# Solve The diagram shows twice as many cations as anions, consistent with the formulation K 2 SO 4.

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1 Sample Exercise 4.1 Relating Relative Numbers of Anions and Cations to Chemical Formulas The accompanying diagram represents an aqueous solution of either MgCl 2, KCl, or K 2 SO 4. Which solution does the drawing best represent? Solution Analyze We are asked to associate the charged spheres in the diagram with ions present in a solution of an ionic substance. Plan We examine each ionic substance given to determine the relative numbers and charges of its ions.we then correlate these ionic species with the ones shown in the diagram. Solve The diagram shows twice as many cations as anions, consistent with the formulation K 2 SO 4. Check Notice that the net charge in the diagram is zero, as it must be if it is to represent an ionic substance.

2 Sample Exercise 4.1 Relating Relative Numbers of Anions and Cations to Chemical Formulas Practice Exercise If you were to draw diagrams representing aqueous solutions of (a) NiSO 4, (b) Ca(NO 3 ) 2, (c) Na 3 PO 4, (d) Al 2 (SO 4 ) 3, how many anions would you show if each diagram contained six cations? Answer: (a) 6, (b) 12, (c) 2, (d) 9

3 Sample Exercise 4.2 Using Solubility Rules Classify these ionic compounds as soluble or insoluble in water: (a) sodium carbonate, Na 2 CO 3, (b) lead sulfate, PbSO 4. Solution Analyze We are given the names and formulas of two ionic compounds and asked to predict whether they are soluble or insoluble in water. Plan We can use Table 4.1 to answer the question. Thus, we need to focus on the anion in each compound because the table is organized by anions. Solve (a) According to Table 4.1, most carbonates are insoluble. But carbonates of the alkali metal cations (such as sodium ion) are an exception to this rule and are soluble. Thus, Na 2 CO 3 is soluble in water. (b) Table 4.1 indicates that although most sulfates are water soluble, the sulfate of is an exception. Thus, PbSO 4 is insoluble in water.

4 Sample Exercise 4.2 Using Solubility Rules Practice Exercise Classify the following compounds as soluble or insoluble in water: (a) cobalt(ii) hydroxide, (b) barium nitrate, (c) ammonium phosphate. Answer: (a) insoluble, (b) soluble, (c) soluble

5 Sample Exercise 4.3 Predicting a Metathesis Reaction (a) Predict the identity of the precipitate that forms when aqueous solutions of BaCl 2 and K 2 SO 4 are mixed. (b) Write the balanced chemical equation for the reaction. Solution Analyze We are given two ionic reactants and asked to predict the insoluble product that they form. Plan We need to write the ions present in the reactants and exchange the anions between the two cations. Once we have written the chemical formulas for these products, we can use Table 4.1 to determine which is insoluble in water. Knowing the products also allows us to write the equation for the reaction. Solve (a) The reactants contain Ba 2+, Cl, K +, and SO 2 4 ions. Exchanging the anions gives us BaSO 4 and KCl. According to Table 4.1, most compounds of SO 2 4 are soluble but those of Ba 2+ are not. Thus, BaSO 4 is insoluble and will precipitate from solution. KCl is soluble. (b) From part (a) we know the chemical formulas of the products, BaSO 4 and KCl. The balanced equation is BaCl 2 (aq) + K 2 SO 4 (aq) BaSO 4 (s) + 2 KCl(aq)

6 Sample Exercise 4.3 Predicting a Metathesis Reaction Practice Exercise (a) What compound precipitates when aqueous solutions of Fe 2 (SO 4 ) 3 and LiOH are mixed? (b) Write a balanced equation for the reaction. (c) Will a precipitate form when solutions of Ba(NO 3 ) 2 and KOH are mixed? Answer: (a) Fe(OH) 3, (b) Fe 2 (SO 4 ) 3 (aq) + 6 LiOH(aq) possible products, Ba(OH) 2 and KNO 3, are water soluble) 2 Fe(OH) 3 (s) + 3 Li 2 SO 4 (aq), (c) no (both

