Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Chapter 7 Solutions 7.5 Dilution of Solutions 1 When water is added to a concentrated solution, there is no change in the number of particles. However, the solute particles spread out as the volume of the diluted solution increases.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Dilution In a dilution, water is added volume increases concentration decreases mass of solute remains the same 2

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Dilution Mass of orange juice in concentrate = mass of orange juice in diluted solution 3

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solute Concentration in Initial 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 4

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Guide to Calculating Dilution Quantities 5

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Dilution: Molarity What is the final concentration when 0.50 L of 6.0 M HCl solution is diluted to a final volume of 1.0 L? Step 1 Prepare a table of the concentrations and volumes of the solutions. C 1 = 6.0 MV 1 = 0.50 L C 2 = ? MV 2 = 1.0 L 6

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Dilution: Molarity What is the final concentration when 0.50 L of 6.0 M HCl solution is diluted to a final volume of 1.0 L? Step 2 Rearrange the dilution expression to solve for the unknown quantity. M 1  V 1 = M 2 V 2 Step 3 Substitute the known quantities into the dilution expression and solve. 6.0 M  0.50 L = 3.0 M HCl 1.0 L 7

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check 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? 8

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution 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? Step 1 Prepare a table of the concentrations and volumes of the solutions. C 1 = 14.0% (m/v)V 1 = 25.0 mL C 2 = 2.00% (m/v)V 2 = ? Step 2 Rearrange the dilution expression to solve for the unknown quantity. C 1 V 1 = C 2 V 2 V 2 = V 1 C 1 C 2 9

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution 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? Step 3 Substitute the known quantities into the dilution expression and solve. V 2 = (25.0 mL)(14.0%) = 175 mL of solution 2.00% 10

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. 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? 11

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution What is the percent (% m/v) of a solution prepared by diluting 10.0 mL of 9.00% NaOH to 60.0 mL? Step 1 Prepare a table of the concentrations and volumes of the solutions. C 1 = 9.00 % (m/v)V 1 = 10.0 mL C 2 = ?V 2 = 60.0 mL Step 2 Rearrange the dilution expression to solve for the unknown quantity. C 1 V 1 = C 2 V 2 C 2 = C 1 V 1 V 2 12

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution What is the percent (% m/v) of a solution prepared by diluting 10.0 mL of 9.00% NaOH to 60.0 mL? Step 3 Substitute the known quantities into the dilution expression and solve. C 2 = (10.0 mL)(9.00%) = 1.50% (m/v) solution 60.0 mL 13

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check What is the molarity (M) of a solution prepared by diluting L of M HNO 3 to L? 14

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution What is the molarity (M) of a solution prepared by diluting L of M HNO 3 to L? Step 1 Prepare a table of the concentrations and volumes of the solutions. M 1 = MV 1 = L M 2 = ?V 2 = L Step 2 Rearrange the dilution expression to solve for the unknown quantity. M 1 V 1 = M 2 V 2 M 2 = M 1 V 1 V 2 15

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution What is the molarity (M) of a solution prepared by diluting L of M HNO 3 to L? Step 3 Substitute the known quantities into the dilution expression and solve. M 2 = (0.600 M)(0.180 L) = M solution L 16