Reactions in Aqueous Solutions

CHAPTER 4 REACTIONS IN AQUEOUS SOLUTIONS Problem Categories Biological: 4.95, 4.98, 4.111, 4.135, 4.144. Conceptual: 4.7, 4.8, 4.11, 4.13, 4.17, 4.18, 4.101, 4.113, 4.115, 4.119, 4.147, 4.148. Descriptive: 4.9, 4.10, 4.12, 4.14, 4.21, 4.22, 4.23, 4.24, 4.33, 4.34, 4.43, 4.44, 4.51, 4.52, 4.53, 4.54, 4.55, 4.56, 4.99, 4.100, 4.111, 4.116, 4.117, 4.118, 4.119, 4.120, 4.121, 4.122, 4.123, 4.124, 4.125, 4.126, 4.127, 4.128, 4.129, 4.131, 4.132, 4.137, 4.139, 4.141, 4.142, 4.143, 4.145, 4.146, 4.149, 4.151, 4.153, 4.154, 4.156. Environmental: 4.80, 4.92, 4.121. Industrial: 4.137, 4.139, 4.140, 4.154. Organic: 4.96, 4.106, 4.135, 4.144. Difficulty Level Easy: 4.7, 4.8, 4.9, 4.10, 4.11, 4.12, 4.17, 4.18, 4.19, 4.20, 4.48, 4.61, 4.70, 4.71, 4.72, 4.132, 4.141, 4.143, 4.147. Medium: 4.13, 4.14, 4.21, 4.22, 4.23, 4.24, 4.31, 4.32, 4.33, 4.34, 4.43, 4.44, 4.45, 4.46, 4.47, 4.49, 4.50, 4.51, 4.52, 4.53, 4.54, 4.55, 4.56, 4.59, 4.60, 4.62, 4.63, 4.64, 4.65, 4.66, 4.69, 4.80, 4.85, 4.86, 4.87, 4.88, 4.91, 4.92, 4.93, 4.94, 4.95, 4.96, 4.99, 4.100, 4.101, 4.103, 4.104, 4.105, 4.106, 4.107, 4.113, 4.114, 4.115, 4.116, 4.117, 4.118, 4.120, 4.121, 4.122, 4.123, 4.124, 4.125, 4.127, 4.129, 4.130, 4.131, 4.133, 4.134, 4.135, 4.137, 4.138, 4.139, 4.140, 4.142, 4.145, 4.146, 4.148, 4.150, 4.153. Difficult: 4.73, 4.74, 4.77, 4.78, 4.79, 4.97, 4.98, 4.102, 4.108, 4.109, 4.110, 4.111, 4.112, 4.119, 4.126, 4.128, 4.136, 4.144, 4.149, 4.151, 4.152, 4.154, 4.155, 4.156, 4.157. 4.7 (a) is a strong electrolyte. The compound dissociates completely into ions in solution. (b) is a nonelectrolyte. The compound dissolves in water, but the molecules remain intact. (c) is a weak electrolyte. A small amount of the compound dissociates into ions in water. 4.8 When NaCl dissolves in water it dissociates into Na and Cl ions. When the ions are hydrated, the water molecules will be oriented so that the negative end of the water dipole interacts with the positive sodium ion, and the positive end of the water dipole interacts with the negative chloride ion. The negative end of the water dipole is near the oxygen atom, and the positive end of the water dipole is near the hydrogen atoms. The diagram that best represents the hydration of NaCl when dissolved in water is choice (c). 4.9 Ionic compounds, strong acids, and strong bases (metal hydroxides) are strong electrolytes (completely broken up into ions of the compound). Weak acids and weak bases are weak electrolytes. Molecular substances other than acids or bases are nonelectrolytes. + − (a) very weak electrolyte (b) strong electrolyte (ionic compound) (c) strong electrolyte (strong acid) (d) weak electrolyte (weak acid) (e) nonelectrolyte (molecular compound - neither acid nor base) 4.10 4.11 Ionic compounds, strong acids, and strong bases (metal hydroxides) are strong electrolytes (completely broken up into ions of the compound). Weak acids and weak bases are weak electrolytes. Molecular substances other than acids or bases are nonelectrolytes. (a) strong electrolyte (ionic) (b) nonelectrolyte (c) weak electrolyte (weak base) (d) strong electrolyte (strong base) Since solutions must be electrically neutral, any flow of positive species (cations) must be balanced by the flow of negative species (anions). Therefore, the correct answer is (d). CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS 4.12 81 (a) Solid NaCl does not conduct. The ions are locked in a rigid lattice structure. (b) Molten NaCl conducts. The ions can move around in the liquid state. + − (c) Aqueous NaCl conducts. NaCl dissociates completely to Na (aq) and Cl (aq) in water. 4.13 Measure the conductance to see if the solution carries an electrical current. If the solution is conducting, then you can determine whether the solution is a strong or weak electrolyte by comparing its conductance with that of a known strong electrolyte. 4.14 Since HCl dissolved in water conducts electricity, then HCl(aq) must actually exists as H (aq) cations and − Cl (aq) anions. Since HCl dissolved in benzene solvent does not conduct electricity, then we must assume that the HCl molecules in benzene solvent do not ionize, but rather exist as un-ionized molecules. 4.17 Refer to Table 4.2 of the text to solve this problem. AgCl is insoluble in water. It will precipitate from − + solution. NaNO3 is soluble in water and will remain as Na and NO3 ions in solution. Diagram (c) best represents the mixture. 4.18 Refer to Table 4.2 of the text to solve this problem. Mg(OH)2 is insoluble in water. It will precipitate from + − solution. KCl is soluble in water and will remain as K and Cl ions in solution. Diagram (b) best represents the mixture. 4.19 Refer to Table 4.2 of the text to solve this problem. + (a) (b) (c) (d) 4.20 Ca3(PO4)2 is insoluble. Mn(OH)2 is insoluble. AgClO3 is soluble. K2S is soluble. Strategy: Although it is not necessary to memorize the solubilities of compounds, you should keep in mind the following useful rules: all ionic compounds containing alkali metal cations, the ammonium ion, and the nitrate, bicarbonate, and chlorate ions are soluble. For other compounds, refer to Table 4.2 of the text. Solution: (a) CaCO3 is insoluble. Most carbonate compounds are insoluble. (b) ZnSO4 is soluble. Most sulfate compounds are soluble. (c) Hg(NO3)2 is soluble. All nitrate compounds are soluble. + 2+ 2+ 2+ (d) HgSO4 is insoluble. Most sulfate compounds are soluble, but those containing Ag , Ca , Ba , Hg , 2+ and Pb are insoluble. (e) NH4ClO4 is soluble. All ammonium compounds are soluble. 4.21 (a) + + − + 2− − → Ag2SO4(s) + 2Na (aq) + 2NO3 (aq) Ionic: 2Ag (aq) + 2NO3 (aq) + 2Na (aq) + SO4 (aq) ⎯⎯ + 2− → Ag2SO4(s) Net ionic: 2Ag (aq) + SO4 (aq) ⎯⎯ (b) − 2+ 2− 2+ − 2+ → BaSO4(s) + Zn (aq) + 2Cl (aq) Ionic: Ba (aq) + 2Cl (aq) + Zn (aq) + SO4 (aq) ⎯⎯ 2+ 2− → BaSO4(s) Net ionic: Ba (aq) + SO4 (aq) ⎯⎯ (c) + 2− 2+ − + − → CaCO3(s) + 2NH4 (aq) + 2Cl (aq) Ionic: 2NH4 (aq) + CO3 (aq) + Ca (aq) + 2Cl (aq) ⎯⎯ 2+ 2− → CaCO3(s) Net ionic: Ca (aq) + CO3 (aq) ⎯⎯ 82 CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS 4.22 (a) Strategy: Recall that an ionic equation shows dissolved ionic compounds in terms of their free ions. A net ionic equation shows only the species that actually take part in the reaction. What happens when ionic compounds dissolve in water? What ions are formed from the dissociation of Na2S and ZnCl2? What happens when the cations encounter the anions in solution? + 2− − 2+ Solution: In solution, Na2S dissociates into Na and S ions and ZnCl2 dissociates into Zn and Cl ions. 2+ 2− According to Table 4.2 of the text, zinc ions (Zn ) and sulfide ions (S ) will form an insoluble compound, zinc sulfide (ZnS), while the other product, NaCl, is soluble and remains in solution. This is a precipitation reaction. The balanced molecular equation is: → ZnS(s) + 2NaCl(aq) Na2S(aq) + ZnCl2(aq) ⎯⎯ The ionic and net ionic equations are: + 2− − 2+ + − → ZnS(s) + 2Na (aq) + 2Cl (aq) Ionic: 2Na (aq) + S (aq) + Zn (aq) + 2Cl (aq) ⎯⎯ 2+ 2− → ZnS(s) Net ionic: Zn (aq) + S (aq) ⎯⎯ Check: Note that because we balanced the molecular equation first, the net ionic equation is balanced as to the number of atoms on each side, and the number of positive and negative charges on the left-hand side of the equation is the same. (b) Strategy: What happens when ionic compounds dissolve in water? What ions are formed from the dissociation of K3PO4 and Sr(NO3)2? What happens when the cations encounter the anions in solution? + 3− 2+ Solution: In solution, K3PO4 dissociates into K and PO4 ions and Sr(NO3)2 dissociates into Sr and − 3− 2+ NO3 ions. According to Table 4.2 of the text, strontium ions (Sr ) and phosphate ions (PO4 ) will form an insoluble compound, strontium phosphate [Sr3(PO4)2], while the other product, KNO3, is soluble and remains in solution. This is a precipitation reaction. The balanced molecular equation is: → Sr3(PO4)2(s) + 6KNO3(aq) 2K3PO4(aq) + 3Sr(NO3)2(aq) ⎯⎯ The ionic and net ionic equations are: + 2+ 3− + − − → Sr3(PO4)2(s) + 6K (aq) + 6NO3 (aq) Ionic: 6K (aq) + 2PO4 (aq) + 3Sr (aq) + 6NO3 (aq) ⎯⎯ 2+ 3− → Sr3(PO4)2(s) Net ionic: 3Sr (aq) + 2PO4 (aq) ⎯⎯ Check: Note that because we balanced the molecular equation first, the net ionic equation is balanced as to the number of atoms on each side, and the number of positive and negative charges on the left-hand side of the equation is the same. (c) Strategy: What happens when ionic compounds dissolve in water? What ions are formed from the dissociation of Mg(NO3)2 and NaOH? What happens when the cations encounter the anions in solution? 