D. Harvey - Modern Analytical Chemistry (794078), страница 52
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141)buffer (p. 167)charge balance equation (p. 159)common ion effect (p. 158)cumulative formation constant (p. 144)dissociation constant (p. 144)enthalpy (p. 137)entropy (p. 137)equilibrium (p. 136)equilibrium constant (p. 138)formation constant (p. 144)Gibb’s free energy (p. 137)Henderson–Hasselbalchequation (p. 169)ionic strength (p.
172)ladder diagram (p. 150)Le Châtelier’s principle (p. 148)ligand (p. 144)mass balance equation (p. 159)Nernst equation (p. 146)oxidation (p. 146)oxidizing agent (p. 146)pH (p. 142)precipitate (p. 139)redox reaction (p. 145)reducing agent (p. 146)reduction (p. 146)solubility product (p. 140)standard state (p. 137)stepwise formation constant (p. 144)6L SUMMARYAnalytical chemistry is more than a collection of techniques; it isthe application of chemistry to the analysis of samples. As you willsee in later chapters, almost all analytical methods use chemical reactivity to accomplish one or more of the following—dissolve thesample, separate analytes and interferents, transform the analyteto a more useful form, or provide a signal.
Equilibrium chemistryand thermodynamics provide us with a means for predictingwhich reactions are likely to be favorable.The most important types of reactions are precipitation reactions, acid–base reactions, metal–ligand complexation reactions,and redox reactions. In a precipitation reaction two or more soluble species combine to produce an insoluble product called a precipitate. The equilibrium properties of a precipitation reaction aredescribed by a solubility product.Acid–base reactions occur when an acid donates a proton to abase.
The equilibrium position of an acid–base reaction is described using either the dissociation constant for the acid, Ka, orthe dissociation constant for the base, Kb. The product of Ka andKb for an acid and its conjugate base is Kw (water’s dissociationconstant).Ligands have electron pairs that they can donate to a metal ion,forming a metal–ligand complex. The formation of the metal–ligand complex ML2, for example, may be described by a stepwiseformation constant in which each ligand is added one at a time;thus, K1 represents the addition of the first ligand to M, and K2represents the addition of the second ligand to ML.
Alternatively,the formation of ML2 can be described by a cumulative, or overallformation constant, β2, in which both ligands are added to M.1400-CH06 9/9/99 7:41 AM Page 176176Modern Analytical ChemistryIn a redox reaction, one of the reactants is oxidized while another reactant is reduced.
Equilibrium constants are rarely usedwhen characterizing redox reactions. Instead, we use the electrochemical potential, positive values of which indicate a favorablereaction. The Nernst equation relates this potential to the concentrations of reactants and products.Le Châtelier’s principle provides a means for predicting howsystems at equilibrium respond to a change in conditions. When astress 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 movingin the direction that relieves the stress.You should be able to describe a system at equilibrium bothqualitatively and quantitatively. Rigorous solutions to equilibriumproblems can be developed by combining equilibrium constantexpressions with appropriate mass balance and charge balanceequations.
Using this systematic approach, you can solve somequite complicated equilibrium problems. When a less rigorous an-swer is needed, a ladder diagram may help you decide the equilibrium system’s composition.Solutions containing a weak acid and its conjugate base showonly a small change in pH upon the addition of small amounts ofstrong acid or strong base. Such solutions are called buffers.Buffers can also be formed using a metal and its metal–ligandcomplex, or an oxidizing agent and its conjugate reducing agent.Both the systematic approach to solving equilibrium problemsand ladder diagrams can be used to characterize a buffer.A quantitative solution to an equilibrium problem may give ananswer that does not agree with the value measured experimentally.
This result occurs when the equilibrium constant based onconcentrations is matrix-dependent. The true, thermodynamicequilibrium constant is based on the activities, a, of the reactantsand products. A species’ activity is related to its molar concentration by an activity coefficient, γ, where ai = γi[ ]i. Activity coefficients often can be calculated, making possible a more rigoroustreatment of equilibria.Experiments6M Suggested EXPERIMENTSThe following experiments involve the experimental determination of equilibrium constants and, in some cases,demonstrate the importance of activity effects.“The Effect of Ionic Strength on an Equilibrium Constant (AClass Study).” In J. A. Bell, ed.
