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Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Chapter 3 Stoichiometry of Formulas and Equations ั ันธ์ของสูตรและสมการ ปริมาณสมพ 3-1 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Mole - Mass Relationships in Chemical Systems 3.1 The Mole 3.2 Determining the Formula of an Unknown Compound 3.3 Writing and Balancing Chemical Equations 3.4 Calculating the Amounts of Reactant and Product 3.5 Fundamentals of Solution Stoichiometry 3-2 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. mole(mol) - the amount of a substance that contains the same number of entities as there are atoms in exactly 12 g of carbon-12. This amount is 6.022x1023. The number is called Avogadro’s number and is abbreviated as N. One mole (1 mol) contains 6.022x1023 entities (to four significant figures) 3-3 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 3.1 Counting objects of fixed relative mass. 12 red marbles @ 7g each = 84g 12 yellow marbles @4g each=48g 3-4 55.85g Fe = 6.022 x 1023 atoms Fe 32.07g S = 6.022 x 1023 atoms S Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 3.2 Oxygen 32.00 g One mole of common substances. CaCO3 100.09 g Water 18.02 g Copper 63.55 g 3-5 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Table 3.1 Term Summary of Mass Terminology Definition Isotopic mass Mass of an isotope of an element Atomic mass Average of the masses of the naturally occurring isotopes of an element weighted according to their abundance (also called atomic weight) Molecular (or formula) mass (also called molecular weight) Sum of the atomic masses of the atoms (or ions) in a molecule (or formula unit) Molar mass (M) Mass of 1 mole of chemical entities (atoms, ions, molecules, formula units) (also called gram-molecular weight) 3-6 Unit amu amu amu g/mol Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Information Contained in the Chemical Formula of Glucose C6H12O6 ( M = 180.16 g/mol) Table 3.2 Carbon (C) Hydrogen (H) Oxygen (O) Atoms/molecule of compound 6 atoms 12 atoms 6 atoms Moles of atoms/ mole of compound 6 moles of atoms 12 moles of atoms 6 moles of atoms Atoms/mole of compound 6(6.022 x 1023) atoms 12(6.022 x 1023) atoms 6(6.022 x 1023) atoms Mass/molecule of compound 6(12.01 amu) =72.06 amu 12(1.008 amu) =12.10 amu 6(16.00 amu) =96.00 amu 72.06 g 12.10 g 96.00 g Mass/mole of compound 3-7 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Interconverting Moles, Mass, and Number of Chemical Entities no. of grams Mass (g) = no. of moles x g 1 mol 1 mol No. of moles = mass (g) x no. of grams No. of entities = no. of moles x 6.022x1023 entities 1 mol 1 mol No. of moles = no. of entities x 6.022x1023 entities 3-8 M Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Summary of the mass-mole-number relationships for elements. Figure 3.3 MASS(g) of element M (g/mol) AMOUNT(mol) of element Avogadro’s number (atoms/mol) 3-9 ATOMS of element Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 3.1 PROBLEM: Calculating the Mass and the Number of Atoms in a Given Number of Moles of an Element (a) Silver (Ag) is used in jewelry and tableware but no longer in U.S. coins. How many grams of Ag are in 0.0342 mol of Ag? (b) Iron (Fe), the main component of steel, is the most important metal in industrial society. How many Fe atoms are in 95.8 g of Fe? PLAN: (a) To convert mol of Ag to g we have to use the #g Ag/mol Ag, the molar mass M. SOLUTION: 0.0342 mol Ag x 107.9 g Ag = 3.69 g Ag mol Ag PLAN: (b) To convert g of Fe to atoms we first have to find the #mols of Fe and then convert mols to atoms. mol Fe SOLUTION: 95.8g Fe x = 1.72 mol Fe 55.85g Fe 6.022x1023atoms Fe 1.72mol Fe x mol Fe 3-10 = 1.04x1024 