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16.4 Calculations Involving Colligative Properties 16.4 chem_TE_ch16.fm Page 491 Tuesday, April 18, 2006 11:27 AM 16.4 Calculations Involving Colligative Properties 16.4 1 FOCUS Connecting to Your World Cooking instructions for a wide Guide for Reading variety of foods, from dried pasta to packaged beans to frozen fruits to Objectives fresh vegetables, often call for the addition of a small amount of salt to the Key Concepts • What are two ways of 16.4.1 Solve problems related to the cooking water. Most people like the flavor of expressing the concentration food cooked with salt. But adding salt can of a solution? molality and mole fraction of a have another effect on the cooking pro- • How are freezing-point solution cess. Recall that dissolved salt elevates depression and boiling-point elevation related to molality? 16.4.2 Describe how freezing-point the boiling point of water. Suppose you Vocabulary depression and boiling-point added a teaspoon of salt to two liters of molality (m) elevation are related to water. A teaspoon of salt has a mass of mole fraction molality. about 20 g. Would the resulting boiling molal freezing-point depression K point increase be enough to shorten constant ( f) the time required for cooking? In this molal boiling-point elevation Guide to Reading constant (K ) section, you will learn how to calculate the b amount the boiling point of the cooking Reading Strategy Build Vocabulary L2 water would rise. Before you read, make a list of the vocabulary terms above. As you Graphic Organizers Use a chart to read, write the symbols or formu- las that apply to each term and organize the definitions and the math- Molality and Mole Fraction describe the symbols or formulas ematical formulas associated with each using words. Recall that colligative properties depend only upon solute concentration. vocabulary term. The unit molality and mole fractions are two additional ways in which chemists express the concentration of a solution. The unit molality (m) is the Reading Strategy L2 number of moles of solute dissolved in 1 kilogram (1000 g) of solvent. Preview Have students preview this Molality is also known as molal concentration. section by reading the key concepts and skimming the headings, visuals, Molality ϭ moles of solute kilogram of solvent and boldfaced materials. Note that molality is not the same as molarity. Molality refers to moles of solute per kilogram of solvent rather than moles of solute per liter of solu- 2 tion. In the case of water as the solvent, 1 kg or 1000 g equals a volume of INSTRUCT 0.500 mol 1000 mL, or 1 L. (29.3 g) You can prepare a solution that is 1.00 molal (1m) in glucose, for exam- NaCl ple, by adding 1.00 mol (180 g) of glucose to 1000 g of water. Figure 16.17 shows how a 0.500 molal (0.500m) solution in sodium chloride is prepared Ask, What effect does adding salt by dissolving 0.500 mol (29.3 g) of NaCl in 1.000 kg (1000 g) of water. have on the cooking process? (Add- ing salt increases the boiling point of the cooking water.) Ask, Do you think the resulting boiling point increase m Figure 16.17 To make a 0.500 solution 1.000 kg would be enough to significantly of NaCl, use a balance to measure 1.000 kg H2O of water and add 0.500 mol (29.3 g) NaCl. shorten the time required for Calculating What would be the molality cooking? (Students are likely to predict, if only 0.500 kg of water were used? correctly, that the change would be neg- ligible.) Section 16.4 Calculations Involving Colligative Properties 491 Molality and Mole Fraction Use Visuals L1 Section Resources Figure 16.17 Display the figure on an Print Technology overhead projector. Ask students to •Guided Reading and Study Workbook, •Interactive Textbook with ChemASAP, write the definition of molality in their Section 16.4 Problem-Solving 16.29, 16.31, 16.33, notebooks. Show the step-by-step pro- •Core Teaching Resources, Section 16.3 16.36; Simulation 21; Assessment 16.4 cedure a chemist would use to prepare Review a 0.500m solution of NaCl. Have stu- •Transparencies, T177–T179 dents confirm your calculations and the •Laboratory Manual, Lab 33 data given in the figure. Answers to... Figure 16.17 1.00m Solutions 491 A ؉ B 5.25 mol؍؍ mol Total moles 4.00 H O Section 16.4 (continued) Figure 16.18 Ethylene 1.25 mol 2 EG A 1.25 ؍ ؍ glycol (EG) is added to B Mole fraction EG water as antifreeze in the A ؉ B 5.25 A proportions shown. A mole Sample Problem 16.6 B 4.00 ؍ fraction is the ratio of the ؍ Mole fraction H2O Answers number of moles of one A ؉ B 5.25 substance to the total 29. 