2+ − + Solution: In solution, Mg(NO3)2 dissociates into Mg and NO3 ions and NaOH dissociates into Na and − 2+ − OH ions. According to Table 4.2 of the text, magnesium ions (Mg ) and hydroxide ions (OH ) will form an insoluble compound, magnesium hydroxide [Mg(OH)2], while the other product, NaNO3, is soluble and remains in solution. This is a precipitation reaction. The balanced molecular equation is: → Mg(OH)2(s) + 2NaNO3(aq) Mg(NO3)2(aq) + 2NaOH(aq) ⎯⎯ CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS 83 The ionic and net ionic equations are: − 2+ + − + − → Mg(OH)2(s) + 2Na (aq) + 2NO3 (aq) Ionic: Mg (aq) + 2NO3 (aq) + 2Na (aq) + 2OH (aq) ⎯⎯ − 2+ → Mg(OH)2(s) Net ionic: Mg (aq) + 2OH (aq) ⎯⎯ Check: Note that because we balanced the molecular equation first, the net ionic equation is balanced as to the number of atoms on each side, and the number of positive and negative charges on the left-hand side of the equation is the same. 4.23 (a) Both reactants are soluble ionic compounds. The other possible ion combinations, Na2SO4 and Cu(NO3)2, are also soluble. (b) Both reactants are soluble. Of the other two possible ion combinations, KCl is soluble, but BaSO4 is insoluble and will precipitate. 2+ 2− Ba (aq) + SO4 (aq) → BaSO4(s) 4.24 4.31 4.32 (a) Add chloride ions. KCl is soluble, but AgCl is not. (b) Add hydroxide ions. Ba(OH)2 is soluble, but Pb(OH)2 is insoluble. (c) Add carbonate ions. (NH4)2CO3 is soluble, but CaCO3 is insoluble. (d) Add sulfate ions. CuSO4 is soluble, but BaSO4 is insoluble. (a) HI dissolves in water to produce H and I , so HI is a Brønsted acid. (b) CH3COO can accept a proton to become acetic acid CH3COOH, so it is a Brønsted base. (c) H2PO4 can either accept a proton, H , to become H3PO4 and thus behaves as a Brønsted base, or can 2− + donate a proton in water to yield H and HPO4 , thus behaving as a Brønsted acid. (d) HSO4 can either accept a proton, H , to become H2SO4 and thus behaves as a Brønsted base, or can 2− + donate a proton in water to yield H and SO4 , thus behaving as a Brønsted acid. + − − − + − + Strategy: What are the characteristics of a Brønsted acid? Does it contain at least an H atom? With the exception of ammonia, most Brønsted bases that you will encounter at this stage are anions. Solution: 3− 2− (a) PO4 in water can accept a proton to become HPO4 , and is thus a Brønsted base. − (b) ClO2 in water can accept a proton to become HClO2, and is thus a Brønsted base. (c) NH4 dissolved in water can donate a proton H , thus behaving as a Brønsted acid. (d) HCO3 can either accept a proton to become H2CO3, thus behaving as a Brønsted base. Or, HCO3 2− + can donate a proton to yield H and CO3 , thus behaving as a Brønsted acid. + + − − Comment: The HCO3 species is said to be amphoteric because it possesses both acidic and basic properties. − 84 CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS 4.33 Recall that strong acids and strong bases are strong electrolytes. They are completely ionized in solution. An ionic equation will show strong acids and strong bases in terms of their free ions. A net ionic equation shows only the species that actually take part in the reaction. (a) + + − − → NH4 (aq) + Br (aq) Ionic: H (aq) + Br (aq) + NH3(aq) ⎯⎯ + + → NH4 (aq) Net ionic: H (aq) + NH3(aq) ⎯⎯ (b) − 2+ → Ba3(PO4)2(s) + 6H2O(l) Ionic: 3Ba (aq) + 6OH (aq) + 2H3PO4(aq) ⎯⎯ − 2+ → Ba3(PO4)2(s) + 6H2O(l) Net ionic: 3Ba (aq) + 6OH (aq) + 2H3PO4(aq) ⎯⎯ (c) − + − 2+ + − → 2H2O(l) Net ionic: 2H (aq) + 2OH (aq) ⎯⎯ 4.34 − 2+ → Mg (aq) + 2ClO4 (aq) + 2H2O(l) Ionic: 2H (aq) + 2ClO4 (aq) + Mg (aq) + 2OH (aq) ⎯⎯ + − → H2O(l) H (aq) + OH (aq) ⎯⎯ or Strategy: Recall that strong acids and strong bases are strong electrolytes. They are completely ionized in solution. An ionic equation will show strong acids and strong bases in terms of their free ions. Weak acids and weak bases are weak electrolytes. They only ionize to a small extent in solution. Weak acids and weak bases are shown as molecules in ionic and net ionic equations. A net ionic equation shows only the species that actually take part in the reaction. (a) Solution: CH3COOH is a weak acid. It will be shown as a molecule in the ionic equation. KOH is a + − + strong base. It completely ionizes to K and OH ions. Since CH3COOH is an acid, it donates an H to the − base, OH , producing water. The other product is the salt, CH3COOK, which is soluble and remains in solution. The balanced molecular equation is: → CH3COOK(aq) + H2O(l) CH3COOH(aq) + KOH(aq) ⎯⎯ The ionic and net ionic equations are: + − − + → CH3COO (aq) + K (aq) + H2O(l) Ionic: CH3COOH(aq) + K (aq) + OH (aq) ⎯⎯ − − → CH3COO (aq) + H2O(l) Net ionic: CH3COOH(aq) + OH (aq) ⎯⎯ (b) Solution: H2CO3 is a weak acid. It will be shown as a molecule in the ionic equation. NaOH is a strong + − + − base. It completely ionizes to Na and OH ions. Since H2CO3 is an acid, it donates an H to the base, OH , producing water. The other product is the salt, Na2CO3, which is soluble and remains in solution. The balanced molecular equation is: → Na2CO3(aq) + 2H2O(l) H2CO3(aq) + 2NaOH(aq) ⎯⎯ The ionic and net ionic equations are: + − + 2− → 2Na (aq) + CO3 (aq) + 2H2O(l) Ionic: H2CO3(aq) + 2Na (aq) + 2OH (aq) ⎯⎯ − 2− → CO3 (aq) + 2H2O(l) Net ionic: H2CO3(aq) + 2OH (aq) ⎯⎯ (c) − + Solution: HNO3 is a strong acid. It completely ionizes to H and NO3 ions. Ba(OH)2 is a strong base. It 2+ − + − completely ionizes to Ba and OH ions. Since HNO3 is an acid, it donates an H to the base, OH , producing water. The other product is the salt, Ba(NO3)2, which is soluble and remains in solution. The balanced molecular equation is: CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS 85 → Ba(NO3)2(aq) + 2H2O(l) 2HNO3(aq) + Ba(OH)2(aq) ⎯⎯ The ionic and net ionic equations are: + − − 2+ − 2+ → Ba (aq) + 2NO3 (aq) + 2H2O(l) Ionic: 2H (aq) + 2NO3 (aq) + Ba (aq) + 2OH (aq) ⎯⎯ + − → 2H2O(l) Net ionic: 2H (aq) + 2OH (aq) ⎯⎯ 4.43 + − → H2O(l) H (aq) + OH (aq) ⎯⎯ Even though the problem doesn’t ask you to assign oxidation numbers, you need to be able to do so in order to determine what is being oxidized or reduced. (i) Half Reactions 4.44 or (ii) Oxidizing Agent − 2+ (a) Sr → Sr + 2e − 2− O2 + 4e → 2O (b) Li → Li + e − − H2 + 2e → 2H (c) Cs → Cs + e − − Br2 + 2e → 2Br (d) Mg → Mg + 2e − 3− N2 + 6e → 2N + O2 Sr H2 Li Br2 Cs N2 Mg − + − 2+ (iii) Reducing Agent − Strategy: In order to break a redox reaction down into an oxidation half-reaction and a reduction halfreaction, you should first assign oxidation numbers to all the atoms in the reaction. In this way, you can determine which element is oxidized (loses electrons) and which element is reduced (gains electrons). Solution: In each part, the reducing agent is the reactant in the first half-reaction and the oxidizing agent is the reactant in the second half-reaction. The coefficients in each half-reaction have been reduced to smallest whole numbers. (a) 3+ The product is an ionic compound whose ions are Fe 3+ → Fe Fe ⎯⎯ − O2 + 4e − + 3e 2− ⎯⎯ → 2O O2 is the oxidizing agent; Fe is the reducing agent. (b) + Na does not change in this reaction. It is a “spectator ion.” 2Br − − ⎯⎯ → Br2 + 2e − Cl2 + 2e − ⎯⎯ → 2Cl − Cl2 is the oxidizing agent; Br is the reducing agent. (c) 4+ Assume SiF4 is made up of Si − and F . 4+ → Si Si ⎯⎯ − F2 + 2e − + 4e − ⎯⎯ → 2F F2 is the oxidizing agent; Si is the reducing agent. 2− and O . 86 CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS (d) + − Assume HCl is made up of H and Cl . + − → 2H + 2e H2 ⎯⎯ − Cl2 + 2e − ⎯⎯ → 2Cl Cl2 is the oxidizing agent; H2 is the reducing agent. 4.45 The oxidation number for hydrogen is +1 (rule 4), and for oxygen is −2 (rule 3). The oxidation number for sulfur in S8 is zero (rule 1). Remember that in a neutral molecule, the sum of the oxidation numbers of all the atoms must be zero, and in an ion the sum of oxidation numbers of all elements in the ion must equal the net charge of the ion (rule 6). H2S (−2), S 2− − (−2), HS (−2) < S8 (0) < SO2 (+4) < SO3 (+6), H2SO4 (+6) The number in parentheses denotes the oxidation number of sulfur. 