atoms Fe amount(mol) of Ag multiply by M of Ag (107.9g/mol) mass(g) of Ag mass(g) of Fe divide by M of Fe (55.85g/mol) amount(mol) of Fe multiply by 6.022x1023 atoms/mol atoms of Fe Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Summary of the mass-mole-number relationships for compounds. Figure 3.3 MASS(g) of compound M (g/mol) chemical formula AMOUNT(mol) of compound Avogadro’s number (molecules/mol) MOLECULES (or formula units) of compound 3-11 AMOUNT(mol) of elements in compound Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 3.2 PROBLEM: Calculating the Moles and Number of Formula Units in a Given Mass of a Compound Ammonium carbonate is white solid that decomposes with warming. Among its many uses, it is a component of baking powder, first extinguishers, and smelling salts. How many formula unit are in 41.6 g of ammonium carbonate? PLAN: After writing the formula for the compound, we find its M by adding the masses of the elements. Convert the given mass, 41.6 g to mols using M and then the mols to formula units with Avogadro’s number. SOLUTION: The formula is (NH4)2CO3. mass(g) of (NH4)2CO3 divide by M amount(mol) of (NH4)2CO3 multiply by 6.022x1023 formula units/mol number of (NH4)2CO3 formula units M = (2 x 14.01 g/mol N)+(8 x 1.008 g/mol H) +(12.01 g/mol C)+(3 x 16.00 g/mol O) = 96.09 g/mol 41.6 g (NH4)2CO3 x 3-12 mol (NH4)2CO3 96.09 g (NH4)2CO3 = x 6.022x1023 formula units (NH4)2CO3 mol (NH4)2CO3 2.61x1023 formula units (NH4)2CO3 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Mass percent from the chemical formula Mass % of element X = atoms of X in formula x atomic mass of X (amu) x 100 molecular (or formula) mass of compound (amu) Mass % of element X = moles of X in formula x molar mass of X (amu) molecular (or formula) mass of compound (amu) 3-13 x 100 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 3.3 Calculating the Mass Percents and Masses of Elements in a Sample of Compound PROBLEM: Glucose (C6H12O6) is the most important nutrient in the living cell for generating chemical potential energy. (a) What is the mass percent of each element in glucose? (b) How many grams of carbon are in 16.55g of glucose? PLAN: We have to find the total mass of glucose and the masses of the constituent elements in order to relate them. SOLUTION: (a) Per mole glucose there are 6 moles of C 12 moles H 6 moles O amount(mol) of element X in 1mol compound multiply by M (g/mol) of X mass(g) of X in 1mol of compound divide by mass(g) of 1mol of compound mass fraction of X multiply by 100 mass % X in compound 3-14 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 3.3 Calculating the Mass Percents and Masses of Elements in a Sample of Compound continued 1.008 g H 12.01 g C 6 mol C x mol C 12 mol H x = 72.06 g C mol H 16.00 g O 6 mol O x = 12.096 g H = 96.00 g O M = 180.16 g/mol mol O (b) mass percent of C = 72.06 g C 180.16 g glucose = 0.3999 x 100 = 39.99 mass %C 12.096 g H mass percent of H = mass percent of O = 3-15 180.16 g glucose 96.00 g O 180.16 g glucose = 0.06714 x 100 = 6.714 mass %H = 0.5329 x 100 = 53.29 mass %O Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Empirical and Molecular Formulas Empirical Formula The simplest formula for a compound that agrees with the elemental analysis and gives rise to the smallest set of whole numbers of atoms. Molecular Formula The formula of the compound as it exists, it may be a multiple of the empirical formula. 