7 Sample Exercise 4.4 Writing a Net Ionic Equation Write the net ionic equation for the precipitation reaction that occurs when aqueous solutions of calcium chloride and sodium carbonate are mixed. Solution Analyze Our task is to write a net ionic equation for a precipitation reaction, given the names of the reactants present in solution. Plan We write the chemical formulas of the reactants and products and then determine which product is insoluble. We then write and balance the molecular equation. Next, we write each soluble strong electrolyte as separated ions to obtain the complete ionic equation. Finally, we eliminate the spectator ions to obtain the net ionic equation. Solve Calcium chloride is composed of calcium ions, Ca 2+, and chloride ions, Cl ; hence, an aqueous solution of the substance is CaCl 2 (aq). Sodium carbonate is composed of Na + ions and CO3 2 ions; hence, an aqueous solution of the compound is Na 2 CO 3 (aq). In the molecular equations for precipitation reactions, the anions and cations appear to exchange partners. Thus, we put Ca 2+ and CO 2 3 together to give CaCO 3 and Na + and Cl together to give NaCl. According to the solubility guidelines in Table 4.1, CaCO 3 is insoluble and NaCl is soluble. The balancedmolecular equation is CaCl 2 (aq) + Na 2 CO 3 (aq) CaCO 3 (s) + 2 NaCl(aq)

8 Sample Exercise 4.4 Writing a Net Ionic Equation In a complete ionic equation, only dissolved strong electrolytes (such as soluble ionic compounds) are written as separate ions. As the (aq) designations remind us, CaCl 2, Na 2 CO 3, and NaCl are all dissolved in the solution. Furthermore, they are all strong electrolytes. CaCO 3 is an ionic compound, but it is not soluble. We do not write the formula of any insoluble compound as its component ions. Thus, the complete ionic equation is Ca 2+ (aq) + 2 Cl (aq) + 2 Na + (aq) + CO 2 3 (aq) CaCO 3 (s) + 2 Na + (aq) + 2 Cl (aq) Cl and Na + are spectator ions. Canceling them gives the following net ionic equation: Ca 2+ (aq) + CO 2 3 (aq) CaCO 3 (s) Check We can check our result by confirming that both the elements and the electric charge are balanced. Each side has one Ca, one C, and three O, and the net charge on each side equals 0. Comment If none of the ions in an ionic equation is removed from solution or changed in some way, all ions are spectator ions and a reaction does not occur. Practice Exercise Write the net ionic equation for the precipitation reaction that occurs when aqueous solutions of silver nitrate and potassium phosphate are mixed. Answer: 3 Ag + (aq) + PO 4 3 (aq) Ag 3 PO 4 (s)

9 Sample Exercise 4.5 Comparing Acid Strengths The following diagrams represent aqueous solutions of acids HX, HY, and HZ, with water molecules omitted for clarity. Rank the acids from strongest to weakest. Solution Analyze We are asked to rank three acids from strongest to weakest, based on schematic drawings of their solutions. Plan We can determine the relative numbers of uncharged molecular species in the diagrams. The strongest acid is the one with the most H + ions and fewest undissociated molecules in solution. The weakest acid is the one with the largest number of undissociated molecules. Solve The order is HY > HZ > HX. HY is a strong acid because it is totally ionized (no HY molecules in solution), whereas both HX and HZ are weak acids, whose solutions consist of a mixture of molecules and ions. Because HZ contains more ions and fewer molecules than HX, it is a stronger acid. Practice Exercise Imagine a diagram showing 10 Na + ions and 10 OH ions. If this solution were mixed with the one pictured above for HY, what species would be present in a diagram that represents the combined solutions after any possible reaction? Answer: The diagram would show 10 Na + ions, 2 OH ions, 8 Y ions, and 8 H 2 O molecules.