4.46 Strategy: In general, we follow the rules listed in Section 4.4 of the text for assigning oxidation numbers. Remember that all alkali metals have an oxidation number of +1 in ionic compounds, and in most cases hydrogen has an oxidation number of +1 and oxygen has an oxidation number of −2 in their compounds. Solution: All the compounds listed are neutral compounds, so the oxidation numbers must sum to zero (Rule 6, Section 4.4 of the text). Let the oxidation number of P = x. (a) (b) (c) x + 1 + (3)(-2) = 0, x = +5 x + (3)(+1) + (2)(-2) = 0, x = +1 x + (3)(+1) + (3)(-2) = 0, x = +3 (d) (e) (f) x + (3)(+1) + (4)(-2) = 0, x = +5 2x + (4)(+1) + (7)(-2) = 0, 2x = 10, x = +5 3x + (5)(+1) + (10)(-2) = 0, 3x = 15, x = +5 The molecules in part (a), (e), and (f) can be made by strongly heating the compound in part (d). Are these oxidation-reduction reactions? Check: In each case, does the sum of the oxidation numbers of all the atoms equal the net charge on the species, in this case zero? 4.47 4.48 See Section 4.4 of the text. (a) ClF: F −1 (rule 5), Cl +1 (rule 6) (b) IF7: F −1 (rule 5), I +7 (rules 5 and 6) (c) CH4: H +1 (rule 4), C −4 (rule 6) (d) C2H2: H +1 (rule 4), C −1 (rule 6) (e) C2H4: H +1 (rule 4), C −2 (rule 6), (f) K2CrO4: K +1 (rule 2), O −2 (rule 3), Cr +6 (rule 6) (g) K2Cr2O7: K +1 (rule 2), O −2 (rule 3), Cr +6 (rule 6) (h) KMnO4: K +1 (rule 2), O −2 (rule 3), Mn +7 (rule 6) (i) NaHCO3: Na +1 (rule 2), H +1 (rule 4), O −2 (rule 3), C +4 (rule 6) (j) Li2: Li 0 (rule 1) (k) (l) KO2: K +1 (rule 2), O −1/2 (rule 6) (m) PF6 : F −1 (rule 5), P +5 (rule 6) (n) KAuCl4: K +1 (rule 2), Cl −1 (rule 5), Au +3 (rule 6) NaIO3: Na +1 (rule 2), O −2 (rule 3), I +5 (rule 6) − All are free elements, so all have an oxidation number of zero. CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS 4.49 (a) Cs2O, +1 2− (f) MoO4 , +6 − (k) SbF6 , +5 (b) CaI2, −1 2− (g) PtCl4 , +2 (c) Al2O3, +3 2− (h) PtCl6 , +4 (d) H3AsO3, +3 (i) SnF2, +2 4.50 (a) N: −3 (b) O: −1/2 (c) C: −1 (d) C: +4 (e) C: +3 (f) O: −2 (g) B: +3 (h) W: +6 87 (e) TiO2, +4 (j) ClF3, +3 4.51 If nitric acid is a strong oxidizing agent and zinc is a strong reducing agent, then zinc metal will probably reduce nitric acid when the two react; that is, N will gain electrons and the oxidation number of N must decrease. Since the oxidation number of nitrogen in nitric acid is +5 (verify!), then the nitrogen-containing product must have a smaller oxidation number for nitrogen. The only compound in the list that doesn’t have a nitrogen oxidation number less than +5 is N2O5, (what is the oxidation number of N in N2O5?). This is never a product of the reduction of nitric acid. 4.52 Strategy: Hydrogen displacement: Any metal above hydrogen in the activity series will displace it from water or from an acid. Metals below hydrogen will not react with either water or an acid. Solution: Only (b) Li and (d) Ca are above hydrogen in the activity series, so they are the only metals in this problem that will react with water. 4.53 In order to work this problem, you need to assign the oxidation numbers to all the elements in the compounds. In each case oxygen has an oxidation number of −2 (rule 3). These oxidation numbers should then be compared to the range of possible oxidation numbers that each element can have. Molecular oxygen is a powerful oxidizing agent. In SO3 alone, the oxidation number of the element bound to oxygen (S) is at its maximum value (+6); the sulfur cannot be oxidized further. The other elements bound to oxygen in this problem have less than their maximum oxidation number and can undergo further oxidation. 4.54 (a) Cu(s) + HCl(aq) → no reaction, since Cu(s) is less reactive than the hydrogen from acids. (b) I2(s) + NaBr(aq) → no reaction, since I2(s) is less reactive than Br2(l). (c) Mg(s) + CuSO4(aq) → MgSO4(aq) + Cu(s), since Mg(s) is more reactive than Cu(s). 2+ 2+ Net ionic equation: Mg(s) + Cu (aq) → Mg (aq) + Cu(s) (d) Cl2(g) + 2KBr(aq) → Br2(l) + 2KCl(aq), since Cl2(g) is more reactive than Br2(l) − − Net ionic equation: Cl2(g) + 2Br (aq) → 2Cl (aq) + Br2(l) 4.55 (a) (c) Disproportionation reaction Decomposition reaction (b) (d) Displacement reaction Combination reaction 4.56 (a) (c) Combination reaction Displacement reaction (b) (d) Decomposition reaction Disproportionation reaction 4.59 First, calculate the moles of KI needed to prepare the solution. mol KI = 2.80 mol KI × (5.00 × 102 mL soln) = 1.40 mol KI 1000 mL soln Converting to grams of KI: 1.40 mol KI × 166.0 g KI = 232 g KI 1 mol KI 88 CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS 4.60 Strategy: How many moles of NaNO3 does 250 mL of a 0.707 M solution contain? How would you convert moles to grams? Solution: From the molarity (0.707 M), we can calculate the moles of NaNO3 needed to prepare 250 mL of solution. 0.707 mol NaNO3 Moles NaNO3 = × 250 mL soln = 0.1768 mol 1000 mL soln Next, we use the molar mass of NaNO3 as a conversion factor to convert from moles to grams. M (NaNO3) = 85.00 g/mol. 0.1768 mol NaNO3 × 85.00 g NaNO3 = 15.0 g NaNO3 1 mol NaNO3 To make the solution, dissolve 15.0 g of NaNO3 in enough water to make 250 mL of solution. Check: As a ball-park estimate, the mass should be given by [molarity (mol/L) × volume (L) = moles × molar mass (g/mol) = grams]. Let's round the molarity to 1 M and the molar mass to 80 g, because we are simply making an estimate. This gives: [1 mol/L × (1/4)L × 80 g = 20 g]. This is close to our answer of 15.0 g. 4.61 mol = M × L 60.0 mL = 0.0600 L mol MgCl 2 = 4.62 0.100 mol MgCl2 × 0.0600 L soln = 6.00 × 10−3 mol MgCl 2 1 L soln Since the problem asks for grams of solute (KOH), you should be thinking that you can calculate moles of solute from the molarity and volume of solution. Then, you can convert moles of solute to grams of solute. ? moles KOH solute = 5.50 moles solute × 35.0 mL solution = 0.1925 mol KOH 1000 mL solution The molar mass of KOH is 56.11 g/mol. Use this conversion factor to calculate grams of KOH. ? grams KOH = 0.1925 mol KOH × 4.63 56.108 g KOH = 10.8 g KOH 1 mol KOH Molar mass of C2H5OH = 46.068 g/mol; molar mass of C12H22O11 = 342.3 g/mol; molar mass of NaCl = 58.44 g/mol. (a) ? mol C2 H5 OH = 29.0 g C2 H5 OH × Molarity = (b) 1 mol C2 H5 OH = 0.6295 mol C2 H5OH 46.068 g C2 H5 OH 0.6295 mol C2 H5 OH mol solute = = 1.16 M L of soln 0.545 L soln ? mol C12 H 22 O11 = 15.4 g C12 H 22 O11 × Molarity = 1 mol C12 H 22 O11 = 0.04499 mol C12 H 22 O11 342.3 g C12 H 22 O11 0.04499 mol C12 H 22 O11 mol solute = = 0.608 M L of soln 74.0 × 10−3 L soln CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS (c) ? mol NaCl = 9.00 g NaCl × Molarity = 4.64 (a) (b) 1 mol CaCl2 = 0.09371 mol CaCl2 110.98 g CaCl2 0.09371 mol CaCl2 = 0.426 M 0.220 L 1 mol C10 H8 = 0.06102 mol C10 H8 128.16 g C10 H8 0.06102 mol C10 H8 = 0.716 M 0.0852 L First, calculate the moles of each solute. Then, you can calculate the volume (in L) from the molarity and the number of moles of solute. (a) ? mol NaCl = 2.14 g NaCl × L soln = (b) (c) 1 mol NaCl = 0.03662 mol NaCl 58.44 g NaCl mol solute 0.03662 mol NaCl = = 0.136 L = 136 mL soln Molarity 0.270 mol/L ? mol C2 H5 OH = 4.30 g C2 H5OH × L soln = 1 mol C2 H5 OH = 0.09334 mol C2 H5OH 46.068 g C 2 H5OH 0.09334 mol C2 H5 OH mol solute = = 0.0622 L = 62.2 mL soln Molarity 1.50 mol/L ? mol CH3COOH = 0.85 g CH3COOH × L soln = 4.66 1 mol CH3OH = 0.205 mol CH3OH 32.042 g CH3OH 0.205 mol CH3OH = 1.37 M 0.150 L ? mol C10 H8 = 7.82 g C10 H8 × M = 4.65 mol solute 0.154 mol NaCl = = 1.78 M L of soln 86.4 × 10−3 L soln ? mol CaCl2 = 10.4 g CaCl2 × M = (c) 1 mol NaCl = 0.154 mol NaCl 58.44 g NaCl ? mol CH3OH = 6.57 g CH3OH × M = 89 1 mol CH3COOH = 0.0142 mol CH3COOH 60.052 g CH3COOH 0.0142 mol CH3COOH mol solute = = 0.047 L = 47 mL soln Molarity 0.30 mol/L A 250 mL sample of 0.100 M solution contains 0.0250 mol of solute (mol = M × L). The computation in each case is the same: (a) 0.0250 mol CsI × 259.8 g CsI = 6.50 g CsI 1 mol CsI 90 CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS 0.0250 mol H 2SO 4 × (c) 0.0250 mol Na 2 CO3 × (d) 0.0250 mol K 2 Cr2 O7 × (e) 0.0250 mol KMnO 4 × 4.69 98.086 g H 2SO 4 = 2.45 g H 2 SO4 1 mol H 2SO 4 (b) 105.99 g Na 2 CO3 = 2.65 g Na 2CO 3 1 mol Na 2 CO3 294.2 g K 2 Cr2 O7 = 7.36 g K 2 Cr2 O7 1 mol K 2 Cr2 O7 158.04 g KMnO 4 = 3.95 g KMnO4 1 mol KMnO4 MinitialVinitial = MfinalVfinal You can solve the equation algebraically for Vinitial. Then substitute in the given quantities to solve for the volume of 2.00 M HCl needed to prepare 1.00 L of a 0.646 M HCl solution. Vinitial = M final × Vfinal 0.646 M × 1.00 L = = 0.323 L = 323 mL 2.00 M M initial To prepare the 0.646 M solution, you would dilute 323 mL of the 2.00 M HCl solution to a final volume of 1.00 L. 4.70 Strategy: Because the volume of the final solution is greater than the original solution, this is a dilution process. Keep in mind that in a dilution, the concentration of the solution decreases, but the number of moles of the solute remains the same. Solution: We prepare for the calculation by tabulating our data. Mi = 0.866 M Mf = ? Vi = 25.0 mL Vf = 500 mL We substitute the data into Equation (4.3) of the text. MiVi = MfVf (0.866 M)(25.0 mL) = Mf(500 mL) Mf = 4.71 (0.866 M )(25.0 mL) = 0.0433 M 500 mL MinitialVinitial = MfinalVfinal You can solve the equation algebraically for Vinitial. Then substitute in the given quantities to solve the for the volume of 4.00 M HNO3 needed to prepare 60.0 mL of a 0.200 M HNO3 