3-16 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 3.4 Determining the Empirical Formula from Masses of Elements PROBLEM: Elemental analysis of a sample of an ionic compound showed 2.82 g of Na, 4.35 g of Cl, and 7.83 g of O. What are the empirical formula and name of the compound? PLAN: Once we find the relative number of moles of each element, we can divide by the lowest mol amount to find the relative mol ratios (empirical formula). mol Na SOLUTION: 2.82 g Na x = 0.123 mol Na 22.99 g Na mass(g) of each element divide by M(g/mol) amount(mol) of each element use # of moles as subscripts mol Cl 4.35 g Cl x 35.45 g Cl = 0.123 mol Cl mol O 7.83 g O x 16.00 g O = 0.489 mol O preliminary formula change to integer subscripts empirical formula 3-17 Na1 Cl1 O3.98 NaClO4 NaClO4 is sodium perchlorate. Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 3.5 Determining a Molecular Formula from Elemental Analysis and Molar Mass PROBLEM: During physical activity. lactic acid (M = 90.08 g/mol) forms in muscle tissue and is responsible for muscle soreness. Elemental analysis shows that this compound contains 40.0 mass% C, 6.71 mass% H, and 53.3 mass% O. (a) Determine the empirical formula of lactic acid. (b) Determine the molecular formula. PLAN: assume 100g lactic acid and find the mass of each element divide each mass by mol mass(M) amount(mol) of each element molecular formula use # mols as subscripts preliminary formula convert to integer subscripts empirical formula 3-18 divide mol mass by mass of empirical formula to get a multiplier Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 3.5 Determining a Molecular Formula from Elemental Analysis and Molar Mass continued SOLUTION: Assuming there are 100 g of lactic acid, the constituents are 40.0 g C x mol C 12.01g C = 3.33 mol C C3.33 3.33 6.71 g H x mol H 53.3 g O x 1.008 g H 16.00 g O = 6.66 mol H = 3.33 mol O H6.66 O3.33 3.33 3.33 molar mass of lactate CH2O empirical formula 90.08 g 3 mass of CH2O 3-19 mol O 30.03 g C3H6O3 is the molecular formula Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 3.4 Combustion train for the determination of the chemical composition of organic compounds. m m CnHm + (n+ ) O2 = n CO(g) + H O(g) 2 2 2 3-20 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 3.6 PROBLEM: Determining a Molecular Formula from Combustion Analysis Vitamin C (M=176.12g/mol) is a compound of C,H, and O found in many natural sources especially citrus fruits. When a 1.000-g sample of vitamin C is placed in a combustion chamber and burned, the following data are obtained: mass of CO2 absorber after combustion = 85.35g mass of CO2 absorber before combustion = 83.85g mass of H2O absorber after combustion = 37.96g mass of H2O absorber before combustion = 37.55g What is the molecular formula of vitamin C? PLAN: difference (after-before) = mass of oxidized element find the mass of each element in its combustion product 3-21 find the mols preliminary formula empirical formula molecular formula Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 3.6 Determining a Molecular Formula from Combustion Analysis continued SOLUTION: CO2 85.35 g - 83.85 g = 1.50 g H2O 37.96 g - 37.55 g = 0.41 g 12.01 g CO2 1.50 g CO 2 x There are 12.01 g C per mol CO2 = 0.409 g C 44.01 g CO2 There are 2.016 g H per mol H2O 0.41 g H2O x 2.016 g H2O = 0.046 g H 18.02 g H2O O must be the difference: 0.409 g C = 0.0341 mol C 12.01 g C C1H1.3O1 3-22 1.000 g - (0.409 + 0.046) = 0.545 0.046 g H = 0.0456 mol H 16.00 g O 1.008 g H C3H4O3 0.545 g O 176.12 g/mol = 2.000 88.06 g Molecular formular = C6H8O6 = 0.0341 mol O Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Table 3.3 Some Compounds with Empirical Formula CH2O (Composition by Mass: 40.0% C, 6.71% H, 53.3% O) M (g/mol) Molecular Formula Whole-Number Multiple formaldehyde CH2O 1 30.03 disinfectant; biological preservative acetic acid C2H4O2 2 60.05 acetate polymers; vinegar (5%soln) lactic acid C3H6O3 3 90.09 sour milk; forms in exercising