and the chemist must perform separate experiments to learn whether a given rate is rapid or not. 

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 ... 

The isolation of crystalline products having mixed polymorphic compositions (often referred to as concomitant polymorphism) remains a topic of interest, even though the phase rule predicts that a system at equilibrium consisting two components (solvent + solute) and three phases (solution + Form I + Form II) is uni variant. Hence, for crystallizations performed at a fixed pressure (typically atmospheric) the system becomes nonvariant and genuine equilibrium can exist at only one temperature. Therefore, concomitant products must be obtained under nonequilibrium conditions. Flexibility in molecular conformation was attributed to the concomitant polymorphs of a spirobicyclic dione [34] and of 3-acetylcoumarin [35],... 

Sometimes the calculation predicts that the fluid as initially constrained is supersaturated with respect to one or more minerals, and hence, is in a metastable equilibrium. If the supersaturated minerals are not suppressed, the model proceeds to calculate the equilibrium state, which it needs to find if it is to follow a reaction path. By allowing supersaturated minerals to precipitate, accounting for any minerals that dissolve as others precipitate, the model determines the stable mineral assemblage and corresponding fluid composition. The model output contains the calculated results for the supersaturated system as well as those for the system at equilibrium. 

Such a method has seldom been used with systems containing an aqueous fluid, probably because the complexity of the solution s free energy surface and the wide range in aqueous solubilities of the elements complicate the numerics of the calculation (e.g., Harvie el al., 1987). Instead, most models employ a procedure of elimination. If the calculation described fails to predict a system at equilibrium, the mineral assemblage is changed to swap undersaturated minerals out of the basis or supersaturated minerals into it, following the steps in the previous chapter the calculation is then repeated. 

How can you measure the position of equilibrium experimentally and predict the concentrations of chemicals in a system at equilibrium ... 

Le Chatelier s principle to predict the direction in which a chemical system at equilibrium will shift when concentration changes... 

In this investigation, you will use Le Chatelier s principle to predict the effect of changing one factor in each system at equilibrium. Then you will test your prediction using a colour change or the appearance (or disappearance) of a precipitate. 

Table 7.2 summarizes the effect of a catalyst, and other effects of changing conditions, on a system at equilibrium. The Sample Problem that follows provides an opportunity for you to use Le Chatelier s principle to predict the equilibrium shift in response to various conditions. 

How a chemical system at equilibrium changes when conditions change was first stated by Henri Louis Le Chatelier (1850-1936) in 1884. Le Chatelier was a professor at a mining school in France who worked on both the theoretical and practical aspects of chemistry. His research on the chemistry of cements led him to formulate a principle to predict how changing the pressure affected a chemical system. In the publication Annals of Mines in 1888, Le Chatelier stated the principle that bears his name Every change of one of the factors... 

A powerful theoretical tool for cosmochemical models is thermodynamics. This formalism considers a system in a state of equilibrium, a consequence of which is that observable properties of a system undergo no net change with time. (We offer a somewhat more rigorous discussion of thermodynamics in Chapter 7). The tools of thermodynamics are not useful for asking questions about a system s evolutionary history. However, with the appropriate equations, we are able to estimate what a system at equilibrium would look like under any environmental conditions. The methods of thermodynamics allow the use of temperature and pressure, plus the system s bulk composition, to predict which minerals will be stable and in what relative amounts they will be present. In this way, the thermodynamic approach to a cosmochemical system can help us measure its stability and predict the direction in which it will change if environmental parameters change. 

If AStot were not equal to 0, either the forward or the reverse direction would be spontaneous. This condition, that AStot = 0 for any system at equilibrium, is of the greatest importance. For instance, if we can find how the entropy varies with the composition of a reaction mixture then by looking for the composition at which AStot = 0, we will be able to predict the composition at which the reaction has no tendency to form more products nor decompose into reactants. 

AuCl2- or even a higher order complex. While it is possible that the enhanced capacity of Au1 for complexation with soft ligands may account for the disparate distributions of Ag and Au, fractionation of Au and Ag may also be caused by a significant Aum chemistry in seawater. The major species of Au111 in seawater are expected to be Au(OH)3 or Au(OH)3C1 (Baes and Mesmer, 1976). Although the analysis ofTumer etal. (1981) indicated that the field of Aum stability is somewhat outside the oxidation-reduction conditions encountered in seawater, a paucity of direct formation-constant observations for both Aum and Au1 creates substantial uncertainties. Furthermore, with respect to thermodynamic predictions of oxidation-reduction behaviour the ocean is not a system at equilibrium. 