10 Sample Exercise 4.6 Identifying Strong, Weak, and Nonelectrolytes Classify these dissolved substances as strong, weak, or nonelectrolyte: CaCl 2, HNO 3, C 2 H 5 OH (ethanol), HCOOH (formic acid), KOH. Solution Analyze We are given several chemical formulas and asked to classify each substance as a strong electrolyte, weak electrolyte, or nonelectrolyte. Plan The approach we take is outlined in Table 4.3. We can predict whether a substance is ionic or molecular based on its composition. As we saw in Section 2.7, most ionic compounds we encounter in this text are composed of a metal and a nonmetal, whereas most molecular compounds are composed only of nonmetals. Solve Two compounds fit the criteria for ionic compounds: CaCl 2 and KOH. Because Table 4.3 tells us that all ionic compounds are strong electrolytes, that is how we classify these two substances. The three remaining compounds are molecular. Two, HNO 3 and HCOOH, are acids. Nitric acid, HNO 3, is a common strong acid, as shown in Table 4.2, and therefore is a strong electrolyte. Because most acids are weak acids, our best guess would be that HCOOH is a weak acid (weak electrolyte). This is correct. The remaining molecular compound, C 2 H 5 OH, is neither an acid nor a base, so it is a nonelectrolyte.

11 Sample Exercise 4.6 Identifying Strong, Weak, and Nonelectrolytes Solve Two compounds fit the criteria for ionic compounds: CaCl 2 and KOH. Because Table 4.3 tells us that all ionic compounds are strong electrolytes, that is how we classify these two substances. The three remaining compounds are molecular. Two, HNO 3 and HCOOH, are acids. Nitric acid, HNO 3, is a common strong acid, as shown in Table 4.2, and therefore is a strong electrolyte. Because most acids are weak acids, our best guess would be that HCOOH is a weak acid (weak electrolyte). This is correct. The remaining molecular compound, C 2 H 5 OH, is neither an acid nor a base, so it is a nonelectrolyte. Comment Although C 2 H 5 OH has an OH group, it is not a metal hydroxide and so not a base. Rather, it is a member of a class of organic compounds that have C OH bonds, which are known as alcohols. Organic compounds containing the COOH group are called carboxylic acids (Chapter 16).Molecules that have this group are weak acids.

12 Sample Exercise 4.6 Identifying Strong, Weak, and Nonelectrolytes Practice Exercise Consider solutions in which 0.1 mol of each of the following compounds is dissolved in 1 L of water: Ca(NO 3 ) 2 (calcium nitrate), C 6 H 12 O 6 (glucose), NaCH 3 COO (sodium acetate), and CH 3 COOH (acetic acid). Rank the solutions in order of increasing electrical conductivity, based on the fact that the greater the number of ions in solution, the greater the conductivity. Answer: C 6 H 12 O 6 (nonelectrolyte) < CH 3 COOH (weak electrolyte, existing mainly in the form of molecules with few ions) < NaCH 3 COO (strong electrolyte that provides two ions, Na + and CH 3 COO ) < Ca(NO 3 ) 2 (strong electrolyte that provides three ions, Ca 2+ and 2 NO 3 )

13 Sample Exercise 4.7 Writing Chemical Equations for a Neutralization Reaction For the reaction between aqueous solutions of acetic acid (CH 3 COOH) and barium hydroxide, Ba(OH) 2, write (a) the balanced molecular equation, (b) the complete ionic equation, (c) the net ionic equation. Solution Analyze We are given the chemical formulas for an acid and a base and asked to write a balanced molecular equation, a complete ionic equation, and a net ionic equation for their neutralization reaction. Solve (a) The salt contains the cation of the base (Ba 2+ ) and the anion of the acid (CH 3 COO ). Thus, the salt formula is Ba(CH 3 COO) 2. According to Table 4.1, this compound is soluble in water. The unbalanced molecular equation for the neutralization reaction is Plan As Equation 4.12 and the italicized statement that follows it indicate, neutralization reactions form two products, H 2 O and a salt. We examine the cation of the base and the anion of the acid to determine the composition of the salt.