solution. Vinitial = M final × Vfinal 0.200 M × 60.00 mL = = 3.00 mL 4.00 M M initial To prepare the 0.200 M solution, you would dilute 3.00 mL of the 4.00 M HNO3 solution to a final volume of 60.0 mL. CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS 4.72 91 You need to calculate the final volume of the dilute solution. Then, you can subtract 505 mL from this volume to calculate the amount of water that should be added. Vfinal = ( 0.125 M )( 505 mL ) M initialVinitial = = 631 mL M final ( 0.100 M ) (631 − 505) mL = 126 mL of water 4.73 Moles of KMnO4 in the first solution: 1.66 mol × 35.2 mL = 0.05843 mol KMnO4 1000 mL soln Moles of KMnO4 in the second solution: 0.892 mol × 16.7 mL = 0.01490 mol KMnO 4 1000 mL soln The total volume is 35.2 mL + 16.7 mL = 51.9 mL. The concentration of the final solution is: M = 4.74 ( 0.05843 + 0.01490) mol 51.9 × 10−3 L = 1.41 M Moles of calcium nitrate in the first solution: 0.568 mol × 46.2 mL soln = 0.02624 mol Ca(NO3 )2 1000 mL soln Moles of calcium nitrate in the second solution: 1.396 mol × 80.5 mL soln = 0.1124 mol Ca(NO3 ) 2 1000 mL soln The volume of the combined solutions = 46.2 mL + 80.5 mL = 126.7 mL. The concentration of the final solution is: (0.02624 + 0.1124) mol M = = 1.09 M 0.1267 L 4.77 → Ca(NO3)2(aq) + 2AgCl(s) The balanced equation is: CaCl2(aq) + 2AgNO3(aq) ⎯⎯ + − We need to determine the limiting reagent. Ag and Cl combine in a 1:1 mole ratio to produce AgCl. Let’s + − calculate the amount of Ag and Cl in solution. mol Ag + = mol Cl− = + 0.100 mol Ag + × 15.0 mL soln = 1.50 × 10−3 mol Ag + 1000 mL soln 0.150 mol CaCl2 2 mol Cl− × × 30.0 mL soln = 9.00 × 10−3 mol Cl− 1000 mL soln 1 mol CaCl2 − Since Ag and Cl combine in a 1:1 mole ratio, AgNO3 is the limiting reagent. Only 1.50 × 10 AgCl can form. Converting to grams of AgCl: 1.50 × 10−3 mol AgCl × 143.35 g AgCl = 0.215 g AgCl 1 mol AgCl −3 mole of 92 CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS 4.78 Strategy: We want to calculate the mass % of Ba in the original compound. Let's start with the definition of mass %. need to find want to calculate mass % Ba = mass Ba × 100% mass of sample given The mass of the sample is given in the problem (0.6760 g). Therefore we need to find the mass of Ba in the original sample. We assume the precipitation is quantitative, that is, that all of the barium in the sample has been precipitated as barium sulfate. From the mass of BaSO4 produced, we can calculate the mass of Ba. There is 1 mole of Ba in 1 mole of BaSO4. Solution: First, we calculate the mass of Ba in 0.4105 g of the BaSO4 precipitate. The molar mass of BaSO4 is 233.4 g/mol. ? mass of Ba = 0.4105 g BaSO 4 × 1 mol BaSO 4 1 mol Ba 137.3 g Ba × × 233.37 g BaSO 4 1 mol BaSO 4 1 mol Ba = 0.24151 g Ba Next, we calculate the mass percent of Ba in the unknown compound. %Ba by mass = 4.79 0.24151 g × 100% = 35.73% 0.6760 g + − → AgCl(s) The net ionic equation is: Ag (aq) + Cl (aq) ⎯⎯ − + + One mole of Cl is required per mole of Ag . First, find the number of moles of Ag . mol Ag + = 0.0113 mol Ag + × (2.50 × 102 mL soln) = 2.825 × 10−3 mol Ag + 1000 mL soln Now, calculate the mass of NaCl using the mole ratio from the balanced equation. 1 mol Cl− (2.825 × 10−3 mol Ag + ) × 1 mol Ag 4.80 The net ionic equation is: 2+ + × 1 mol NaCl 1 mol Cl − 58.44 g NaCl = 0.165 g NaCl 1 mol NaCl × 2− → CuS(s) Cu (aq) + S (aq) ⎯⎯ 2+ 2+ The answer sought is the molar concentration of Cu , that is, moles of Cu dimensional analysis method is used to convert, in order: g of CuS → moles CuS → moles Cu [Cu 2+ ] = 0.0177 g CuS × 2+ 2+ → moles Cu ions per liter of solution. The per liter soln 1 mol CuS 1 mol Cu 2+ 1 × × = 2.31 × 10−4 M 95.62 g CuS 1 mol CuS 0.800 L CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS 4.85 93 The reaction between KHP (KHC8H4O4) and KOH is: KHC8H4O4(aq) + KOH(aq) → H2O(l) + K2C8H4O4(aq) We know the volume of the KOH solution, and we want to calculate the molarity of the KOH solution. want to calculate M of KOH = need to find mol KOH L of KOH soln given If we can determine the moles of KOH in the solution, we can then calculate the molarity of the solution. From the mass of KHP and its molar mass, we can calculate moles of KHP. Then, using the mole ratio from the balanced equation, we can calculate moles of KOH. 1 mol KHP 1 mol KOH × = 2.0654 × 10−3 mol KOH 204.22 g KHP 1 mol KHP ? mol KOH = 0.4218 g KHP × From the moles and volume of KOH, we calculate the molarity of the KOH solution. M of KOH = 4.86 mol KOH 2.0654 × 10−3 mol KOH = = 0.1106 M L of KOH soln 18.68 × 10−3 L soln The reaction between HCl and NaOH is: HCl(aq) + NaOH(aq) → H2O(l) + NaCl(aq) We know the volume of the NaOH solution, and we want to calculate the molarity of the NaOH solution. want to calculate M of NaOH = need to find mol NaOH L of NaOH soln given If we can determine the moles of NaOH in the solution, we can then calculate the molarity of the solution. From the volume and molarity of HCl, we can calculate moles of HCl. Then, using the mole ratio from the balanced equation, we can calculate moles of NaOH. ? mol NaOH = 17.4 mL HCl × 0.312 mol HCl 1 mol NaOH × = 5.429 × 10−3 mol NaOH 1000 mL soln 1 mol HCl From the moles and volume of NaOH, we calculate the molarity of the NaOH solution. M of NaOH = mol NaOH 5.429 × 10−3 mol NaOH = = 0.217 M L of NaOH soln 25.0 × 10−3 L soln 94 CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS 4.87 (a) In order to have the correct mole ratio to solve the problem, you must start with a balanced chemical equation. → NaCl(aq) + H2O(l) HCl(aq) + NaOH(aq) ⎯⎯ From the molarity and volume of the HCl solution, you can calculate moles of HCl. Then, using the mole ratio from the balanced equation above, you can calculate moles of NaOH. ? mol NaOH = 25.00 mL × 2.430 mol HCl 1 mol NaOH × = 6.075 × 10−2 mol NaOH 1000 mL soln 1 mol HCl Solving for the volume of NaOH: moles of solute M liters of solution = volume of NaOH = (b) 6.075 × 10−2 mol NaOH = 4.278 × 10−2 L = 42.78 mL 1.420 mol/L This problem is similar to part (a). The difference is that the mole ratio between base and acid is 2:1. → Na2SO4(aq) + H2O(l) H2SO4(aq) + 2NaOH(aq) ⎯⎯ ? mol NaOH = 25.00 mL × volume of NaOH = (c) 4.500 mol H 2SO4 2 mol NaOH × = 0.2250 mol NaOH 1000 mL soln 1 mol H 2SO4 0.2250 mol NaOH = 0.1585 L = 158.5 mL 1.420 mol/L This problem is similar to parts (a) and (b). The difference is that the mole ratio between base and acid is 3:1. → Na3PO4(aq) + 3H2O(l) H3PO4(aq) + 3NaOH(aq) ⎯⎯ ? mol NaOH = 25.00 mL × volume of NaOH = 4.88 1.500 mol H3 PO 4 3 mol NaOH × = 0.1125 mol NaOH 1000 mL soln 1 mol H3 PO4 0.1125 mol NaOH = 0.07923 L = 79.23 mL 1.420 mol/L Strategy: We know the molarity of the HCl solution, and we want to calculate the volume of the HCl solution. given M of HCl = need to find mol HCl L of HCl soln want to calculate If we can determine the moles of HCl, we can then use the definition of molarity to calculate the volume of HCl needed. From the volume and molarity of NaOH or Ba(OH)2, we can calculate moles of NaOH or Ba(OH)2. Then, using the mole ratio from the balanced equation, we can calculate moles of HCl. CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS 95 Solution: (a) In order to have the correct mole ratio to solve the problem, you must start with a balanced chemical equation. → NaCl(aq) + H2O(l) HCl(aq) + NaOH(aq) ⎯⎯ ? mol HCl = 10.0 mL × 0.300 mol NaOH 1 mol HCl × = 3.00 × 10−3 mol HCl 1000 mL of solution 1 mol NaOH From the molarity and moles of HCl, we calculate volume of HCl required to neutralize the NaOH. (b) liters of solution = moles of solute M volume of HCl = 3.00 × 10−3 mol HCl = 6.00 × 10−3 L = 6.00 mL 0.500 mol/L This problem is similar to part (a). The difference is that the mole ratio between acid and base is 2:1. → BaCl2(aq) +2H2O(l) 2HCl(aq) + Ba(OH)2(aq) ⎯⎯ ? mol HCl = 10.0 mL × 4.00 × 10−3 mol HCl = 8.00 × 10−3 L = 8.00 mL 0.500 mol/L volume of HCl = 4.91 2+ The balanced equation is given in the problem. The mole ratio between Fe First, calculate the moles of Fe 26.00 mL soln × 2+ 2+ M = 2− and Cr2O7 is 6:1. 2− that react with Cr2O7 . 0.0250 mol Cr2 O72− 6 mol Fe2+ × = 3.90 × 10−3 mol Fe2+ 1000 mL soln 1 mol Cr2 O72− The molar concentration of Fe 4.92 0.200 mol Ba(OH)2 2 mol HCl × = 4.00 × 10−3 mol HCl 1000 mL of solution 1 mol Ba(OH)2 is: 3.90 × 10−3 mol Fe2+ 25.0 × 10−3 L soln = 0.156 M Strategy: We want to calculate the grams of SO2 in the sample of air. From the molarity and volume of KMnO4, we can calculate moles of KMnO4. Then, using the mole ratio from the balanced equation, we can calculate moles of SO2. How do we convert from moles of SO2 to grams of SO2? Solution: The balanced equation is given in the problem. − 2− → 5SO4 5SO2 + 2MnO4 + 2H2O ⎯⎯ + 2Mn 2+ + + 4H The moles of KMnO4 required for the titration are: 0.00800 mol KMnO 4 × 7.37 mL = 5.896 × 10−5 mol KMnO4 1000 mL soln 96 CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS We use the mole ratio from the balanced equation and the molar mass of SO2 as conversion factors to convert to grams of SO2. (5.896 × 10−5 mol KMnO4 ) × 4.93 5 mol SO 2 64.07 g SO2 × = 9.44 × 10−3 g SO 2 2 mol KMnO4 1 mol SO 2 2+ The balanced equation is given in Problem 4.91. The mole ratio between Fe First, calculate the moles of Cr2O7 23.30 mL soln × 2− and Cr2O7 2− is 6:1. that reacted. 