muscle erythrose C4H8O4 4 120.10 part of sugar metabolism ribose C5H10O5 5 150.13 component of nucleic acids and B2 glucose C6H12O6 6 180.16 major energy source of the cell Name CH2O 3-23 C2H4O2 C3H6O3 C4H8O4 Use or Function C5H10O5 C6H12O6 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Table 3.4 Two Pairs of Constitutional Isomers C4H10 Property Butane C2H6O 2-Methylpropane Ethanol Dimethyl Ether M(g/mol) 58.12 58.12 46.07 46.07 Boiling Point -0.50C -11.060C 78.50C -250C Density at 200C 0.579 g/mL 0.549 g/mL (gas) (gas) Structural formulas H H H H H H C C C C H H H H H C C C C H H H H H H H H Space-filling models 3-24 0.789 g/mL 0.00195 g/mL (liquid) (gas) H H C C H H H H H H OH H C H O C H H Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The formation of HF gas on the macroscopic and molecular levels. Figure 3.6 3-25 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 3.7 3-26 A three-level view of the chemical reaction in a flashbulb. Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. translate the statement balance the atoms adjust the coefficients check the atom balance specify states of matter 3-27 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 3.7 PROBLEM: PLAN: Balancing Chemical Equations Within the cylinders of a car’s engine, the hydrocarbon octane (C8H18), one of many components of gasoline, mixes with oxygen from the air and burns to form carbon dioxide and water vapor. Write a balanced equation for this reaction. SOLUTION: translate the statement C8H18 + balance the atoms adjust the coefficients check the atom balance O2 3-28 H2O C8H18 + 25/2 O2 8 CO2 + 9 H2O 2C8H18 + 25O2 16CO2 + 18H2O 2C8H18 + 25O2 16CO2 + 18H2O 2C8H18(l) + 25O2 (g) specify states of matter CO2 + 16CO2 (g) + 18H2O (g) Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 3.8 Summary of the mass-mole-number relationships in a chemical reaction. MASS(g) of compound A MASS(g) of compound B M (g/mol) of compound A AMOUNT(mol) of compound A molar ratio from balanced equation Avogadro’s number (molecules/mol) MOLECULES (or formula units) of compound A 3-29 M (g/mol) of compound B AMOUNT(mol) of compound B Avogadro’s number (molecules/mol) MOLECULES (or formula units) of compound B Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 3.8 Calculating Amounts of Reactants and Products PROBLEM: In a lifetime, the average American uses 1750 lb(794 g) of copper in coins, plumbing, and wiring. Copper is obtained from sulfide ores, such as chalcocite, or copper(I) sulfide, by a multistep process. After an initial grinding, the first step is to “roast” the ore (heat it strongly with oxygen gas) to form powdered copper(I) oxide and gaseous sulfur dioxide. (a) How many moles of oxygen are required to roast 10.0 mol of copper(I) sulfide? (b) How many grams of sulfur dioxide are formed when 10.0 mol of copper(I) sulfide is roasted? (c) How many kilograms of oxygen are required to form 2.86 kg of copper(I) oxide? PLAN: write and balance equation find mols O2 3-30 find mols SO2 find mols Cu2O find g SO2 find mols O2 find kg O2 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 3.8 Calculating Amounts of Reactants and Products continued SOLUTION: 2Cu2S(s) + 3O2(g) 2Cu2O(s) + 2SO2(g) (a) How many moles of oxygen are required to roast 10.0 mol of copper(I) sulfide? 3mol O2 (a) 10.0mol Cu2S x = 15.0mol O2 2mol Cu2S (b) How many grams of sulfur dioxide are formed when 10.0 mol of copper(I) sulfide is roasted? (b) 10.0mol Cu2S x 2mol SO2 x 64.07g SO2 2mol Cu2S mol SO2 = 641g SO2 (c) How many kilograms of oxygen are required to form 2.86 kg of copper(I) oxide? 