# 1 Chapter 7 Solutions 7.5 Molarity and Dilution Copyright © 2009 by Pearson Education, Inc.

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1 Chapter 7 Solutions 7.5 Molarity and Dilution Copyright © 2009 by Pearson Education, Inc.

2 Molarity (M) is a concentration term for solutions. gives the moles of solute in 1 L of solution. moles of solute liter of solution

3 Preparing a 1.0 Molar Solution A 1.00 M NaCl solution is prepared by weighing out 58.5 g of NaCl (1.00 mole) and adding water to make 1.00 liter of solution. Copyright © 2009 by Pearson Education, Inc.

4 What is the molarity of 0.500 L of NaOH solution if it contains 6.00 g of NaOH? STEP 1: Given 6.00 g of NaOH in 0.500 L of solution Need molarity (mole/L) STEP 2: Plan g NaOH mole NaOH molarity Calculation of Molarity

5 Calculation of Molarity (continued) STEP 3: Conversion factors 1 mole of NaOH = 40.0 g of NaOH 1 mole NaOH and 40.0 g NaOH 40.0 g NaOH 1 mole NaOH STEP 4: Calculate molarity. 6.00 g NaOH x 1 mole NaOH = 0.150 mole 40.0 g NaOH 0.150 mole = 0.300 mole = 0.300 M NaOH 0.500 L 1 L

6 What is the molarity of 325 mL of a solution containing 46.8 g of NaHCO 3 ? 1) 0.557 M 2) 1.44 M 3) 1.71 M Learning Check

7 3) 1.71 M 46.8 g NaHCO 3 x 1 mole NaHCO 3 = 0.557 mole NaHCO 3 84.0 g NaHCO 3 0.557 mole of NaHCO 3 = 1.71 M NaHCO 3 0.325 L Solution

8 What is the molarity of 225 mL of a KNO 3 solution containing 34.8 g of KNO 3 ? 1)0.344 M 2)1.53 M 3)15.5 M Learning Check

9 2)1.53 M 34.8 g KNO 3 x 1 mole KNO 3 = 0.344 mole of KNO 3 101.1 g KNO 3 M = mole = 0.344 mole KNO 3 = 1.53 M L 0.225 L In one setup: 34.8 g KNO 3 x 1 mole KNO 3 x 1 = 1.53 M 101.1 g KNO 3 0.225 L Solution

10 Molarity Conversion Factors The units of molarity are used as conversion factors in calculations with solutions. MolarityEquality 3.5 M HCl1 L = 3.5 moles of HCl Written as Conversion Factors 3.5 moles HCl and 1 L 1 L3.5 moles HCl

11 Calculations Using Molarity How many grams of KCl are needed to prepare 125 mL of a 0.720 M KCl solution? STEP 1: Given 125 mL (0.125 L) of 0.720 M KCl Need g of KCl STEP 2: Plan L KCl moles KCl g KCl

12 Calculations Using Molarity STEP 3: Conversion factors 1 mole of KCl = 74.6 g 1 mole KCl and 74.6 g KCl 74.6 g KCl 1 mole KCl 1 L KCl = 0.720 mole of KCl 1 L and 0.720 mole KCl 0.720 mole KCl 1 L STEP 4: Calculate grams. 0.125 L x 0.720 mole KCl x 74.6 g KCl = 6.71 g of KCl 1 L 1 mole KCl

13 How many grams of AlCl 3 are needed to prepare 125 mL of a 0.150 M solution? 1) 20.0 g of AlCl 3 2) 16.7 g of AlCl 3 3) 2.50 g of AlCl 3 Learning Check

14 Solution 3) 2.50 g AlCl 3 0.125 L x 0.150 mole x 133.5 g = 2.50 g of AlCl 3 1 L 1 mole

15 How many milliliters of 2.00 M HNO 3 contain 24.0 g of HNO 3 ? 1) 12.0 mL 2) 83.3 mL 3) 190. mL Learning Check

16 24.0 g HNO 3 x 1 mole HNO 3 x 1000 mL 63.0 g HNO 3 2.00 mole HNO 3 Molarity factor inverted = 190. mL of HNO 3 Solution

17 D ilution In a dilution water is added. volume increases. concentration decreases. Copyright © 2009 by Pearson Education, Inc.

18 Comparing Initial and Diluted Solutions In the initial and diluted solution, the moles of solute are the same. the concentrations and volumes are related by the following equations: For percent concentration: C 1 V 1 = C 2 V 2 initial diluted For molarity: M 1 V 1 = M 2 V 2 initial diluted

Guide to Calculating Dilution Quantities 19 Copyright © 2009 by Pearson Education, Inc.

20 Dilution Calculations with Percent What volume of a 2.00% (m/v) HCl solution can be prepared by diluting 25.0 mL of 14.0% (m/v) HCl solution? Prepare a table: C 1 = 14.0% (m/v)V 1 = 25.0 mL C 2 = 2.00% (m/v)V 2 = ? Solve dilution equation for unknown and enter values: C 1 V 1 = C 2 V 2 V 2 = V 1 C 1 = (25.0 mL)(14.0%) = 175 mL C 2 2.00%

21 Learning Check What is the percent (% m/v) of a solution prepared by diluting 10.0 mL of 9.00% NaOH to 60.0 mL?

22 Solution What is the percent (% m/v) of a solution prepared by diluting 10.0 mL of 9.00% NaOH to 60.0 mL? Prepare a table: C 1 = 9.00 %(m/v)V 1 = 10.0 mL C 2 = ?V 2 = 60.0 mL Solve dilution equation for unknown and enter values: C 1 V 1 = C 2 V 2 C 2 = C 1 V 1 = (10.0 mL)(9.00%) = 1.50% (m/v) V 2 60.0 mL

23 Dilution Calculations with Molarity What is the molarity (M) of a solution prepared by diluting 0.180 L of 0.600 M HNO 3 to 0.540 L? Prepare a table: M 1 = 0.600 MV 1 = 0.180 L M 2 = ?V 2 = 0.540 L Solve dilution equation for unknown and enter values: M 1 V 1 = M 2 V 2 M 2 = M 1 V 1 = (0.600 M)(0.180 L) = 0.200 M V 2 0.540 L

24 Learning Check What is the final volume (mL) of 15.0 mL of a 1.80 M KOH diluted to give a 0.300 M solution? 1) 27.0 mL 2) 60.0 mL 3) 90.0 mL

25 Solution What is the final volume (mL) of 15.0 mL of a 1.80 M KOH diluted to give a 0.300 M solution? Prepare a table: M 1 = 1.80 MV 1 = 15.0 mL M 2 = 0.300MV 2 = ? Solve dilution equation for V 2 and enter values: M 1 V 1 = M 2 V 2 V 2 = M 1 V 1 = (1.80 M)(15.0 mL) = 90.0 mL M 2 0.300 M