14 Sample Exercise 4.7 Writing Chemical Equations for a Neutralization Reaction To balance this equation, we must provide two molecules of CH 3 COOH to furnish the two CH 3 COO ions and to supply the two H + ions needed to combine with the two OH ions of the base. The balanced molecular equation is (b) To write the complete ionic equation, we identify the strong electrolytes and break them into ions. In this case Ba(OH) 2 and Ba(CH 3 COO) 2 are both water-soluble ionic compounds and hence strong electrolytes. Thus, the complete ionic equation is (c) Eliminating the spectator ion, Ba 2+, and simplifying coefficients gives the net ionic equation: Check We can determine whether the molecular equation is balanced by counting the number of atoms of each kind on both sides of the arrow (10 H, 6 O, 4 C, and 1 Ba on each side). However, it is often easier to check equations by counting groups: There are 2 CH 3 COO groups, as well as 1 Ba, and 4 additional H atoms and 2 additional O atoms on each side of the equation. The net ionic equation checks out because the numbers of each kind of element and the net charge are the same on both sides of the equation.

15 Sample Exercise 4.7 Writing Chemical Equations for a Neutralization Reaction Practice Exercise For the reaction of phosphorous acid (H 3 PO 3 ) and potassium hydroxide (KOH), write (a) the balanced molecular equation and (b) the net ionic equation. Answer: (a) H 3 PO 3 (aq) + 3 KOH(aq) 3 H 2 O(l) + K 3 PO 3 (aq), (b) H 3 PO 3 (aq) + 3 OH (aq) 3 H 2 O(l) + PO 3 3 (aq). (H 3 PO 3 is a weak acid and therefore a weak electrolyte, whereas KOH, a strong base, and K 3 PO 3, an ionic compound, are strong electrolytes.)

16 Sample Exercise 4.8 Determining Oxidation Numbers Determine the oxidation number of sulfur in (a) H 2 S, (b) S 8, (c) SCl 2, (d) Na 2 SO 3, (e) SO 4 2. Solution Analyze We are asked to determine the oxidation number of sulfur in two molecular species, in the elemental form, and in two substances containing ions. Plan In each species the sum of oxidation numbers of all the atoms must equal the charge on the species. We will use the rules outlined previously to assign oxidation numbers. Solve (a) When bonded to a nonmetal, hydrogen has an oxidation number of +1 (rule 3b). Because the H 2 S molecule is neutral, the sum of the oxidation numbers must equal zero (rule 4). Letting x equal the oxidation number of S, we have 2(+1) + x = 0. Thus, S has an oxidation number of 2. (b) Because this is an elemental form of sulfur, the oxidation number of S is 0 (rule 1). (c) Because this is a binary compound, we expect chlorine to have an oxidation number of 1 (rule 3c). The sum of the oxidation numbers must equal zero (rule 4). Letting x equal the oxidation number of S, we have x + 2( 1) = 0. Consequently, the oxidation number of S must be +2. (d) Sodium, an alkali metal, always has an oxidation number of +1 in its compounds (rule 2). Oxygen has a common oxidation state of 2 (rule 3a). Letting x equal the oxidation number of S, we have 2(+1) + x + 3( 2) = 0. Therefore, the oxidation number of S in this compound is +4. (e) The oxidation state of O is 2 (rule 3a). The sum of the oxidation numbers equals 2, the net charge of the SO 4 2 ion (rule 4). Thus, we have x + 4( 2) = 2. From this relation we conclude that the oxidation number of S in this ion is +6.