Chemical Principles in Practice.Addison-Wesley: Reading, MA, 1967.In this experiment the equilibrium constant for thedissociation of bromocresol green is measured at severalionic strengths. Results are extrapolated to zero ionic strengthto find the thermodynamic equilibrium constant.“Equilibrium Constants for Calcium Iodate Solubility andIodic Acid Dissociation.” In J. A. Bell, ed. Chemical Principlesin Practice. Addison-Wesley: Reading, MA, 1967.The effect of pH on the solubility of Ca(IO3)2 is studied inthis experiment.“The Solubility of Silver Acetate.” In J. A. Bell, ed. ChemicalPrinciples in Practice.
Addison-Wesley: Reading, MA, 1967.In this experiment the importance of the soluble silveracetate complexes AgCH3COO(aq) and Ag(CH3COO)2–(aq)in describing the solubility of AgCH3COO(s) is investigated.Green, D. B.; Rechtsteiner, G.; Honodel, A. “Determinationof the Thermodynamic Solubility Product, Ksp, of PbI2Assuming Nonideal Behavior,” J. Chem. Educ.
1996, 73,789–792.The thermodynamic solubility product for PbI2 isdetermined in this experiment by measuring its solubility atseveral ionic strengths.6N PROBLEMS1. Write equilibrium constant expressions for the followingreactions. Determine the value for the equilibrium constantfor each reaction using appropriate equilibrium constantsfrom Appendix 3.a. NH3(aq) + HCl(aq) NH4+(aq) + Cl–(aq)b. PbI2(s) + S2–(aq) PbS(s) + 2I–(aq)c. CdY2–(aq) + 4CN–(aq) Cd(CN)42–(aq) + Y4–(aq)[Y4– is EDTA]d.
AgCl(s) + 2NH3(aq) Ag(NH3)2+(aq) + Cl–(aq)e. BaCO3(s) + 2H3O+(aq) Ba2+(aq) + H2CO3(aq) + 2H2O(l)ttttt2. Using a ladder diagram, explain why the following reactionH3PO4(aq) + F–(aq)t HF(aq) + H PO2–(aq)4is favorable, whereasH3PO4(aq) + 2F–(aq)t 2HF(aq) + H PO22–(aq)4is unfavorable. Determine the equilibrium constant for thesereactions, and verify that they are consistent with your ladderdiagram.1400-CH06 9/9/99 7:41 AM Page 177Chapter 6 Equilibrium Chemistry3. Calculate the potential for the following redox reaction whenthe [Fe3+] = 0.050 M, [Fe2+] = 0.030 M, [Sn2+] = 0.015 M and[Sn4+] = 0.020 M2Fe3+(aq) + Sn2+(aq)t Sn4+(aq)+ 2Fe2+(aq)4.
Balance the following redox reactions, and calculate thestandard-state potential and the equilibrium constant foreach. Assume that the [H3O+] is 1 M for acidic solutions, andthat the [OH–] is 1 M for basic solutions.a. MnO4–(aq) + H2SO3(aq) Mn2+(aq) +SO42–(aq)(acidic solution)b. IO3–(aq) + I–(aq) I2(s)(acidic solution)c. ClO–(aq) + I– IO3–(aq) + Cl–(aq)(basic solution)ttt5. Sulfur can be determined quantitatively by oxidizing toSO42– and precipitating as BaSO4.
The solubility reactionfor BaSO4 isBaSO4(s)t Ba2+(aq)+ SO42–(aq)How will the solubility of BaSO4 be affected by (a) decreasingthe pH of the solution; (b) adding BaCl2; (c) decreasing thevolume of the solution?6. Write charge balance and mass balance equations for thefollowing solutionsa. 0.1 M NaClb. 0.1 M HClc. 0.1 M HFd. 0.1 M NaH2PO4e.