3 (c) 2.86kg Cu2O x 10 g Cu2O x mol Cu2O = 20.0mol Cu2O kg Cu2O 143.10g Cu2O 20.0mol Cu2O x 3-31 3mol O2 x 2mol Cu2O 32.00g O2 mol O2 x kg O2 103g O2 = 0.959kg O2 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 3.9 PROBLEM: Writing an Overall Equation for a Reaction Sequence Roasting is the first step in extracting copper from chalcocite, the ore used in the previous problem. In the next step, copper(I) oxide reacts with powdered carbon to yield copper metal and carbon monoxide gas. Write a balanced overall equation for the two-step process. PLAN: SOLUTION: write balanced equations for each step 2Cu2S(s) + 3O2(g) cancel reactants and products common to both sides of the equations 2Cu2O(s) + 2C(s) sum the equations 3-32 2Cu2S(s)+3O2(g)+2C(s) 2Cu2O(s) + 2SO2(g) 4Cu(s) + 2CO(g) 4Cu(s)+2SO2(g)+2CO(g) Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 3.10 3-33 An ice cream sundae analogy for limiting reactions. Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Table 3.5 Information Contained in a Balanced Equation Viewed in Terms of Reactants C3H8(g) + 5O2(g) molecules 1 molecule C3H8 + 5 molecules O2 amount (mol) 1 mol C3H8 + 5 mol O2 mass (amu) 44.09 amu C3H8 + 160.00 amu O2 mass (g) total mass (g) 3-34 44.09 g C3H8 + 160.00 g O2 204.09 g Products 3CO2(g) + 4H2O(g) 3 molecules CO2 + 4 molecules H2O 3 mol CO2 + 4 mol H2O 132.03 amu CO2 + 72.06 amu H2O 132.03 g CO2 + 72.06 g H2O 204.09 g Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 3.10 PROBLEM: Using Molecular Depictions to Solve a LimitingReactant Problem Nuclear engineers use chlorine trifluoride in the processing of uranium fuel for power plants. This extremely reactive substance is formed as a gas in special metal containers by the reaction of elemental chlorine and fluorine. (a) Suppose the box shown at left represents a container of the reactant mixture before the reaction occurs (with chlorine colored green). Name the limiting reactant, and draw the container contents after the reaction is complete. (b) When the reaction is run again with 0.750 mol of Cl2 and 3.00 mol of F2, what mass of chlorine trifluoride will be prepared? PLAN: Write a balanced chemical equation. Compare the number of molecules you have to the number needed for the products. Determine the reactant that is in excess. The other reactant is the limiting reactant. 3-35 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 3.10 Using Molecular Depictions to Solve a LimitingReactant Problem continued SOLUTION: Cl2(g) + 3F2(g) 2ClF3(g) (a) You need a ratio of 2 Cl and 6 F for the reaction. You have 6 Cl and 12 F. 6 Cl would require 18 F. 12 F need only 4 Cl (2 Cl2 molecules). There isn’t enough F, therefore it must be the limiting reactant. F2 Cl2 You will make 4 ClF2 molecules (4 Cl, 12 F) and have 2 Cl2 molecules left over. (b) We know the molar ratio of F2/Cl2 should be 3/1. 3.00 mol F2 0.750 mol Cl2 4 = 1 Since we find that the ratio is 4/1, that means F2 is in excess and Cl2 is the limiting reactant. 0.750 mol Cl2 x 2 mol ClF3 x 92.5 g ClF3 = 1 mol Cl 1 mol ClF3 3-36 139 g ClF3 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 3.11 PROBLEM: Calculating Amounts of Reactant and Product in Reactions Involving a Limiting Reactant A fuel mixture used in the early days of rocketry is composed of two liquids, hydrazine(N2H4) and dinitrogen tetraoxide(N2O4), which ignite on contact to form nitrogen gas and water vapor. How many grams of nitrogen gas form when 1.00x102 g of N2H4 and 2.00x102 g of N2O4 are mixed? PLAN: We always start with a balanced chemical equation and find the number of mols of reactants and products which have been given. In this case one of the reactants is in molar excess and the other will limit the extent of the reaction. mass of N2H4 mass of N2O4 divide by M mol of N2H4 multiply by M mol of N2O4 