17 Sample Exercise 4.8 Determining Oxidation Numbers Comment These examples illustrate that the oxidation number of a given element depends on the compound in which it occurs. The oxidation numbers of sulfur, as seen in these examples, range from 2 to +6. Practice Exercise What is the oxidation state of the boldfaced element in (a) P 2 O 5, (b) NaH, (c) Cr 2 O 2 7, (d) SnBr 4, (e) BaO 2? Answer: (a) +5, (b) 1, (c) +6, (d) +4, (e) 1

18 Sample Exercise 4.9 Writing Equations for Oxidation-Reduction Reactions Write the balanced molecular and net ionic equations for the reaction of aluminum with hydrobromic acid. Solution Analyze We must write two equations molecular and net ionic for the redox reaction between a metal and an acid. Plan Metals react with acids to form salts and H 2 gas. To write the balanced equations, we must write the chemical formulas for the two reactants and then determine the formula of the salt, which is composed of the cation formed by the metal and the anion of the acid. Solve The reactants are Al and HBr. The cation formed by Al is Al 3+, and the anion from hydrobromic acid is Br. Thus, the salt formed in the reaction is AlBr 3.Writing the reactants and products and then balancing the equation gives the molecular equation: 2 Al(s) + 6 HBr(aq) 2 AlBr 3 (aq) + 3 H 2 (g) Both HBr and AlBr 3 are soluble strong electrolytes. Thus, the complete ionic equation is 2 Al(s) + 6 H + (aq) + 6 Br (aq) 2 Al 3+ (aq) + 6 Br (aq) + 3 H 2 (g) Because Br is a spectator ion, the net ionic equation is 2 Al(s) + 6 H + (aq) 2 Al 3+ (aq) + 3 H 2 (g)

19 Sample Exercise 4.9 Writing Equations for Oxidation-Reduction Reactions Comment The substance oxidized is the aluminum metal because its oxidation state changes from 0 in the metal to +3 in the cation, thereby increasing in oxidation number. The H + is reduced because its oxidation state changes from +1 in the acid to 0 in H 2. Practice Exercise (a) Write the balanced molecular and net ionic equations for the reaction between magnesium and cobalt(ii) sulfate. (b) What is oxidized and what is reduced in the reaction? Answer: (a) Mg(s) + CoSO 4 (aq) MgSO 4 (aq) + Co(s); Mg(s) + Co 2+ (aq) Mg 2+ (aq) + Co(s), (b) Mg is oxidized and Co 2+ is reduced.

20 Sample Exercise 4.10 Determining When an Oxidation-Reduction Reaction Can Occur Will an aqueous solution of iron(ii) chloride oxidize magnesium metal? If so, write the balanced molecular and net ionic equations for the reaction. Solution Analyze We are given two substances an aqueous salt, FeCl 2, and a metal, Mg and asked if they react with each other. Plan A reaction occurs if the reactant that is a metal in its elemental form (Mg) is located above the reactant that is a metal in its oxidized form (Fe 2+ ) in Table 4.5. If the reaction occurs, the Fe 2+ ion in FeCl 2 is reduced to Fe, and the Mg is oxidized to Mg 2+.

21 Sample Exercise 4.10 Determining When an Oxidation-Reduction Reaction Can Occur Solve Because Mg is above Fe in the table, the reaction occurs. To write the formula for the salt produced in the reaction, we must remember the charges on common ions. Magnesium is always present in compounds as Mg 2+ ; the chloride ion is Cl. The magnesium salt formed in the reaction is MgCl 2, meaning the balanced molecular equation is Mg(s) + FeCl 2 (aq) MgCl 2 (aq) + Fe(s) Both FeCl 2 and MgCl 2 are soluble strong electrolytes and can be written in ionic form, which shows us that Cl is a spectator ion in the reaction. The net ionic equation is Mg(s) + Fe 2+ (aq) Mg 2+ (aq) + Fe(s) The net ionic equation shows that Mg is oxidized and Fe 2+ is reduced in this reaction. Check Note that the net ionic equation is balanced with respect to both charge and mass. Practice Exercise Which of the following metals will be oxidized by Pb(NO 3 ) 2 : Zn, Cu, Fe? Answer: Zn and Fe