MgCO3 (saturated solution)f. 0.1 M Ag(CN)2– (from AgNO3 and KCN)g. 0.1 M HCl and 0.050 M NaNO27. Using the systematic approach, calculate the pH of thefollowing solutionsa. 0.050 M HClO4b. 1.00 × 10–7 M HClc. 0.025 M HClOd. 0.010 M HCOOHe. 0.050 M Ba(OH)2f. 0.010 M C5H5N8. Construct ladder diagrams for the following diprotic weakacids (H2L), and estimate the pH of 0.10 M solutions of H2L,HL–, and L2–. Using the systematic approach, calculate the pHof each of these solutions.a. maleic acidb. malonic acidc. succinic acid9.
Ignoring activity effects, calculate the solubility of Hg2Cl2 inthe followinga. A saturated solution of Hg2Cl2b. 0.025 M Hg2(NO3)2 saturated with Hg2Cl2c. 0.050 M NaCl saturated with Hg2Cl210. The solubility of CaF2 is controlled by the following tworeactionsCaF2(s) Ca2+(aq) + F–(aq)tHF(aq) + H2O(l)t H O (aq) +F (aq)3+–177Calculate the solubility of CaF2 in a solution buffered to a pHof 7.00. Use a ladder diagram to help simplify the calculations.How would your approach to this problem change if the pHis buffered to 2.00? What is the solubility of CaF2 at this pH?11.
Calculate the solubility of Mg(OH)2 in a solution buffered toa pH of 7.00. How does this compare with its solubility inunbuffered water?12. Calculate the solubility of Ag3PO4 in a solution buffered to apH of 9.00.13. Determine the equilibrium composition of saturated solutionof AgCl. Assume that the solubility of AgCl is influenced bythe following reactions.t Ag (aq) + Cl (aq)Ag (aq) + Cl (aq) t AgCl(aq)AgCl(aq) + Cl (aq) t AgCl (aq)+AgCl(s)+––––214. Calculate the ionic strength of the following solutionsa. 0.050 M NaClb.
0.025 M CuCl2c. 0.10 M Na2SO415. Repeat the calculations in problem 9, this time correcting foractivity effects.16. With the permission of your instructor, carry out thefollowing experiment. In a beaker, mix equal volumes of0.001 M NH4SCN and 0.001 M FeCl3 (the latter solutionmust be acidified with concentrated HNO3 at a ratio of 4drops/L to prevent the precipitation of Fe(OH)3). Dividesolution in half, and add solid KNO3 to one portion at aratio of 4 g per 100 mL. Compare the colors of the twosolutions (see Color Plate 3), and explain why they aredifferent.
The relevant reaction isFe3+(aq) + SCN–(aq)t Fe(SCN)2+(aq)17. Over what pH range do you expect Ca3(PO4)2 to have itsminimum solubility?18. Construct ladder diagrams for the following systems, anddescribe the information that can be obtained from eacha.
HF and H3PO4b. Ag(CN)2–, Ni(CN)42– and Fe(CN)64–c. Cr2O72–/Cr3+ and Fe3+/Fe2+19. Calculate the pH of the following acid–base buffersa. 100 mL of 0.025 M formic acid and 0.015 M sodiumformateb. 50.00 mL of 0.12 M NH3 and 3.50 mL of 1.0 M HClc. 5.00 g of Na2CO3 and 5.00 g of NaHCO3 in 0.100 L20. Calculate the pH of the buffers in problem 19 after adding5.0 × 10–4 mol of HCl.21. Calculate the pH of the buffers in problem 19 after adding5.0 × 10–4 mol of NaOH.22. Consider the following hypothetical complexation reactionbetween a metal, M, and a ligand, LM(aq) + L(aq)t ML(aq)1400-CH06 9/9/99 7:41 AM Page 178178Modern Analytical Chemistrywith a formation constant of 1.5 × 108. Derive an equation,similar to the Henderson–Hasselbalch equation, which relatespM to the concentrations of L and ML. What will be the pMfor a solution containing 0.010 mol of M and 0.020 mol of L?What will the pM be if 0.002 mol of M are added?23.
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