0.0194 mol Cr2 O72− = 4.52 × 10−4 mol Cr2 O72− 1000 mL soln Use the mole ratio from the balanced equation to calculate the mass of iron that reacted. (4.52 × 10−4 mol Cr2 O72− ) × 6 mol Fe2+ 1 mol Cr2 O72− × 55.85 g Fe 2+ 1 mol Fe 2+ = 0.1515 g Fe 2+ The percent by mass of iron in the ore is: 0.1515 g × 100% = 54.3% 0.2792 g 4.94 The balanced equation is given in the problem. − + 2MnO4 + 5H2O2 + 6H ⎯⎯ → 5O2 + 2Mn 2+ + 8H2O First, calculate the moles of potassium permanganate in 36.44 mL of solution. 0.01652 mol KMnO 4 × 36.44 mL = 6.0199 × 10−4 mol KMnO4 1000 mL soln Next, calculate the moles of hydrogen peroxide using the mole ratio from the balanced equation. (6.0199 × 10−4 mol KMnO 4 ) × 5 mol H 2 O 2 = 1.505 × 10−3 mol H 2 O 2 2 mol KMnO 4 Finally, calculate the molarity of the H2O2 solution. The volume of the solution is 0.02500 L. Molarity of H 2O2 = 4.95 1.505 × 10−3 mol H2 O2 = 0.06020 M 0.02500 L First, calculate the moles of KMnO4 in 24.0 mL of solution. 0.0100 mol KMnO4 × 24.0 mL = 2.40 × 10−4 mol KMnO 4 1000 mL soln Next, calculate the mass of oxalic acid needed to react with 2.40 × 10 from the balanced equation. (2.40 × 10−4 mol KMnO4 ) × −4 mol KMnO4. Use the mole ratio 5 mol H 2 C2 O 4 90.036 g H 2 C2 O4 × = 0.05402 g H 2 C 2 O 4 2 mol KMnO 4 1 mol H 2 C2 O 4 CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS 97 The original sample had a mass of 1.00 g. The mass percent of H2C2O4 in the sample is: mass % = 4.96 0.05402 g × 100% = 5.40% H 2C2O4 1.00 g From the reaction of oxalic acid with NaOH, the moles of oxalic acid in 15.0 mL of solution can be determined. Then, using this number of moles and other information given, the volume of the KMnO4 solution needed to react with a second sample of oxalic acid can be calculated. First, calculate the moles of oxalic acid in the solution. H2C2O4(aq) + 2NaOH(aq) → Na2C2O4(aq) + 2H2O(l) 0.0252 L × 0.149 mol NaOH 1 mol H 2 C2 O 4 × = 1.877 × 10−3 mol H 2 C2 O 4 1 L soln 2 mol NaOH Because we are reacting a second sample of equal volume (15.0 mL), the moles of oxalic acid will also be −3 1.877 × 10 mole in this second sample. The balanced equation for the reaction between oxalic acid and KMnO4 is: + − 2− 2MnO4 + 16H + 5C2O4 2+ → 2Mn + 10CO2 + 8H2O Let’s calculate the moles of KMnO4 first, and then we will determine the volume of KMnO4 needed to react with the 15.0 mL sample of oxalic acid. (1.877 × 10−3 mol H 2 C2 O 4 ) × 2 mol KMnO4 = 7.508 × 10−4 mol KMnO 4 5 mol H 2 C2 O4 Using Equation (4.2) of the text: M = n V VKMnO4 = 4.97 7.508 × 10−4 mol n = = 0.00615 L = 6.15 mL M 0.122 mol/L 2− The balanced equation shows that 2 moles of electrons are lost for each mole of SO3 that reacts. The − − electrons are gained by IO3 . We need to find the moles of electrons gained for each mole of IO3 that reacts. Then, we can calculate the final oxidation state of iodine. The number of moles of electrons lost by SO3 32.5 mL × 2− is: 0.500 mol SO32− 2 mol e− × = 0.0325 mol e− lost 1000 mL soln 1 mol SO32− − The number of moles of iodate, IO3 , that react is: 1.390 g KIO3 × 1 mol KIO3 1 mol IO3− × = 6.4953 × 10−3 mol IO3− 214.0 g KIO3 1 mol KIO3 98 CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS −3 − 6.4953 × 10 mole of IO3 gain 0.0325 mole of electrons. The number of moles of electrons gained per − mole of IO3 is: 0.0325 mol e − 6.4953 × 10−3 mol IO3− = 5.00 mol e − /mol IO3− − − The oxidation number of iodine in IO3 is +5. Since 5 moles of electrons are gained per mole of IO3 , the final oxidation state of iodine is +5 − 5 = 0. The iodine containing product of the reaction is most likely elemental iodine, I2. 4.98 The balanced equation is: − + 2− 2MnO4 + 16H + 5C2O4 mol MnO4− = ⎯⎯ → 2Mn 2+ + 10CO2 + 8H2O 9.56 × 10−4 mol MnO4− × 24.2 mL = 2.314 × 10−5 mol MnO4− 1000 mL of soln 2+ Using the mole ratio from the balanced equation, we can calculate the mass of Ca blood. (2.314 × 10−5 mol MnO4− ) × 5 mol C2 O24− 2 mol MnO4− × 1 mol Ca 2+ 1 mol C2 O42− × 40.08 g Ca 2+ 1 mol Ca 2+ in the 10.0 mL sample of = 2.319 × 10−3 g Ca 2+ Converting to mg/mL: 2.319 × 10−3 g Ca 2+ 1 mg × = 0.232 mg Ca 2+ /mL of blood 10.0 mL of blood 0.001 g 4.99 In redox reactions the oxidation numbers of elements change. To test whether an equation represents a redox process, assign the oxidation numbers to each of the elements in the reactants and products. If oxidation numbers change, it is a redox reaction. − (a) On the left the oxidation number of chlorine in Cl2 is zero (rule 1). On the right it is −1 in Cl (rule 2) − and +1 in OCl (rules 3 and 5). Since chlorine is both oxidized and reduced, this is a disproportionation redox reaction. (b) The oxidation numbers of calcium and carbon do not change. This is not a redox reaction; it is a precipitation reaction. (c) The oxidation numbers of nitrogen and hydrogen do not change. This is not a redox reaction; it is an acid-base reaction. (d) The oxidation numbers of carbon, chlorine, chromium, and oxygen do not change. This is not a redox reaction; it doesn’t fit easily into any category, but could be considered as a type of combination reaction. (e) The oxidation number of calcium changes from 0 to +2, and the oxidation number of fluorine changes from 0 to −1. This is a combination redox reaction. (f) Redox (k) The oxidation numbers of lithium, oxygen, hydrogen, and nitrogen do not change. This is not a redox reaction; it is an acid-base reaction between the base, LiOH, and the acid, HNO3. (g) Precipitation (h) Redox (i) Redox (j) Redox CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS 99 4.100 First, the gases could be tested to see if they supported combustion. O2 would support combustion, CO2 would not. Second, if CO2 is bubbled through a solution of calcium hydroxide [Ca(OH)2], a white precipitate of CaCO3 forms. No reaction occurs when O2 is bubbled through a calcium hydroxide solution. 4.101 Choice (d), 0.20 M Mg(NO3)2, should be the best conductor of electricity; the total ion concentration in this solution is 0.60 M. The total ion concentrations for solutions (a) and (c) are 0.40 M and 0.50 M, respectively. We can rule out choice (b), because acetic acid is a weak electrolyte. 4.102 Starting with a balanced chemical equation: → MgCl2(aq) + H2(g) Mg(s) + 2HCl(aq) ⎯⎯ From the mass of Mg, you can calculate moles of Mg. Then, using the mole ratio from the balanced equation above, you can calculate moles of HCl reacted. 4.47 g Mg × 1 mol Mg 2 mol HCl × = 0.3677 mol HCl reacted 24.31 g Mg 1 mol Mg Next we can calculate the number of moles of HCl in the original solution. 2.00 mol HCl × (5.00 × 102 mL) = 1.00 mol HCl 1000 mL soln Moles HCl remaining = 1.00 mol − 0.3677 mol = 0.6323 mol HCl conc. of HCl after reaction = 4.103 mol HCl 0.6323 mol HCl = = 1.26 mol/L = 1.26 M L soln 0.500 L The balanced equation for the displacement reaction is: → ZnSO4(aq) + Cu(s) Zn(s) + CuSO4(aq) ⎯⎯ The moles of CuSO4 that react with 7.89 g of zinc are: 7.89 g Zn × 1 mol CuSO4 1 mol Zn × = 0.1207 mol CuSO 4 65.39 g Zn 1 mol Zn The volume of the 0.156 M CuSO4 solution needed to react with 7.89 g Zn is: L of soln = 0.1207 mol CuSO4 mole solute = = 0.774 L = 774 mL M 0.156 mol/L 2+ Would you expect Zn to displace Cu 4.104 from solution, as shown in the equation? The balanced equation is: → CO2(g) + H2O(l) + 2NaCl(aq) 2HCl(aq) + Na2CO3(s) ⎯⎯ The mole ratio from the balanced equation is 2 moles HCl : 1 mole Na2CO3. The moles of HCl needed to react with 0.256 g of Na2CO3 are: 0.256 g Na 2 CO3 × 1 mol Na 2 CO3 2 mol HCl × = 4.831 × 10−3 mol HCl 105.99 g Na 2 CO3 1 mol Na 2 CO3 100 CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS Molarity HCl = 4.105 moles HCl 4.831 × 10−3 mol HCl = = 0.171 mol/L = 0.171 M L soln 0.0283 L soln → NaA(aq) + H2O(l) The neutralization reaction is: HA(aq) + NaOH(aq) ⎯⎯ The mole ratio between the acid and NaOH is 1:1. The moles of HA that react with NaOH are: 20.27 mL soln × 0.1578 mol NaOH 1 mol HA × = 3.1986 × 10−3 mol HA 1000 mL soln 1 mol NaOH 3.664 g of the acid reacted with the base. The molar mass of the acid is: Molar mass = 4.106 3.664 g HA 3.1986 × 10−3 mol HA = 1146 g/mol Starting