22 Sample Exercise 4.11 Calculating Molarity Calculate the molarity of a solution made by dissolving 23.4 g of sodium sulfate (Na 2 SO 4 ) in enough water to form 125 ml of solution. Solution Analyze We are given the number of grams of solute (23.4 g), its chemical formula (Na 2 SO 4 ), and the volume of the solution (125 ml) and asked to calculate the molarity of the solution. Plan We can calculate molarity using Equation To do so, we must convert the number of grams of solute to moles and the volume of the solution from milliliters to liters. Solve The number of moles of Na 2 SO 4 is obtained by using its molar mass: Converting the volume of the solution to liters: Thus, the molarity is

23 Sample Exercise 4.11 Calculating Molarity Check Because the numerator is only slightly larger than the denominator, it is reasonable for the answer to be a little over 1 M. The units are appropriate for molarity, and three significant figures are appropriate for the answer because each of the initial pieces of data had three significant figures. Practice Exercise Calculate the molarity of a solution made by dissolving 5.00 g of glucose (C 6 H 12 O 6 ) in sufficient water to form exactly 100 ml of solution. Answer: M

24 Sample Exercise 4.12 Calculating Molar Concentrations of Ions What is the molar concentration of each ion present in a M aqueous solution of calcium nitrate? Solution Analyze We are given the concentration of the ionic compound used to make the solution and asked to determine the concentrations of the ions in the solution. Plan We can use the subscripts in the chemical formula of the compound to determine the relative ion concentrations. Solve Calcium nitrate is composed of calcium ions (Ca 2+ ) and nitrate ions (NO 3 ), so its chemical formula is Ca(NO 3 ) 2. Because there are two NO 3 ions for each Ca 2+ ion, each mole of Ca(NO 3 ) 2 that dissolves dissociates into 1 mol of Ca 2+ and 2 mol of NO 3. Thus, a solution that is M in Ca(NO 3 ) 2 is M in Ca 2+ and M = M in NO 3 : Check The concentration of NO 3 ions is twice that of Ca 2+ ions, as the subscript 2 after the NO 3 in the chemical formula Ca(NO 3 ) 2 suggests it should be. Practice Exercise What is the molar concentration of K + ions in a M solution of potassium carbonate? Answer: M

25 Sample Exercise 4.13 Using Molarity to Calculate Grams of Solute How many grams of Na 2 SO 4 are required to make L of M Na 2 SO 4? Solution Analyze We are given the volume of the solution (0.350 L), its concentration (0.500 M), and the identity of the solute Na 2 SO 4 and asked to calculate the number of grams of the solute in the solution. Plan We can use the definition of molarity (Equation 4.32) to determine the number of moles of solute, and then convert moles to grams using the molar mass of the solute. Solve Calculating the moles of Na 2 SO 4 using the molarity and volume of solution gives

26 Sample Exercise 4.13 Using Molarity to Calculate Grams of Solute Because each mole of Na 2 SO 4 has a mass of 142 g, the required number of grams of Na 2 SO 4 is Check The magnitude of the answer, the units, and the number of significant figures are all appropriate. Practice Exercise (a) How many grams of Na 2 SO 4 are there in 15 ml of 0.50 M Na 2 SO 4? (b) How many milliliters of 0.50 M Na 2 SO 4 solution are needed to provide mol of this salt? Answer: (a) 1.1 g, (b) 76 ml

27 Sample Exercise 4.14 Preparing a Solution by Dilution How many milliliters of 3.0 M H 2 SO 4 are needed to make 450 ml of 0.10 M H 2 SO 4? Solution Analyze We need to dilute a concentrated solution. We are given the molarity of a more concentrated solution (3.0 M) and the volume and molarity of a more dilute one containing the same solute (450 ml of 0.10 M solution). We must calculate the volume of the concentrated solution needed to prepare the dilute solution. Plan We can calculate the number of moles of solute, H 2 SO 4, in the dilute solution and then calculate the volume of the concentrated solution needed to supply this amount of solute. Alternatively, we can directly apply Equation Let s compare the two methods. Solve Calculating the moles of H 2 SO 4 in the dilute solution: Calculating the volume of the concentrated solution that contains mol H 2 SO 4 : Converting liters to milliliters gives 15 ml.

