Modern Analytical Cheymistry - Chapter 6

Chapter 6 Equilibrium Chemistry Regardless of the problem on which an analytical chemist is working, its solution ultimately requires a knowledge of chemistry and the ability to reason with that knowledge. For example, an analytical chemist developing a method for studying the effect of pollution on spruce trees needs to know, or know where to find, the structural and chemical differences between p-hydroxybenzoic acid and p-hydroxyacetophenone, two common phenols found in the needles of spruce trees (Figure 6.1). Chemical reasoning is a product of experience and is constructed from knowledge acquired in the classroom, the laboratory, and the chemical literature. The material in this text assumes familiarity with topics covered in the courses and laboratory work you have already completed. This chapter provides a review of equilibrium chemistry. Much of the material in this chapter should be familiar to you, but other ideas are natural extensions of familiar topics. 135 136 Modern Analytical Chemistry O OH O CH3 6A Reversible Reactions and Chemical Equilibria OH OH (a) (b) Figure 6.1 Structures of (a) p-hydroxybenzoic acid and (b) p-hydroxyacetophenone. CaCO3 Ca2+ Time Figure 6.2 Change in mass of undissolved Ca2+ and solid CaCO3 over time during the precipitation of CaCO3. equilibrium A system is at equilibrium when the concentrations of reactants and products remain constant. In 1798, the chemist Claude Berthollet (1748–1822) accompanied a French military expedition to Egypt. While visiting the Natron Lakes, a series of salt water lakes carved from limestone, Berthollet made an observation that contributed to an im-portant discovery. Upon analyzing water from the Natron Lakes, Berthollet found large quantities of common salt, NaCl, and soda ash, Na2CO3, a result he found sur-prising. Why would Berthollet find this result surprising and how did it contribute to an important discovery? Answering these questions provides an example of chemical reasoning and introduces the topic of this chapter. Berthollet “knew” that a reaction between Na2CO3 and CaCl2 goes to comple-tion, forming NaCl and a precipitate of CaCO3 as products. Na2CO3 + CaCl2 ® 2NaCl + CaCO3 Understanding this, Berthollet expected that large quantities of NaCl and Na2CO3 could not coexist in the presence of CaCO3. Since the reaction goes to completion, adding a large quantity of CaCl2 to a solution of Na2CO3 should produce NaCl and CaCO3, leaving behind no unreacted Na2CO3. In fact, this result is what he ob-served in the laboratory. The evidence from Natron Lakes, where the coexistence of NaCl and Na2CO3 suggests that the reaction has not gone to completion, ran counter to Berthollet’s expectations. Berthollet’s important insight was recognizing that the chemistry occurring in the Natron Lakes is the reverse of what occurs in the laboratory. CaCO3 + 2NaCl ® Na2CO3 + CaCl2 Using this insight Berthollet reasoned that the reaction is reversible, and that the relative amounts of “reactants” and “products” determine the direction in which the reaction occurs, and the final composition of the reaction mixture. We recog-nize a reaction’s ability to move in both directions by using a double arrow when writing the reaction. Na2CO3 + CaCl2 t2NaCl + CaCO3 Berthollet’s reasoning that reactions are reversible was an important step in understanding chemical reactivity. When we mix together solutions of Na2CO3 and CaCl2, they react to produce NaCl and CaCO3. If we monitor the mass of dissolved Ca2+ remaining and the mass of CaCO3 produced as a function of time, the result will look something like the graph in Figure 6.2. At the start of the reaction the mass of dissolved Ca2+ decreases and the mass of CaCO3 in-creases. Eventually, however, the reaction reaches a point after which no further changes occur in the amounts of these species. Such a condition is called a state of equilibrium. Although a system at equilibrium appears static on a macroscopic level, it is important to remember that the forward and reverse reactions still occur. A reac-tion at equilibrium exists in a “steady state,” in which the rate at which any species forms equals the rate at which it is consumed. 6B Thermodynamics and Equilibrium Chemistry Thermodynamics is the study of thermal, electrical, chemical, and mechanical forms of energy. The study of thermodynamics crosses many disciplines, including physics, engineering, and chemistry. Of the various branches of thermodynamics, Chapter 6 Equilibrium Chemistry 137 the most important to chemistry is the study of the changes in energy occurring during a chemical reaction. Consider, for example, the general equilibrium reaction shown in equation 6.1, involving the solutes A, B, C, and D, with stoichiometric coefficients a, b, c, and d. aA + bB tcC + dD 6.1 By convention, species to the left of the arrows are called reactants, and those on the right side of the arrows are called products. As Berthollet discovered, writing a reac-tion in this fashion does not guarantee that the reaction of A and B to produce C and D is favorable. Depending on initial conditions, the reaction may move to the left, to the right, or be in a state of equilibrium. Understanding the factors that determine the final position of a reaction is one of the goals of chemical thermodynamics. Chemical systems spontaneously react in a fashion that lowers their overall free energy. At a constant temperature and pressure, typical of many bench-top chemi-cal reactions, the free energy of a chemical reaction is given by the Gibb’s free en-ergy function ΔG = ΔH – T ΔS 6.2 where T is the temperature in kelvins, and ΔG, ΔH, and ΔS are the differences in the Gibb’s free energy, the enthalpy, and the entropy between the products and reactants. Enthalpy is a measure of the net flow of energy, as heat, during a chemical re-action. Reactions in which heat is produced have a negative ΔH and are called exothermic. Endothermic reactions absorb heat from their surroundings and have a positive ΔH. Entropy is a measure