with a balanced chemical equation: → CH3COONa(aq) + H2O(l) CH3COOH(aq) + NaOH(aq) ⎯⎯ From the molarity and volume of the NaOH solution, you can calculate moles of NaOH. Then, using the mole ratio from the balanced equation above, you can calculate moles of CH3COOH. 5.75 mL solution × 1 mol CH3COOH 1.00 mol NaOH × = 5.75 × 10−3 mol CH3COOH 1000 mL of solution 1 mol NaOH Molarity CH 3COOH = 4.107 5.75 × 10−3 mol CH3COOH = 0.115 M 0.0500 L Let’s call the original solution, soln 1; the first dilution, soln 2; and the second dilution, soln 3. Start with the concentration of soln 3, 0.00383 M. From the concentration and volume of soln 3, we can find the concentration of soln 2. Then, from the concentration and volume of soln 2, we can find the concentration of soln 1, the original solution. M2V2 = M3V3 M2 = M 3V3 (0.00383 M )(1.000 × 103 mL) = = 0.1532 M 25.00 mL V2 M1 = M 2V2 (0.1532 M )(125.0 mL) = = 1.28 M 15.00 mL V1 M1V1 = M2V2 4.108 The balanced equation is: → Zn(NO3)2(aq) + 2Ag(s) Zn(s) + 2AgNO3(aq) ⎯⎯ Let x = mass of Ag produced. We can find the mass of Zn reacted in terms of the amount of Ag produced. x g Ag × 1 mol Ag 1 mol Zn 65.39 g Zn × × = 0.303 x g Zn reacted 107.9 g Ag 2 mol Ag 1 mol Zn The mass of Zn remaining will be: 2.50 g − amount of Zn reacted = 2.50 g Zn − 0.303x g Zn CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS 101 The final mass of the strip, 3.37 g, equals the mass of Ag produced + the mass of Zn remaining. 3.37 g = x g Ag + (2.50 g Zn − 0.303 x g Zn) x = 1.25 g = mass of Ag produced mass of Zn remaining = 3.37 g − 1.25 g = 2.12 g Zn or mass of Zn remaining = 2.50 g Zn − 0.303x g Zn = 2.50 g − (0.303)(1.25 g) = 2.12 g Zn 4.109 → BaSO4(s) + 2NaOH(aq) The balanced equation is: Ba(OH)2(aq) + Na2SO4(aq) ⎯⎯ moles Ba(OH)2: (2.27 L)(0.0820 mol/L) = 0.1861 mol Ba(OH)2 moles Na2SO4: (3.06 L)(0.0664 mol/L) = 0.2032 mol Na2SO4 Since the mole ratio between Ba(OH)2 and Na2SO4 is 1:1, Ba(OH)2 is the limiting reagent. The mass of BaSO4 formed is: 1 mol BaSO 4 233.37 g BaSO4 0.1861 mol Ba(OH)2 × × = 43.4 g BaSO4 1 mol Ba(OH)2 mol BaSO 4 4.110 → NaNO3(aq) + H2O(l) The balanced equation is: HNO3(aq) + NaOH(aq) ⎯⎯ mol HNO3 = 0.211 mol HNO3 × 10.7 mL soln = 2.258 × 10−3 mol HNO3 1000 mL soln mol NaOH = 0.258 mol NaOH × 16.3 mL soln = 4.205 × 10−3 mol NaOH 1000 mL soln Since the mole ratio from the balanced equation is 1 mole NaOH : 1 mole HNO3, then 2.258 × 10 −3 HNO3 will react with 2.258 × 10 mol NaOH. mol NaOH remaining = (4.205 × 10 −3 mol) − (2.258 × 10 −3 mol) = 1.947 × 10 −3 −3 mol mol NaOH 10.7 mL + 16.3 mL = 27.0 mL = 0.0270 L molarity NaOH = 4.111 (a) 1.947 × 10−3 mol NaOH = 0.0721 M 0.0270 L 2+ Magnesium hydroxide is insoluble in water. It can be prepared by mixing a solution containing Mg ions such as MgCl2(aq) or Mg(NO3)2(aq) with a solution containing hydroxide ions such as NaOH(aq). Mg(OH)2 will precipitate, which can then be collected by filtration. The net ionic reaction is: 2+ − Mg (aq) + 2OH (aq) → Mg(OH)2(s) (b) The balanced equation is: → MgCl2 + 2H2O 2HCl + Mg(OH)2 ⎯⎯ The moles of Mg(OH)2 in 10 mL of milk of magnesia are: 10 mL soln × 0.080 g Mg(OH) 2 1 mol Mg(OH)2 × = 0.0137 mol Mg(OH)2 1 mL soln 58.326 g Mg(OH)2 102 CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS Moles of HCl reacted = 0.0137 mol Mg(OH) 2 × Volume of HCl = 4.112 2 mol HCl = 0.0274 mol HCl 1 mol Mg(OH) 2 mol solute 0.0274 mol HCl = = 0.78 L M 0.035 mol/L The balanced equations for the two reactions are: → XSO4(aq) + H2(g) X(s) + H2SO4(aq) ⎯⎯ → Na2SO4(aq) + 2H2O(l) H2SO4(aq) + 2NaOH(aq) ⎯⎯ First, let’s find the number of moles of excess acid from the reaction with NaOH. 0.0334 L × 0.500 mol NaOH 1 mol H 2SO4 × = 8.35 × 10−3 mol H 2SO4 1 L soln 2 mol NaOH The original number of moles of acid was: 0.100 L × 0.500 mol H 2SO4 = 0.0500 mol H 2SO4 1 L soln The amount of sulfuric acid that reacted with the metal, X, is (0.0500 mol H2SO4) − (8.35 × 10 −3 mol H2SO4) = 0.04165 mol H2SO4. Since the mole ratio from the balanced equation is 1 mole X : 1 mole H2SO4, then the amount of X that reacted is 0.04165 mol X. molar mass X = 1.00 g X = 24.0 g/mol 0.04165 mol X The element is magnesium. 4.113 Add a known quantity of compound in a given quantity of water. Filter and recover the undissolved compound, then dry and weigh it. The difference in mass between the original quantity and the recovered quantity is the amount that dissolved in the water. 4.114 First, calculate the number of moles of glucose present. 0.513 mol glucose × 60.0 mL = 0.03078 mol glucose 1000 mL soln 2.33 mol glucose × 120.0 mL = 0.2796 mol glucose 1000 mL soln Add the moles of glucose, then divide by the total volume of the combined solutions to calculate the molarity. 60.0 mL + 120.0 mL = 180.0 mL = 0.180 L Molarity of final solution = 4.115 (0.03078 + 0.2796) mol glucose = 1.72 mol/L = 1.72 M 0.180 L First, you would accurately measure the electrical conductance of pure water. The conductance of a solution of the slightly soluble ionic compound X should be greater than that of pure water. The increased conductance would indicate that some of the compound X had dissolved. CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS 103 4.116 Iron(II) compounds can be oxidized to iron(III) compounds. The sample could be tested with a small amount of a strongly colored oxidizing agent like a KMnO4 solution, which is a deep purple color. A loss of color would imply the presence of an oxidizable substance like an iron(II) salt. 4.117 The three chemical tests might include: (1) (2) (3) 4.118 Electrolysis to ascertain if hydrogen and oxygen were produced, The reaction with an alkali metal to see if a base and hydrogen gas were produced, and The dissolution of a metal oxide to see if a base was produced (or a nonmetal oxide to see if an acid was produced). Since both of the original solutions were strong electrolytes, you would expect a mixture of the two solutions to also be a strong electrolyte. However, since the light dims, the mixture must contain fewer ions than the + − original solution. Indeed, H from the sulfuric acid reacts with the OH from the barium hydroxide to form water. The barium cations react with the sulfate anions to form insoluble barium sulfate. + 2+ 2− − → 2H2O(l) + BaSO4(s) 2H (aq) + SO4 (aq) + Ba (aq) + 2OH (aq) ⎯⎯ Thus, the reaction depletes the solution of ions and the conductivity decreases. 4.119 (a) Check with litmus paper, react with carbonate or bicarbonate to see if CO2 gas is produced, react with a base and check with an indicator. (b) Titrate a known quantity of acid with a standard NaOH solution. Since it is a monoprotic acid, the moles of NaOH reacted equals the moles of the acid. Dividing the mass of acid by the number of moles gives the molar mass of the acid. (c) Visually compare the conductivity of the acid with a standard NaCl solution of the same molar concentration. A strong acid will have a similar conductivity to the NaCl solution. The conductivity of a weak acid will be considerably less than the NaCl solution. 4.120 You could test the conductivity of the solutions. Sugar is a nonelectrolyte and an aqueous sugar solution will not conduct electricity; whereas, NaCl is a strong electrolyte when dissolved in water. Silver nitrate could be added to the solutions to see if silver chloride precipitated. In this particular case, the solutions could also be tasted. 4.121 (a) → PbSO4(s) + 2NaNO3(aq) Pb(NO3)2(aq) + Na2SO4(aq) ⎯⎯ 2+ 2− → PbSO4(s) Pb (aq) + SO4 (aq) ⎯⎯ (b) First, calculate the moles of Pb 0.00450 g Na 2SO4 × 2+ in the polluted water. 1 mol Pb(NO3 )2 1 mol Na 2SO4 1 mol Pb 2+ × × = 3.168 × 10−5 mol Pb 2+ 142.05 g Na 2SO4 1 mol Na 2SO4 1 mol Pb(NO3 ) 2 2+ The volume of the polluted water sample is 500 mL (0.500 L). The molar concentration of Pb [Pb 2+ ] = 4.122 is: mol Pb 2+ 3.168 × 10−5 mol Pb 2+ = = 6.34 × 10−5 M L of soln 0.500 L soln In a redox reaction, the oxidizing agent gains one or more electrons. In doing so, the oxidation number of the element gaining the electrons must become more negative. In the case of chlorine, the −1 oxidation number is already the most negative state possible. The chloride ion cannot accept any more electrons; therefore, hydrochloric acid is not an oxidizing agent. 104 CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS 4.123 (a) An acid and a base react to form water and a salt. Potassium iodide is a salt; therefore, the acid and base are chosen to produce this salt. → KI(aq) + H2O(l) KOH(aq) + HI(aq) ⎯⎯ The water could be evaporated to isolate the KI. (b) Acids react with carbonates to form carbon dioxide gas. Again, chose the acid and carbonate salt so that KI is produced. → 2KI(aq) + CO2(g) + H2O(l) 2HI(aq) + K2CO3(aq) ⎯⎯ 4.124 The reaction is too violent. This could cause the hydrogen gas produced to ignite, and an explosion could result. 