28 Sample Exercise 4.14 Preparing a Solution by Dilution If we apply Equation 4.34, we get the same result: Either way, we see that if we start with 15 ml of 3.0 M H 2 SO 4 and dilute it to a total volume of 450 ml, the desired 0.10 M solution will be obtained. Check The calculated volume seems reasonable because a small volume of concentrated solution is used to prepare a large volume of dilute solution. Comment The first approach can also be used to find the final concentration when two solutions of different concentrations are mixed, whereas the second approach, using Equation 4.34, can be used only for diluting a concentrated solution with pure solvent. Practice Exercise (a) What volume of 2.50 M lead(ii) nitrate solution contains mol of Pb 2+? (b) How many milliliters of 5.0 M K 2 Cr 2 O 7 solution must be diluted to prepare 250 ml of 0.10 M solution? (c) If 10.0 ml of a 10.0 M stock solution of NaOH is diluted to 250 ml, what is the concentration of the resulting stock solution? Answer: (a) L = 20.0 ml, (b) 5.0 ml, (c) 0.40 M

29 Sample Exercise 4.15 Using Mass Relations in a Neutralization Reaction How many grams of Ca(OH) 2 are needed to neutralize 25.0 ml of M HNO 3? Solution Analyze The reactants are an acid, HNO 3, and a base, Ca(OH) 2. The volume and molarity of HNO 3 are given, and we are asked how many grams of Ca(OH) 2 are needed to neutralize this quantity of HNO 3. Plan Following the steps outlined by the green arrows in Figure 4.18, we use the molarity and volume of the HNO 3 solution (substance B in Figure 4.18) to calculate the number of moles of HNO 3. We then use the balanced equation to relate moles of HNO 3 to moles of Ca(OH) 2 (substance A). Finally, we use the molar mass to convert moles to grams of Ca(OH)2: FIGURE 4.18 Procedure for solving stoichiometry problems involving reactions between a pure substance A and a solution containing a known concentration of substance B. Starting from a known mass of substance A, we follow the red arrows to determine either the volume of the solution containing B (if the molarity of B is known) or the molarity of the solution containing B (if the volume of B is known). Starting from either a known volume or known molarity of the solution containing B, we follow the green arrows to determine the mass of substance A.

30 Sample Exercise 4.15 Using Mass Relations in a Neutralization Reaction Solve The product of the molar concentration of a solution and its volume in liters gives the number of moles of solute: Because this is a neutralization reaction, HNO 3 and Ca(OH) 2 react to form H 2 O and the salt containing Ca 2+ and NO 3 : Thus, 2 mol HNO 3 mol Ca(OH) 2. Therefore, Check The answer is reasonable because a small volume of dilute acid requires only a small amount of base to neutralize it.

31 Sample Exercise 4.15 Using Mass Relations in a Neutralization Reaction Practice Exercise (a) How many grams of NaOH are needed to neutralize 20.0 ml of M H 2 SO 4 solution? (b) How many liters of M HCl(aq) are needed to react completely with mol of Pb(NO 3 ) 2 (aq), forming a precipitate of PbCl 2 (s)? Answer: (a) g, (b) L

