D. Harvey - Modern Analytical Chemistry (794078), страница 42
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“Detection and Determination of Error inAnalytical Methodology. Part II. Correction for CorrigibleSystematic Error in the Course of Real Sample Analysis,” J.Assoc. Off. Anal. Chem. 1983, 66, 1283–1294.Cardone, M. J. “Detection and Determination of Error inAnalytical Methodology. Part IIB. Direct CalculationalTechnique for Making Corrigible Systematic ErrorCorrections,” J. Assoc. Off. Anal. Chem. 1985, 68, 199–202.5J REFERENCES1. Battino, R.; Williamson, A.
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R. Chemometrics,Wiley-Interscience: New York, 1986; (b) Deming, S. N.; Morgan,S. L. Experimental Design: A Chemometric Approach, Elsevier:Amsterdam, 1987.11. Beebe, K. R.; Kowalski, B. R. Anal. Chem. 1987, 59,1007A–1017A.12. Cardone, M. J. Anal. Chem. 1986, 58, 433–438.13. Cardone, M. J. Anal. Chem. 1986, 58, 438–445.14.
Wojciechowski, M; Balcerzak, J. Anal. Chim. Acta 1991, 249,433–445.15. Troost, J. R.; Olavesen, E. Y. Anal. Chem. 1996, 68, 708–711.16. Franke, J. P.; de Zeeuw, R. A.; Hakkert, R. Anal. Chem. 1978, 50,1374–1380.1400-CH06 9/9/99 7:40 AM Page 135Chapter 6Equilibrium ChemistryRegardless of the problem on which an analytical chemist isworking, its solution ultimately requires a knowledge of chemistry andthe ability to reason with that knowledge. For example, an analyticalchemist developing a method for studying the effect of pollution onspruce trees needs to know, or know where to find, the structuraland chemical differences between p-hydroxybenzoic acid andp-hydroxyacetophenone, two common phenols found in the needles ofspruce trees (Figure 6.1).
Chemical reasoning is a product of experienceand is constructed from knowledge acquired in the classroom, thelaboratory, and the chemical literature.The material in this text assumes familiarity with topics covered inthe courses and laboratory work you have already completed. Thischapter provides a review of equilibrium chemistry. Much of thematerial in this chapter should be familiar to you, but other ideas arenatural extensions of familiar topics.1351400-CH06 9/9/99 7:40 AM Page 136136Modern Analytical ChemistryOOHCH3OOHOH(a)(b)Figure 6.1Structures of (a) p-hydroxybenzoic acid and(b) p-hydroxyacetophenone.6A Reversible Reactions and Chemical EquilibriaIn 1798, the chemist Claude Berthollet (1748–1822) accompanied a French militaryexpedition to Egypt.
While visiting the Natron Lakes, a series of salt water lakescarved from limestone, Berthollet made an observation that contributed to an important discovery. Upon analyzing water from the Natron Lakes, Berthollet foundlarge quantities of common salt, NaCl, and soda ash, Na2CO3, a result he found surprising. Why would Berthollet find this result surprising and how did it contributeto an important discovery? Answering these questions provides an example ofchemical reasoning and introduces the topic of this chapter.Berthollet “knew” that a reaction between Na2CO3 and CaCl2 goes to completion, forming NaCl and a precipitate of CaCO3 as products.Na2CO3 + CaCl2 → 2NaCl + CaCO3Understanding this, Berthollet expected that large quantities of NaCl and Na2CO3could 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 andCaCO3, leaving behind no unreacted Na2CO3. In fact, this result is what he observed in the laboratory. The evidence from Natron Lakes, where the coexistence ofNaCl and Na2CO3 suggests that the reaction has not gone to completion, rancounter to Berthollet’s expectations. Berthollet’s important insight was recognizingthat the chemistry occurring in the Natron Lakes is the reverse of what occurs in thelaboratory.CaCO3 + 2NaCl → Na2CO3 + CaCl2CaCO3GramsUsing this insight Berthollet reasoned that the reaction is reversible, and that therelative amounts of “reactants” and “products” determine the direction in whichthe reaction occurs, and the final composition of the reaction mixture.
We recognize a reaction’s ability to move in both directions by using a double arrow whenwriting the reaction.Ca2+TimeFigure 6.2Change in mass of undissolved Ca2+ andsolid CaCO3 over time during theprecipitation of CaCO3.equilibriumA system is at equilibrium when theconcentrations of reactants and productsremain constant.Na2CO3 + CaCl2t 2NaCl + CaCO3Berthollet’s reasoning that reactions are reversible was an important step inunderstanding chemical reactivity. When we mix together solutions of Na2CO3and CaCl2, they react to produce NaCl and CaCO3.
If we monitor the mass ofdissolved Ca 2+ remaining and the mass of CaCO 3 produced as a function oftime, the result will look something like the graph in Figure 6.2. At the start ofthe reaction the mass of dissolved Ca2+ decreases and the mass of CaCO3 increases. Eventually, however, the reaction reaches a point after which no furtherchanges occur in the amounts of these species. Such a condition is called a stateof equilibrium.Although a system at equilibrium appears static on a macroscopic level, it isimportant to remember that the forward and reverse reactions still occur.
A reaction at equilibrium exists in a “steady state,” in which the rate at which any speciesforms equals the rate at which it is consumed.6B Thermodynamics and Equilibrium ChemistryThermodynamics is the study of thermal, electrical, chemical, and mechanicalforms of energy. The study of thermodynamics crosses many disciplines, includingphysics, engineering, and chemistry. Of the various branches of thermodynamics,1400-CH06 9/9/99 7:40 AM Page 137Chapter 6 Equilibrium Chemistry137the most important to chemistry is the study of the changes in energy occurringduring 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 + bBt cC + dD6.1By convention, species to the left of the arrows are called reactants, and those on theright side of the arrows are called products.
As Berthollet discovered, writing a reaction in this fashion does not guarantee that the reaction of A and B to produce C andD is favorable. Depending on initial conditions, the reaction may move to the left, tothe right, or be in a state of equilibrium. Understanding the factors that determinethe final position of a reaction is one of the goals of chemical thermodynamics.Chemical systems spontaneously react in a fashion that lowers their overall freeenergy. At a constant temperature and pressure, typical of many bench-top chemical reactions, the free energy of a chemical reaction is given by the Gibb’s free energy function∆G = ∆H – T ∆S6.2where T is the temperature in kelvins, and ∆G, ∆H, and ∆S are the differences in theGibb’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 reaction.
Reactions in which heat is produced have a negative ∆H and are calledexothermic. Endothermic reactions absorb heat from their surroundings and have apositive ∆H. Entropy is a measure of randomness, or disorder. The entropy of anindividual species is always positive and tends to be larger for gases than for solidsand for more complex rather than simpler molecules.
Reactions that result in alarge number of simple, gaseous products usually have a positive ∆S.The sign of ∆G can be used to predict the direction in which a reaction movesto reach its equilibrium position. A reaction is always thermodynamically favoredwhen enthalpy decreases and entropy increases. Substituting the inequalities ∆H < 0and ∆S > 0 into equation 6.2 shows that ∆G is negative when a reaction is thermodynamically favored. When ∆G is positive, the reaction is unfavorable as written(although the reverse reaction is favorable). Systems at equilibrium have a ∆Gof zero.As a system moves from a nonequilibrium to an equilibrium position, ∆G mustchange from its initial value to zero.
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