4.125 All three products are water insoluble. Use this information in formulating your answer. 4.126 (a) → Mg(OH)2(s) + 2NaCl(aq) MgCl2(aq) + 2NaOH(aq) ⎯⎯ (b) → AgI(s) + NaNO3(aq) AgNO3(aq) + NaI(aq) ⎯⎯ (c) → Ba3(PO4)2(s) + 6H2O(l) 3Ba(OH)2(aq) + 2H3PO4(aq) ⎯⎯ − The solid sodium bicarbonate would be the better choice. The hydrogen carbonate ion, HCO3 , behaves as a Brønsted base to accept a proton from the acid. − + → H2CO3(aq) ⎯⎯ → H2O(l) + CO2(g) HCO3 (aq) + H (aq) ⎯⎯ The heat generated during the reaction of hydrogen carbonate with the acid causes the carbonic acid, H2CO3, that was formed to decompose to water and carbon dioxide. The reaction of the spilled sulfuric acid with sodium hydroxide would produce sodium sulfate, Na2SO4, and 2− water. There is a possibility that the Na2SO4 could precipitate. Also, the sulfate ion, SO4 is a weak base; therefore, the “neutralized” solution would actually be basic. → Na2SO4(aq) + 2H2O(l) H2SO4(aq) + 2NaOH(aq) ⎯⎯ Also, NaOH is a caustic substance and therefore is not safe to use in this manner. 4.127 (a) (b) (c) (d) (e) 4.128 (a) (b) (c) (d) A soluble sulfate salt such as sodium sulfate or sulfuric acid could be added. Barium sulfate would precipitate leaving sodium ions in solution. Potassium carbonate, phosphate, or sulfide could be added which would precipitate the magnesium cations, leaving potassium cations in solution. Add a soluble silver salt such as silver nitrate. AgBr would precipitate, leaving nitrate ions in solution. Add a solution containing a cation other than ammonium or a Group 1A cation to precipitate the phosphate ions; the nitrate ions will remain in solution. Add a solution containing a cation other than ammonium or a Group 1A cation to precipitate the carbonate ions; the nitrate ions will remain in solution. Table salt, NaCl, is very soluble in water and is a strong electrolyte. Addition of AgNO3 will precipitate AgCl. Table sugar or sucrose, C12H22O11, is soluble in water and is a nonelectrolyte. Aqueous acetic acid, CH3COOH, the primary ingredient of vinegar, is a weak electrolyte. It exhibits all of the properties of acids (Section 4.3). Baking soda, NaHCO3, is a water-soluble strong electrolyte. It reacts with acid to release CO2 gas. Addition of Ca(OH)2 results in the precipitation of CaCO3. CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS (e) (f) (g) (h) (i) (j) (k) 105 Washing soda, Na2CO3⋅10H2O, is a water-soluble strong electrolyte. It reacts with acids to release CO2 gas. Addition of a soluble alkaline-earth salt will precipitate the alkaline-earth carbonate. Aqueous washing soda is also slightly basic (Section 4.3). Boric acid, H3BO3, is weak electrolyte and a weak acid. Epsom salt, MgSO4⋅7H2O, is a water-soluble strong electrolyte. Addition of Ba(NO3)2 results in the precipitation of BaSO4. Addition of hydroxide precipitates Mg(OH)2. Sodium hydroxide, NaOH, is a strong electrolyte and a strong base. Addition of Ca(NO3)2 results in the precipitation of Ca(OH)2. Ammonia, NH3, is a sharp-odored gas that when dissolved in water is a weak electrolyte and a weak base. NH3 in the gas phase reacts with HCl gas to produce solid NH4Cl. Milk of magnesia, Mg(OH)2, is an insoluble, strong base that reacts with acids. The resulting magnesium salt may be soluble or insoluble. CaCO3 is an insoluble salt that reacts with acid to release CO2 gas. CaCO3 is discussed in the Chemistry in Action essays entitled, “An Undesirable Precipitation Reaction” and “Metal from the Sea” in Chapter 4. With the exception of NH3 and vinegar, all the compounds in this problem are white solids. 4.129 2− 2− → SO4 (aq) + H2O(l) Reaction 1: SO3 (aq) + H2O2(aq) ⎯⎯ − 2− → BaSO4(s) + 2Cl (aq) Reaction 2: SO4 (aq) + BaCl2(aq) ⎯⎯ 4.130 The balanced equation for the reaction is: → AgCl(s) + XNO3(aq) XCl(aq) + AgNO3(aq) ⎯⎯ where X = Na, or K From the amount of AgCl produced, we can calculate the moles of XCl reacted (X = Na, or K). 1.913 g AgCl × 1 mol AgCl 1 mol XCl × = 0.013345 mol XCl 143.35 g AgCl 1 mol AgCl Let x = number of moles NaCl. Then, the number of moles of KCl = 0.013345 mol − x. The sum of the NaCl and KCl masses must equal the mass of the mixture, 0.8870 g. We can write: mass NaCl + mass KCl = 0.8870 g ⎡ 58.44 g NaCl ⎤ ⎡ 74.55 g KCl ⎤ ⎢ x mol NaCl × ⎥ + ⎢(0.013345 − x) mol KCl × ⎥ = 0.8870 g 1 mol NaCl ⎦ ⎣ 1 mol KCl ⎦ ⎣ x = 6.6958 × 10 −3 = moles NaCl −3 mol KCl = 0.013345 − x = 0.013345 mol − (6.6958 × 10 mol) = 6.6492 × 10 Converting moles to grams: mass NaCl = (6.6958 × 10−3 mol NaCl) × mass KCl = (6.6492 × 10−3 mol KCl) × 58.44 g NaCl = 0.3913 g NaCl 1 mol NaCl 74.55 g KCl = 0.4957 g KCl 1 mol KCl −3 mol KCl 106 CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS The percentages by mass for each compound are: % NaCl = % KCl = 0.3913 g × 100% = 44.11% NaCl 0.8870 g 0.4957 g × 100% = 55.89% KCl 0.8870 g 4.131 The oxidation number of carbon in CO2 is +4. This is the maximum oxidation number of carbon. Therefore, carbon in CO2 cannot be oxidized further, as would happen in a combustion reaction, and hence CO2 is not flammable. In CO, however, the oxidation number of C is +2. The carbon in CO can be oxidized further and hence CO is flammable. 4.132 This is an acid-base reaction with H from HNO3 combining with OH from AgOH to produce water. The other product is the salt, AgNO3, which is soluble (nitrate salts are soluble, see Table 4.2 of the text). + − AgOH(s) + HNO3(aq) → H2O(l) + AgNO3(aq) + − Because the salt, AgNO3, is soluble, it dissociates into ions in solution, Ag (aq) and NO3 (aq). The diagram that corresponds to this reaction is (a). 4.133 Cl2O (Cl = +1) Cl2O7 (Cl = +7) Cl2O3 (Cl = +3) ClO2 (Cl = +4) 4.134 The number of moles of oxalic acid in 5.00 × 10 mL is: Cl2O6 (Cl = +6) 2 0.100 mol H 2 C2 O 4 × (5.00 × 102 mL) = 0.0500 mol H 2 C2 O4 1000 mL soln The balanced equation shows a mole ratio of 1 mol Fe2O3 : 6 mol H2C2O4. The mass of rust that can be removed is: 0.0500 mol H 2 C2 O4 × 4.135 1 mol Fe 2 O3 159.7 g Fe 2 O3 × = 1.33 g Fe2 O 3 6 mol H 2 C2 O 4 1 mol Fe2 O3 Since aspirin is a monoprotic acid, it will react with NaOH in a 1:1 mole ratio. First, calculate the moles of aspirin in the tablet. 12.25 mL soln × 0.1466 mol NaOH 1 mol aspirin × = 1.7959 × 10−3 mol aspirin 1000 mL soln 1 mol NaOH Next, convert from moles of aspirin to grains of aspirin. 1.7959 × 10−3 mol aspirin × 4.136 The precipitation reaction is: + 180.15 g aspirin 1 grain × = 4.99 grains aspirin in one tablet 1 mol aspirin 0.0648 g − → AgBr(s) Ag (aq) + Br (aq) ⎯⎯ − In this problem, the relative amounts of NaBr and CaBr2 are not known. However, the total amount of Br in − the mixture can be determined from the amount of AgBr produced. Let’s find the number of moles of Br . CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS 1.6930 g AgBr × 107 1 mol AgBr 1 mol Br − × = 9.0149 × 10−3 mol Br − 187.8 g AgBr 1 mol AgBr − The amount of Br comes from both NaBr and CaBr2. Let x = number of moles NaBr. Then, the number of 9.0149 × 10−3 mol − x . The moles of CaBr2 are divided by 2, because 1 mol of CaBr2 2 − produces 2 moles of Br . The sum of the NaBr and CaBr2 masses must equal the mass of the mixture, 0.9157 g. We can write: moles of CaBr2 = mass NaBr + mass CaBr2 = 0.9157 g ⎡ 199.88 g CaBr2 ⎤ 102.89 g NaBr ⎤ ⎡⎛ 9.0149 × 10−3 − x ⎞ ⎥ = 0.9157 g ⎟ mol CaBr2 × ⎢ x mol NaBr × ⎥ + ⎢⎜⎜ ⎟ 1 mol NaBr ⎦ ⎢⎝ 2 1 mol CaBr ⎥⎦ ⎣ 2 ⎠ ⎣ 2.95x = 0.014751 x = 5.0003 × 10 −3 = moles NaBr Converting moles to grams: mass NaBr = (5.0003 × 10−3 mol NaBr) × 102.89 g NaBr = 0.51448 g NaBr 1 mol NaBr The percentage by mass of NaBr in the mixture is: % NaBr = 4.137 (a) 0.51448 g × 100% = 56.18% NaBr 0.9157 g → 2HF(g) + CaSO4(s) CaF2(s) + H2SO4(aq) ⎯⎯ → 2HCl(aq) + Na2SO4(aq) 2NaCl(s) + H2SO4(aq) ⎯⎯ (b) − − HBr and HI cannot be prepared similarly, because Br and I would be oxidized to the element, Br2 and I2, respectively. → Br2(l) + SO2(g) + Na2SO4(aq) + 2H2O(l) 2NaBr(s) + 2H2SO4(aq) ⎯⎯ (c) 4.138 → 3HBr(g) + H3PO3(aq) PBr3(l) + 3H2O(l) ⎯⎯ − There are two moles of Cl per one mole of CaCl2. (a) 25.3 g CaCl2 × 1 mol CaCl2 2 mol Cl− × = 0.4559 mol Cl− 110.98 g CaCl2 1 mol CaCl2 Molarity Cl − = (b) 0.4559 mol Cl− = 1.40 mol/L = 1.40 M 0.325 L soln We need to convert from mol/L to grams in 0.100 L. 1.40 mol Cl− 35.45 g Cl × × 0.100 L soln = 4.96 g Cl − − 1 L soln 1 mol Cl 108 CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS 4.139 Electric furnace method: → P4O10(s) P4(s) + 5O2(g) ⎯⎯ redox → 4H3PO4(aq) P4O10(s) + 6H2O(l) ⎯⎯ acid-base Wet process: → 3H3PO4(aq) + HF(aq) + 5CaSO4(s) Ca5(PO4)3F(s) + 5H2SO4(aq) ⎯⎯ This is a precipitation and an acid-base reaction. 