Le Chatelier s principle predicts that when heat is added at constant pressure to a system at equilibrium, the reaction will shift in the direction that absorbs heat until a new equilibrium is established. For an endothermic process, the reaction will shift to the right towards product formation. For an exothermic process, the reaction will shift to the left towards reactant formation. If you understand the application of Le Chatelier s principle to concentration changes then writing "heat" on the appropriate side of the equation will help you understand its application to changes in temperature. 

Many reactions, however, do not run to completion. They will reach a point where they stop, but in this chapter you will learn that when they are in this state they are not really stopped at all. These reactions, where the products can readily reform the reactants, are known as reversible reactions. The way these reactions proceed is analogous to the systems in equilibrium that were discussed in Chapters 8 and 10 (vapor equilibrium and solutions). In the next three chapters, you will study the equilibrium of chemical reactions and learn more about the factors associated with it. The focus of this chapter is to introduce the equilibrium constant, which provides data about the relationships between reactants and products in a system at equilibrium, and Le Chatelier s Principle, which allows you to predict the effects of different stressors on reaction equilibria. 

You may well be familiar with a rule that helps to predict how a system at equilibrium responds to a change in external conditions—Le Chatelier s principle. This says that if we disturb a system at equilibrium it will respond so as to minimize the effect of the disturbance. An example of a disturbance is adding more starting material to a reaction mixture at equilibrium. What happens More product is formed to use up this extra material. This is a consequence of the equilibrium constant being, well... constant and hardly needs anybody s principle. 

Because chemical equilibrium involves rates of reactions, this chapter first investigates the factors that affect the rate of a reaction (Section 18.1). The molecular basis of chemical equilibrium and some of its terminology are then presented in Section 18.2. LeChatelier s principle, discussed in Section 18.3, explains qualitatively how to predict what happens to a system at equilibrium when a change is imposed on the system. Section 18.4 presents the equilibrium constant, which allows us to obtain quantitative results for systems at equilibrium. 

When the conditions that affect the rate of a chemical reaction are changed in a system at equilibrium, the rates of the forward and the reverse reaction may be affected differently. If these rates become different, more reactants or products are produced. The direction of the shift of an equilibrium can be predicted qualitatively using LeChatelier s principle. LeChatelier s principle states that if a stress is applied to a system at equilibrium, the equilibrium will tend to shift in a direction to relieve that stress. 

We can qualitatively predict the effects of changes in concentration, pressure, and temperature on a system at equilibrium by using Le Chatelier s principle, which states that if a change in conditions (a stress ) is imposed on a system at equilibrium, the equilibrium position unll shift in a direction that tends to reduce that change in conditions. Although this rule, put forth by Henri Le Chatelier in 1884, sometimes oversimplifies the situation, it works remarkably well. 

To see how we can predict the effects of a change in concentration on a system at equilibrium, we will consider the ammonia synthesis reaction. Suppose there is an equilibrium position described by these concentrations ... 

If energy in the form of heat is added to this system at equilibrium, Le Chatelier s principle predicts that the shift will be in the direction that consumes energy, in this case to the left. Note that this shift decreases the concentration of NH3 and increases the concentrations of N2 and H2, thus decreasing the value of K. The experimentally observed change in K with temperature t... 

In summary, to use Le Chatelier s principle to describe the effect of a temperature change on a system at equilibrium, treat energy as a reactant (in an endothermic process) or as a product (in an exothermic process), and predict the direction of the shift as if an actual reactant or product is added or removed. Although Le Chatelier s principle cannot predict the size of the change in A, it can correctly predict the direction of the change. 

We have seen how Le Chatelier s principle can be used to predict the effect of several types of changes on a system at equilibrium. As a summary of these ideas, Table 6.4 shows how various changes affect the equilibrium position of the endothermic reaction... 

Pourbaix diagrams, or pH-potential diagrams, have been constructed to facilitate the prediction of the various phases (reactions and reaction products) that are stable in an aqueous electrochemical system at equilibrium. " Boundary lines in such diagrams divide the areas of stability for different phases and are derived from the use of Nemst equation... 

The effects of changing conditions on a system at equilibrium can be predicted using Le Chatelier s Principle. 

In 1888, the French chemist Henri-Louis Le ChStelier discovered that there are ways to control equilibria to make reactions, including this one, more productive. He proposed what is now called Le Chatelier s principle If a stress is applied to a system at equilibrium, the system shifts in the direction that relieves the stress. A stress is any kind of change in a system at equilibrium that upsets the equilibrium. You can use Le Chatelier s principle to predict how changes in concentration, volume (pressure), and temperature affect equilibrium. Changes in volume and pressure are interrelated because decreasing the volume of a reaction vessel at constant temperature increases the pressure inside. Conversely, increasing the volume decreases the pressure. 

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