1. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Chapter 7 Solutions 7.4 Concentration of a Solution 1

2. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution Concentration The concentration of a solution is expressed as amount of solute x amount of solution Units of concentration include: Mass percent (m/m) Volume percent (v/v) Mass/volume percent (m/v) Molarity (moles solute/liters solution) 2

3. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Mass Percent Mass percent (% m/m) is the concentration by mass of solute in a solution mass percent = g of solute  100 g of solute + g of solvent amount in g of solute in 100 g of solution (conversion factor for mass percent) mass percent = g of solute x 100 g of solution 3

4. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Mass of Solute: Mass Solution 4

5. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Calculating Mass Percent The calculation of mass percent (% m/m) requires the grams of solute (g KCl) and grams of solution (g KCl + g water) or g of KCl 8.00 g g of solvent (water) 42.00 g g of KCl solution = 50.00 g 8.00 g KCl (solute)  100 = 16.0% (m/m) 50.00 g KCl solution 5

6. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Guide to Calculating Solution Concentration 6

7. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check A solution is prepared by mixing 15.0 g of Na 2 CO 3 and 235 g of H 2 O. Calculate the mass percent (% m/m) of the solution. A. 15.0% (m/m) Na 2 CO 3 B. 6.38% (m/m) Na 2 CO 3 C. 6.00% (m/m) Na 2 CO 3 7

8. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution A solution is prepared by mixing 15.0 g of Na 2 CO 3 and 235 g of H 2 O. Calculate the mass percent (% m/m) of the solution. Step 1 Determine the quantities of solute and solution. mass solute = 15.0 g Na 2 CO 3 mass solution = 15.0 g Na 2 CO 3 + 235 g H 2 O = 250. g Step 2 Write the concentration expression. Use g solute/g solution ratio: mass % (m/m) = g solute  100 g solution 8

9. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution A solution is prepared by mixing 15.0 g of Na 2 CO 3 and 235 g of H 2 O. Calculate the mass percent (% m/m) of the solution. Step 3 Substitute solute and solution quantities into the expression. mass % (m/m) = 15.0 g Na 2 CO 3  100 = 6.00% Na 2 CO 3 250. g solution The answer is C, 6.00% Na 2 CO 3. 9

10. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Volume Percent The volume percent (% v/v) is percent volume (mL) of solute (liquid) to volume (mL) of solution volume % (v/v) = mL of solute  100 mL of solution solute (mL) in 100 mL of solution (conversion factor for volume percent) volume % (v/v) = mL of solute 100 mL of solution 10

11. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Mass/Volume Percent The mass/volume percent (% m/v) is percent mass (g) of solute to volume (mL) of solution mass/volume % (m/v) = g of solute  100 mL of solution solute (g) in 100 mL of solution (conversion factor for mass/volume percent) mass/volume % (m/v) = g of solute 100 mL of solution 11

12. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check Write two conversion factors for each solution. A. 8.50% (m/m) NaOH B. 5.75% (v/v) ethanol C. 4.8% (m/v) HCl 12

13. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution A. 8.50 g NaOH and 100 g solution 100 g solution 8.50 g NaOH B. 5.75 mL alcohol and 100 mL solution 100 mL solution 5.75 mL alcohol C. 4.8 g HCl and 100 mL HCl 100 mL solution 4.8 g HCl 13

14. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Molarity Molarity (moles of solute/liter of solution) is moles of solute per volume (L) of solution. M = moles solute = 1.0 mole NaCl liter of solution 1 L solution = 1.0 M NaCl solution 14

15. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Preparing a 1.0 M Solution A 1.0 M NaCl solution is prepared by weighing out 58.5 g of NaCl (1.0 mole) and adding water to make 1.00 liter of solution 15

16. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Molarity Calculations What is the molarity of 0.500 L of NaOH solution if it contains 6.00 g of NaOH? Step 1 Determine the quantities of solute and solution. Solute: 1 mole of NaOH = 40.0 grams of NaOH 1 mole NaOH and 40.0 g NaOH x 40.0 g NaOH1 mole NaOH 6.00 g NaOH  1 mole NaOH = 0.150 mole of NaOH 40.0 g NaOH The volume of the solution is 0.500 L. 16

17. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Molarity Calculations What is the molarity of 0.500 L of NaOH solution if it contains 6.00 g of NaOH? Step 2 Write the concentration expression. M = moles solute L solution Step 3 Substitute solute and solution quantities into the expression. M = moles solute = 0.150 mole NaOH = 0.300 M NaOH L solution 0.500 L solution 17

18. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check What is the molarity of 0.225 L of a KNO 3 solution containing 34.8 g of KNO 3 ? A. 0.344 M B. 1.53 M C. 15.5 M 18

19. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution What is the molarity of 0.225 L of a KNO 3 solution containing 34.8 g of KNO 3 ? Step 1 Determine the quantities of solute and solution. Solute: 1 mole of KNO 3 = 101.1 grams of KNO 3 1 mole KNO 3 and 101.1 g KNO 3 101.1 g KNO 3 1 mole KNO 3 34.8 g KNO 3  1 mole KNO 3 = 0.344 mole of KNO 3 101.1 g KNO 3 The volume of the solution is 0.225 L. 19

20. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution Step 2 Write the concentration expression. M = moles solute L solution Step 3 Substitute solute and solution quantities into the expression. M = moles solute = 0.344 mole of KNO 3 = 1.53 M KNO 3 L solution 0.225 L solution The answer is B, 1.53 M KNO 3. 20

21. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Molarity as a Conversion Factor 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 L 3.5 moles HCl 21

22. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Conversion Factors from Concentrations 22

23. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check How many grams of NaOH are needed to prepare 75.0 g of 14.0% (m/m) NaOH solution? A.10.5 g of NaOH B.75.0 g of NaOH C.536 g of NaOH 23

24. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution How many grams of NaOH are needed to prepare 75.0 g of 14.0% (m/m) NaOH solution? Using the conversion factor for mass percent: 75.0 g solution  14.0 g NaOH = 10.5 g of NaOH 100 g solution 14.0% (m/m) factor The answer is A, 10.5 g of NaOH. 24

25. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check How many milliliters of a 5.75% (v/v) ethanol solution can be prepared from 2.25 mL of ethanol? A. 2.56 mL B. 12.9 mL C. 39.1 mL 25

26. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution How many milliliters of a 5.75% (v/v) ethanol solution can be prepared from 2.25 mL of ethanol? Using the conversion factor for volume percent: 2.25 mL ethanol  100 mL solution = 39.1 mL of solution 5.75 mL ethanol 5.75% (v/v) inverted The answer is C, 39.1 mL of solution. 26

27. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check How many grams of AlCl 3 are needed to prepare 125 mL of a 0.150 M solution? A. 20.0 g of AlCl 3 B. 16.7 g of AlCl 3 C. 2.50 g of AlCl 3 27

28. Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution How many grams of AlCl 3 are needed to prepare 125 mL of a 0.150 M solution? 0.125 L  0.150 mole AlCl 3  133.5 g AlCl 3 = 2.50 g of AlCl 3 1 L 1 mole AlCl 3 molarity molar mass conversion factor The answer is C, 2.50 g of AlCl 3. 28