of randomness, or disorder. The entropy of an individual species is always positive and tends to be larger for gases than for solids and for more complex rather than simpler molecules. Reactions that result in a large number of simple, gaseous products usually have a positive ΔS. The sign of ΔG 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 ΔH < 0 and ΔS > 0 into equation 6.2 shows that ΔG is negative when a reaction is thermo-dynamically favored. When ΔG is positive, the reaction is unfavorable as written (although the reverse reaction is favorable). Systems at equilibrium have a ΔG of zero. As a system moves from a nonequilibrium to an equilibrium position, ΔG must change from its initial value to zero. At the same time, the species involved in the reaction undergo a change in their concentrations. The Gibb’s free energy, there-fore, must be a function of the concentrations of reactants and products. As shown in equation 6.3, the Gibb’s free energy can be divided into two terms. Gibb’s free energy A thermodynamic function for systems at constant temperature and pressure that indicates whether or not a reaction is favorable (ΔG < 0), unfavorable (ΔG > 0), or at equilibrium (ΔG = 0). enthalpy A change in enthalpy indicates the heat absorbed or released during a chemical reaction at constant pressure. entropy A measure of disorder. ΔG = ΔG° + RT ln Q 6.3 The first term, ΔG°, is the change in Gibb’s free energy under standard-state condi-tions; 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 pres-sures or concentrations. For reaction 6.1 the reaction quotient is standard state Condition in which solids and liquids are in pure form, gases have partial pressures of 1 atm, solutes have concentrations of 1 M, and the temperature is 298 K. [C] [D] [A] [B] 6.4 where the terms in brackets are the molar concentrations of the solutes. Note that the reaction quotient is defined such that the concentrations of products are placed 138 Modern Analytical Chemistry equilibrium constant For a reaction at equilibrium, the equilibrium constant determines the relative concentrations of products and reactants. in the numerator, and the concentrations of reactants are placed in the denominator. In addition, each concentration term is raised to a power equal to its stoichiometric coefficient in the balanced chemical reaction. Partial pressures are substituted for concentrations when the reactant or product is a gas. The concentrations of pure solids and pure liquids do not change during a chemical reaction and are excluded from the reaction quotient. At equilibrium the Gibb’s free energy is zero, and equation 6.3 simplifies to ΔG° = –RT ln K where K is an equilibrium constant that defines the reaction’s equilibrium posi-tion. The equilibrium constant is just the numerical value obtained when substitut-ing the concentrations of reactants and products at equilibrium into equation 6.4; thus, [C] q[D] q [A] q[B] q where the subscript “eq” indicates a concentration at equilibrium. Although the subscript “eq” is usually omitted, it is important to remember that the value of K is determined by the concentrations of solutes at equilibrium. As written, equation 6.5 is a limiting law that applies only to infinitely dilute solutions, in which the chemical behavior of any species in the system is unaffected by all other species. Corrections to equation 6.5 are possible and are discussed in more detail at the end of the chapter. 6C Manipulating Equilibrium Constants We will use two useful relationships when working with equilibrium constants. First, if we reverse a reaction’s direction, the equilibrium constant for the new reac-tion is simply the inverse of that for the original reaction. For example, the equilib-rium constant for the reaction A + 2B t AB2 is the inverse of that for the reaction [AB2] 1 [A][B] AB2 t A + 2B 1 [A][B] 2 K1 [AB2] Second, if we add together two reactions to obtain a new reaction, the equilibrium constant for the new reaction is the product of the equilibrium constants for the original reactions. A + C t AC AC + C t AC2 [AC] 1 [A][C] [AC2] 2 [AC][C] A + 2C t AC2 [AC] [AC2] [AC2] 3 1 2 [A][C] [AC][C] [A][C] Chapter 6 Equilibrium Chemistry 139 EXAMPLE 6.1 Calculate the equilibrium constant for the reaction 2A + B tC + 3D given the following information Rxn 1: A + B D Rxn 2: A + E C + D + F Rxn 3: C + E B Rxn 4: F + C D + B SOLUTION The overall reaction is given as K1 = 0.40 K2 = 0.10 K3 = 2.0 K4 = 5.0 Rxn 1 + Rxn 2 – Rxn 3 + Rxn 4 If Rxn 3 is reversed, giving Rxn 5: B t C + E K5 = K3 = 2.0 = 0.50 then the overall reaction is Rxn 1 + Rxn 2 + Rxn 5 + Rxn 4 and the overall equilibrium constant is Koverall = K1 ´ K2 ´ K5 ´ K4 = 0.40 ´ 0.10 ´ 0.50 ´ 5.0 = 0.10 6D Equilibrium Constants for Chemical Reactions Several types of reactions are commonly used in analytical procedures, either in preparing samples for analysis or during the analysis itself. The most important of these are precipitation reactions, acid–base reactions, complexation reactions, and oxidation–reduction reactions. In this section we review these reactions and their equilibrium constant expressions. 6D.1 Precipitation Reactions A precipitation reaction occurs when two or more soluble species combine to form an insoluble product that we call a precipitate. The most common precipitation re-action is a metathesis reaction, in which two soluble ionic compounds exchange parts. When a solution of lead nitrate is added to a solution of potassium chloride, for example, a precipitate of lead chloride forms. We usually write the balanced re-action as a net ionic equation, in which only the precipitate and those ions involved in the reaction are included. Thus, the precipitation of PbCl2 is written as Pb2+(aq) + 2Cl–(aq) tPbCl2(s) In the equilibrium treatment of precipitation, however, the reverse reaction de-scribing the dissolution of the precipitate is more frequently encountered. PbCl2(s) tPb2+(aq) + 2Cl–(aq) precipitate An insoluble solid that forms when two or more soluble reagents are combined. ... - tailieumienphi.vn