4.140 − + (a) → NH3(aq) + H2O(l) NH4 (aq) + OH (aq) ⎯⎯ (b) From the amount of NaOH needed to neutralize the 0.2041 g sample, we can find the amount of the 0.2041 g sample that is NH4NO3. First, calculate the moles of NaOH. 0.1023 mol NaOH × 24.42 mL soln = 2.4982 × 10−3 mol NaOH 1000 mL of soln Using the mole ratio from the balanced equation, we can calculate the amount of NH4NO3 that reacted. (2.4982 × 10−3 mol NaOH) × 1 mol NH 4 NO3 80.052 g NH 4 NO3 × = 0.19999 g NH 4 NO3 1 mol NaOH 1 mol NH 4 NO3 The purity of the NH4NO3 sample is: % purity = 0.19999 g × 100% = 97.99% 0.2041 g 4.141 In a redox reaction, electrons must be transferred between reacting species. In other words, oxidation numbers must change in a redox reation. In both O2 (molecular oxygen) and O3 (ozone), the oxidation number of oxygen is zero. This is not a redox reaction. 4.142 Using the rules for assigning oxidation numbers given in Section 4.4, H is +1, F is −1, so the oxidation number of O must be zero. 4.143 (a) + − OH (b) NH4 4.144 ⎯⎯ → + H3O + + NH2 + H2O − ⎯⎯ → H2O + NH3 NH3 The balanced equation is: → 3CH3COOH + 2Cr2(SO4)3 + 2K2SO4 + 11H2O 3CH3CH2OH + 2K2Cr2O7 + 8H2SO4 ⎯⎯ From the amount of K2Cr2O7 required to react with the blood sample, we can calculate the mass of ethanol (CH3CH2OH) in the 10.0 g sample of blood. CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS 109 First, calculate the moles of K2Cr2O7 reacted. 0.07654 mol K 2 Cr2 O7 × 4.23 mL = 3.238 × 10−4 mol K 2 Cr2 O7 1000 mL soln Next, using the mole ratio from the balanced equation, we can calculate the mass of ethanol that reacted. 3.238 × 10−4 mol K 2 Cr2 O7 × 3 mol ethanol 46.068 g ethanol × = 0.02238 g ethanol 2 mol K 2 Cr2 O7 1 mol ethanol The percent ethanol by mass is: % by mass ethanol = 0.02238 g × 100% = 0.224% 10.0 g This is well above the legal limit of 0.1 percent by mass ethanol in the blood. The individual should be prosecuted for drunk driving. 4.145 Notice that nitrogen is in its highest possible oxidation state (+5) in nitric acid. It is reduced as it decomposes to NO2. → 4NO2 + O2 + 2H2O 4HNO3 ⎯⎯ The yellow color of “old” nitric acid is caused by the production of small amounts of NO2 which is a brown gas. This process is accelerated by light. 4.146 (a) → ZnSO4(aq) + H2(g) Zn(s) + H2SO4(aq) ⎯⎯ (b) → 2KCl(s) + 3O2(g) 2KClO3(s) ⎯⎯ (c) → 2NaCl(aq) + CO2(g) + H2O(l) Na2CO3(s) + 2HCl(aq) ⎯⎯ (d) → N2(g) + 2H2O(g) NH4NO2(s) ⎯⎯⎯ heat 4.147 Because the volume of the solution changes (increases or decreases) when the solid dissolves. 4.148 NH4Cl exists as NH4 and Cl . To form NH3 and HCl, a proton (H ) is transferred from NH4 to Cl . Therefore, this is a Brønsted acid-base reaction. 4.149 (a) The precipitate CaSO4 formed over Ca preventing the Ca from reacting with the sulfuric acid. (b) Aluminum is protected by a tenacious oxide layer with the composition Al2O3. (c) These metals react more readily with water. + − + + − → 2NaOH(aq) + H2(g) 2Na(s) + 2H2O(l) ⎯⎯ (d) The metal should be placed below Fe and above H. (e) Any metal above Al in the activity series will react with Al . Metals from Mg to Li will work. 3+ 110 CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS 4.150 (a) First Solution: 0.8214 g KMnO4 × M = 1 mol KMnO4 = 5.1974 × 10−3 mol KMnO 4 158.04 g KMnO4 5.1974 × 10−3 mol KMnO4 mol solute = = 1.0395 × 10−2 M L of soln 0.5000 L Second Solution: M1V1 = M2V2 −2 (1.0395 × 10 M)(2.000 mL) = M2(1000 mL) −5 M2 = 2.079 × 10 M Third Solution: M1V1 = M2V2 −5 (2.079 × 10 M)(10.00 mL) = M2(250.0 mL) −7 M2 = 8.316 × 10 M (b) From the molarity and volume of the final solution, we can calculate the moles of KMnO4. Then, the mass can be calculated from the moles of KMnO4. 8.316 × 10−7 mol KMnO4 × 250 mL = 2.079 × 10−7 mol KMnO4 1000 mL of soln 158.04 g KMnO4 = 3.286 × 10−5 g KMnO4 2.079 × 10−7 mol KMnO 4 × 1 mol KMnO 4 This mass is too small to directly weigh accurately. 4.151 (a) The balanced equations are: → Cu(NO3)2(aq) + 2NO2(g) + 2H2O(l) 1) Cu(s) + 4HNO3(aq) ⎯⎯ Redox → Cu(OH)2(s) + 2NaNO3(aq) 2) Cu(NO3)2(aq) + 2NaOH(aq) ⎯⎯ Precipitation heat (b) → CuO(s) + H2O(g) 3) Cu(OH)2(s) ⎯⎯⎯ Decomposition → CuSO4(aq) + H2O(l) 4) CuO(s) + H2SO4(aq) ⎯⎯ Acid-Base → Cu(s) + ZnSO4(aq) 5) CuSO4(aq) + Zn(s) ⎯⎯ Redox → ZnCl2(aq) + H2(g) 6) Zn(s) + 2HCl(aq) ⎯⎯ Redox 1 mol Cu = 1.032 mol Cu . The mole ratio between 63.55 g Cu product and reactant in each reaction is 1:1. Therefore, the theoretical yield in each reaction is 1.032 moles. 187.57 g Cu(NO3 )2 = 194 g Cu(NO 3 )2 1) 1.032 mol × 1 mol Cu(NO3 ) 2 We start with 65.6 g Cu, which is 65.6 g Cu × 2) 1.032 mol × 97.566 g Cu(OH)2 = 101 g Cu(OH)2 1 mol Cu(OH)2 3) 1.032 mol × 79.55 g CuO = 82.1 g CuO 1 mol CuO CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS (c) 4.152 4) 1.032 mol × 159.62 g CuSO 4 = 165 g CuSO4 1 mol CuSO 4 5) 1.032 mol × 63.55 g Cu = 65.6 g Cu 1 mol Cu All of the reaction steps are clean and almost quantitative; therefore, the recovery yield should be high. 2+ 3+ 2+ The first titration oxidizes Fe to Fe . This titration gives the amount of Fe in solution. Zn metal is 3+ 2+ 2+ 3+ added to reduce all Fe back to Fe . The second titration oxidizes all the Fe back to Fe . We can find 3+ the amount of Fe in the original solution by difference. − 2+ Titration #1: The mole ratio between Fe 23.0 mL soln × [Fe2+ ] = and MnO4 is 5:1. 0.0200 mol MnO−4 5 mol Fe2+ × = 2.30 × 10−3 mol Fe2+ − 1000 mL soln 1 mol MnO4 mol solute 2.30 × 10−3 mol Fe2+ = = 0.0920 M L of soln 25.0 × 10−3 L soln − 2+ Titration #2: The mole ratio between Fe 40.0 mL soln × and MnO4 is 5:1. 0.0200 mol MnO−4 5 mol Fe2+ × = 4.00 × 10−3 mol Fe2+ 1000 mL soln 1 mol MnO−4 2+ 3+ In this second titration, there are more moles of Fe in solution. This is due to Fe 2+ 3+ being reduced by Zn to Fe . The number of moles of Fe in solution is: (4.00 × 10 [Fe3+ ] = 4.153 −3 mol) − (2.30 × 10 −3 mol) = 1.70 × 10 −3 in the original solution 3+ mol Fe mol solute 1.70 × 10−3 mol Fe3+ = = 0.0680 M L of soln 25.0 × 10−3 L soln Place the following metals in the correct positions on the periodic table framework provided in the problem. (a) Li, Na (Group 1A) (b) Mg (Group 2A), Fe (Group 8B) (c) Zn, Cd (Group 2B) Two metals that do not react with water or acid are Ag and Au (Group 1B). 4.154 111 (a) − 2+ The precipitation reaction is: → Mg(OH)2(s) Mg (aq) + 2OH (aq) ⎯⎯ The acid-base reaction is: → MgCl2(aq) + 2H2O(l) Mg(OH)2(s) + 2HCl(aq) ⎯⎯ The redox reactions are: Mg − 2+ + 2e − ⎯⎯ → Cl2 + 2e 2Cl ⎯⎯ → Mg − → Mg + Cl2 MgCl2 ⎯⎯ (b) NaOH is much more expensive than CaO. (c) Dolomite has the advantage of being an additional source of magnesium that can also be recovered. 112 CHAPTER 4: REACTIONS IN AQUEOUS SOLUTIONS 4.155 The reaction between Mg(NO3)2 and NaOH is: Mg(NO3)2(aq) + 2NaOH(aq) → Mg(OH)2(s) + 2NaNO3(aq) + − Magnesium hydroxide, Mg(OH)2, precipitates from solution. Na and NO3 are spectator ions. This is most likely a limiting reagent problem as the amounts of both reactants are given. Let’s first determine which reactant is the limiting reagent before we try to determine the concentration of ions remaining in the solution. 1.615 g Mg(NO3 )2 × 1.073 g NaOH × 1 mol Mg(NO3 )2 = 0.010888 mol Mg(NO3 ) 2 148.33 g Mg(NO3 )2 1 mol NaOH = 0.026826 mol NaOH 39.998 g NaOH From the balanced equation, we need twice as many moles of NaOH compared to Mg(NO3)2. We have more than twice as much NaOH (2 × 0.010888 mol = 0.021776 mol) and therefore Mg(NO3)2 is the limiting reagent. + − + − − NaOH is in excess and ions of Na , OH , and NO3 will remain in solution. Because Na and NO3 are spectator − ions, the number of moles after reaction will equal the initial number of moles. The excess moles of OH need to 2+ be calculated based on the amount that reacts with Mg . The combined volume of the two solutions is: 22.02 mL + 28.64 mL = 50.66 mL = 0.05066 L. [Na + ] = 0.026826 mol NaOH × 1 mol Na + 1 × = 0.5295 M 1 mol NaOH 0.05066 L [NO−3 ] = 0.010888 mol Mg(NO3 )2 × 2 mol NO3− 1 × = 0.4298 M 1 mol Mg(NO3 )2 0.05066 L − The moles of OH reacted are: 0.010888 mol Mg 2+ × 2 mol OH− 1 mol Mg 2+ = 0.021776 mol OH − reacted − The moles of excess OH are: − 0.026826 mol − 0.021776 mol = 0.005050 mol OH [OH − ] = 0.005050 mol = 0.09968 M 0.05066 L 2+ The concentration of Mg 4.156 is approximately zero as almost all of it will precipitate as Mg(OH)2. Because only B and C react with 0.5 M HCl, they are more electropositive than A and D. The fact that when B is added to a solution containing the ions of the other metals, metallic A, C, and D are formed indicates that B is the most electropositive metal. Because A reacts with 6 M HNO3, A is more electropositive than D. The metals arranged in increasing order as reducing agents are: D