molar ratio mol of N2 3-37 limiting mol N2 mol of N2 g N2 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 3.11 Calculating Amounts of Reactant and Product in Reactions Involving a Limiting Reactant continued SOLUTION: 2 N2H4(l) + N2O4(l) mol N2H4 1.00x102g N2H4 x 32.05g N2H4 3 mol N2 3.12mol N2H4 x = 3.12 mol N2H4 N2O4 x 4.68mol N2 x mol N2O4 92.02g N2O4 2.17mol N2O4 x 3 mol N2 mol N2O4 3-38 N2H4 is the limiting reactant because it produces less product, N2, than does N2O4. = 4.68mol N2 2mol N2H4 2.00x102g 3 N2(g) + 4 H2O(l) = 2.17mol N2O4 = 6.51mol N2 28.02g N2 mol N2 = 131g N2 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 3.11 The effect of side reactions on yield. A +B C (reactants) (main product) D (side products) 3-39 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 3.12 Calculating Percent Yield PROBLEM: Silicon carbide (SiC) is an important ceramic material that is made by allowing sand(silicon dioxide, SiO2) to react with powdered carbon at high temperature. Carbon monoxide is also formed. When 100.0 kg of sand is processed, 51.4 kg of SiC is recovered. What is the percent yield of SiC from this process? PLAN: SOLUTION: write balanced equation SiO2(s) + 3C(s) SiC(s) + 2CO(g) 103 g SiO2 mol SiO2 x = 1664 mol SiO2 100.0 kg SiO x 2 find mol reactant & product kg SiO2 60.09 g SiO2 mol SiO2 = mol SiC = 1664 find g product predicted 1664 mol SiC x mol SiC actual yield/theoretical yield x 100 percent yield 51.4 kg 66.73 kg 3-40 40.10 g SiC x 100 x =77.0% kg 103g = 66.73 kg Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 3.13 PROBLEM: PLAN: Calculating the Molarity of a Solution Glycine (H2NCH2COOH) is the simplest amino acid. What is the molarity of an aqueous solution that contains 0.715 mol of glycine in 495 mL? Molarity is the number of moles of solute per liter of solution. mol of glycine divide by volume concentration(mol/mL) glycine 103mL = 1L molarity(mol/L) glycine 3-41 SOLUTION: 0.715 mol glycine 495 mL soln x 1000mL 1L = 1.44 M glycine Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 3.12 Summary of mass-mole-number-volume relationships in solution. MASS (g) of compound in solution M (g/mol) AMOUNT (mol) of compound in solution Avogadro’s number (molecules/mol) MOLECULES (or formula units) of compound in solution 3-42 M (g/mol) VOLUME (L) of solution Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 3.14 A “buffered” solution maintains acidity as a reaction occurs. In living cells phosphate ions play a key buffering role, so biochemistry often study reactions in such solutions. How many grams of solute are in 1.75 L of 0.460 M sodium monohydrogen phosphate? PROBLEM: PLAN: volume of soln Calculating Mass of Solute in a Given Volume of Solution Molarity is the number of moles of solute per liter of solution. Knowing the molarity and volume leaves us to find the # moles and then the # of grams of solute. The formula for the solute is Na2HPO4. multiply by M moles of solute SOLUTION: 1.75 L x 0.460 moles 1L multiply by M grams of solute 3-43 0.805 mol Na2HPO4 x = 0.805 mol Na2HPO4 141.96 g Na2HPO4 mol Na2HPO4 = 114 g Na2HPO4 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 3.12 Laboratory preparation of molar solutions. A •Weigh the solid needed. •Transfer the solid to a volumetric flask that contains about half the final volume of solvent. 3-44 C Add solvent until the solution reaches its final volume. B Dissolve the solid thoroughly by swirling. Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 3.13 3-45 Converting a concentrated solution to a dilute solution. Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 3.14 PROBLEM: Preparing a Dilute Solution from a Concentrated Solution “Isotonic saline” is a 0.15 M aqueous solution of NaCl that simulates the total concentration of ions found in many cellular fluids. Its uses range from a cleaning rinse for contact lenses to a washing medium for red blood cells. How would you prepare 0.80 L of isotomic saline from a 6.0 M stock solution? PLAN: It is important to realize the number of moles of solute does not change during the dilution but the volume does. The new volume will be the sum of the two volumes, that is, the total final volume. MdilxVdil = #mol solute = MconcxVconc volume of dilute soln multiply by M of dilute solution moles of NaCl in dilute soln = mol NaCl in concentrated soln divide by M of concentrated soln L of concentrated soln 3-46 SOLUTION: 0.80 L soln x 0.15 mol NaCl = 0.12 mol NaCl L soln 0.12 mol NaCl x L solnconc = 0.020 L soln 6 mol Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 3.15 Calculating Amounts of Reactants and Products for a Reaction in Solution PROBLEM: Specialized cells in the stomach release HCl to aid digestion. If they release too much, the excess can be neutralized with antacids. A common antacid contains magnesium hydroxide, which reacts with the acid to form water and magnesium chloride solution. As a government chemist testing commercial antacids, you use 0.10M HCl to simulate the acid concentration in the stomach. How many liters of “stomach acid” react with a tablet containing 0.10g of magnesium hydroxide? PLAN: Write a balanced equation for the reaction; find the grams of Mg(OH)2; determine the mol ratio of reactants and products; use mols to convert to molarity. L HCl mass Mg(OH)2 divide by M mol Mg(OH)2 mol HCl mol ratio 3-47 divide by M Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 3.15 Calculating Amounts of Reactants and Products for a Reaction in Solution continued SOLUTION: Mg(OH)2(s) + 2HCl(aq) 0.10g Mg(OH)2 x 1.7x10-3 mol Mg(OH)2 58.33g Mg(OH)2 mol Mg(OH)2 x MgCl2(aq) + 2H2O(l) = 1.7x10-3 mol Mg(OH)2 2 mol HCl = 3.4x10-3 mol HCl 1 mol Mg(OH)2 3.4x10-3 mol HCl x 1L 0.10mol HCl 3-48 = 3.4x10-2 L HCl Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 3.16 PROBLEM: PLAN: 3-49 Solving Limiting-Reactant Problems for Reactions in Solution Mercury and its compounds have many uses, from fillings for teeth (as an alloy with silver, copper, and tin) to the industrial production of chlorine. Because of their toxicity, however, soluble mercury compounds, such mercury(II) nitrate, must be removed from industrial wastewater. One removal method reacts the wastewater with sodium sulfide solution to produce solid mercury(II) sulfide and sodium nitrate solution. In a laboratory simulation, 0.050L of 0.010M mercury(II) nitrate reacts with 0.020L of 0.10M sodium sulfide. How many grams of mercury(II) sulfide form? As usual, write a balanced chemical reaction. Since this is a problem concerning a limiting reactant, we proceed as we would for a limiting reactant problem. Find the amount of product which would be made from each reactant. Then choose the reactant that gives the lesser amount of product. Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 3.16 Solving Limiting-Reactant Problems for Reactions in Solution continued SOLUTION: Hg(NO3)2(aq) + Na2S(aq) L of Hg(NO3)2 0.050 L Hg(NO3)2 multiply by M mol Hg(NO3)2 x mol ratio mol HgS HgS(s) + 2NaNO3(aq) 0.020 L Hg(NO3)2 x 0.010 mol/L x 0.10 mol/L multiply by M 1 mol HgS 1 mol HgS 1 mol Hg(NO3)2 = 5.0x10-4 mol HgS x 1 mol Na2S = 2.0x10-3 mol HgS Hg(NO3)2 is the limiting reagent. 5.0x10-4 3-50 mol HgS x L of Na2S 232.7g HgS 1 mol HgS = 0.12 g HgS mol Na2S mol ratio mol HgS Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 3.15 3-51 An overview of the key mass-mole-number stoichiometry relationships.