750 g water × 0.400 mol NaF / number of moles of all 1000 g water × 42.0 g NaF / substances in the solution. SAMPLE PROBLEM 16.6 × 1 Inferring What is the sum 1 mol NaF = 1.26 10 g NaF of all mole fractions in a Using Solution Molality × solution? 30. 10.0 g NaCl / 600 g water 1 mol How many grams of potassium iodide must be dissolved in 500.0 g of NaCl / 58.5 g NaCl × 1000 g water/ water to produce a 0.060 molal KI solution? 1 kg water = 2.85 × 10−1m NaCl Analyze List the knowns and the unknown. Practice Problems Plus L2 Knowns Unknown ϭ ϭ ϭ How many grams of lithium bromide • mass of water 500.0g 0.5000 kg • mass of solute ? g KI • solution concentration ϭ 0.060m must be dissolved in 444 g of water • molar mass KI ϭ 166.0 g/mol to prepare a 0.140m LiBr solution? According to the definition of molal, the final solution must contain (5.40 g LiBr) 0.060 mol KI per 1000 g H2O. Use the molality as a conversion factor to convert from mass of water to moles of the solute (KI). Then use the Discuss L2 molar mass of KI to convert from mol KI to g KI. The steps are ¡ ¡ Write the expressions defining molar- mass of H2O mol KI g KI. ity and molality on the board. Compare Calculate Solve for the unknown. the chemical quantities in each expres- Math Handbook ϫ 0.060 mol KI ϫ 166.0 g KI ϭ sion. Point out that molarity is denoted 0.5000 kg H2O 5.0 g KI For help with dimensional 1.000 kg H2O 1 mol KI by M and molality by m. Explain that analysis, go to page R66. the molality of a solution does not vary Evaluate Does the result make sense? with temperature because the mass of A 1 molal KI solution is one molar mass of KI (166.0 g) dissolved in 1000 g of water. The desired molal concentration (0.060m) is about 1 the solvent does not change. In con- 20 of that value, so the mass of KI should be much less than the molar trast, the molarity of a solution does mass. The answer is correctly expressed to two significant figures. vary with temperature because the liq- uid can expand and contract. When Practice Problems studying colligative properties such as 29. How many grams of sodium 30. Calculate the molality of a boiling-point elevation and freezing- Problem-Solving 16.29 Solve fluoride are needed to prepare solution prepared by dissolv- point depression, it is preferable to use Problem 29 with the help of an a 0.400m NaF solution that ing 10.0 g NaCl in 600 g of interactive guided tutorial. a concentration that does not depend contains 750 g of water? water. withChemASAP on temperature. The concentration of a solution also can be expressed as a mole frac- tion, as shown in Figure 16.18. The mole fraction of a solute in a solution is Math Handbook the ratio of the moles of that solute to the total number of moles of solvent n n and solute. In a solution containing A mol of solute A and B mol of solvent For a math refresher and practice, X X B, the mole fraction of solute A ( A) and the mole fraction of solvent B ( B) direct students to dimensional can be expressed as follows. analysis, page R66. n n X ϭ A X ϭ B A n + n B n + n A B A B Checkpoint What is a mole fraction? 492 Chapter 16 Differentiated Instruction Facts and Figures Less Proficient Readers L1 Mole Fraction Uses Have students write sentences using the Explain that the mole fraction compares the words molarity and molality, and have number of moles of a solute to the total them circle the letter in each word that number of moles in the solution. Organic makes them distinct. The mnemonic, ‘r’ for chemists, who frequently work with non- molarity and liter may help. aqueous solvent systems, often use this method of expressing concentration. The mole fraction is also used when calculating the vapor pressure of a solution. 492 Chapter 16 chem_TE_ch16.fm Page 493 Friday, April 15, 2005 12:17 PM SAMPLE PROBLEM 16.7 Figure 16.19 The concentration of Sample Problem 16.7 antifreeze used in an automobile cooling system can be described Calculating Mole Fractions by mole fractions. Answers Ethylene glycol (C H O ) is added to automobile cooling systems to 31. X = 0.190; X = 0.810 2 6 2 C2H5OH H2O protect against cold weather.
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