32 Sample Exercise 4.16 Determining Solution Concentration by an Acid Base Titration One commercial method used to peel potatoes is to soak them in a NaOH solution for a short time, then remove them and spray off the peel. The NaOH concentration is normally 3 to 6 M, and the solution must be analyzed periodically. In one such analysis, 45.7 ml of M H 2 SO 4 is required to neutralize 20.0 ml of NaOH solution. What is the concentration of the NaOH solution? Solution Analyze We are given the volume (45.7 ml) and molarity (0.500 M) of an H 2 SO 4 solution (the standard solution) that reacts completely with 20.0 ml of NaOH solution. We are asked to calculate the molarity of the NaOH solution. Plan Following the steps of Figure 4.20, we use the H 2 SO 4 volume and molarity to calculate the number of moles of H 2 SO 4. Then we can use this quantity and the balanced equation for the reaction to calculate moles of NaOH. Finally, we can use moles of NaOH and the NaOH volume to calculate NaOH molarity. FIGURE 4.20 Procedure for determining the concentration of a solution from titration with a standard solution.

33 Sample Exercise 4.16 Determining Solution Concentration by an Acid Base Titration Solve The number of moles of H 2 SO 4 is the product of the volume and molarity of this solution: Acids react with metal hydroxides to form water and a salt. Thus, the balanced equation for the neutralization reaction is According to the balanced equation,. Therefore, Knowing the number of moles of NaOH in 20.0 ml of solution allows us to calculate the molarity of this solution:

34 Sample Exercise 4.16 Determining Solution Concentration by an Acid Base Titration Practice Exercise What is the molarity of an NaOH solution if 48.0 ml neutralizes 35.0 ml of M H 2 SO 4? Answer: M

35 Sample Exercise 4.17 Determining the Quantity of Solute by Titration The quantity of Cl in a municipal water supply is determined by titrating the sample with Ag +. The precipitation reaction taking place during the titration is Ag + (aq) + Cl (aq) AgCl(s) The end point in this type of titration is marked by a change in color of a special type of indicator. (a) How many grams of chloride ion are in a sample of the water if 20.2 ml of M Ag + is needed to react with all the chloride in the sample? (b) If the sample has a mass of 10.0 g, what percent Cl does it contain? Solution Analyze We are given the volume (20.2 ml) and molarity (0.100 M) of a solution of Ag + and the chemical equation for reaction of this ion with Cl.We are asked to calculate the number of grams of Cl in the sample and the mass percent of Cl in the sample. (a) Plan We can use the procedure outlined by the green arrows in Figure 4.18.We begin by using the volume and molarity of Ag + to calculate the number of moles of Ag + used in the titration. We then use the balanced equation to determine the moles of Cl in the sample and from that the grams of Cl. Solve

36 Sample Exercise 4.17 Determining the Quantity of Solute by Titration From the balanced equation we see that we have. Using this information and the molar mass of Cl, (b) Plan To calculate the percentage of Cl in the sample, we compare the number of grams of Cl in the sample, g, with the original mass of the sample, 10.0 g. Solve Comment Chloride ion is one of the most common ions in water and sewage. Ocean water contains 1.92% Cl. Whether water containing Cl tastes salty depends on the other ions present. If the only accompanying ions are Na +, a salty taste may be detected with as little as 0.03% Cl.

37 Sample Exercise 4.17 Determining the Quantity of Solute by Titration Practice Exercise A sample of an iron ore is dissolved in acid, and the iron is converted to Fe 2+. The sample is then titrated with ml of M MnO 4 solution. The oxidation-reduction reaction that occurs during titration is MnO 4 (aq) + 5 Fe 2+ (aq) + 8 H + (aq) Mn 2+ (aq) + 5 Fe 3+ (aq) + 4 H 2 O(l) (a) How many moles of MnO 4 were added to the solution? (b) How many moles of Fe 2+ were in the sample? (c) How many grams of iron were in the sample? (d) If the sample had a mass of g, what is the percentage of iron in the sample? Answer: (a) mol MnO 4, (b) mol Fe 2+, (c) g, (d) 33.21%

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