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

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

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.

Calculation of Molarity 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 (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

Learning Check What is the molarity of 325 mL of a solution containing 46.8 g of NaHCO3? 1) 0.557 M 2) 1.44 M 3) 1.71 M

Solution 3) 1.71 M 46.8 g NaHCO3 x 1 mole NaHCO3 = 0.557 mole NaHCO3 0.557 mole of NaHCO3 = 1.71 M NaHCO3 0.325 L

Learning Check What is the molarity of 225 mL of a KNO3 solution containing 34.8 g of KNO3? 1) 0.344 M 2) 1.53 M 3) 15.5 M

Solution 2) 1.53 M 34.8 g KNO3 x 1 mole KNO3 = 0.344 mole of KNO3 M = mole = 0.344 mole KNO3 = 1.53 M L 0.225 L In one setup: 34.8 g KNO3 x 1 mole KNO3 x 1 = 1.53 M 101.1 g KNO3 0.225 L

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

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

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

Learning Check 125 mL of a 0.150 M solution? 1) 20.0 g of AlCl3 How many grams of AlCl3 are needed to prepare 125 mL of a 0.150 M solution? 1) 20.0 g of AlCl3 2) 16.7 g of AlCl3 3) 2.50 g of AlCl3

Solution 3) 2.50 g AlCl3 0.125 L x 0.150 mole x 133.5 g = 2.50 g of AlCl3 1 L 1 mole

Learning Check How many milliliters of 2.00 M HNO3 contain 24.0 g of 1) 12.0 mL 2) 83.3 mL 3) 190. mL

Solution 24.0 g HNO3 x 1 mole HNO3 x 1000 mL 63.0 g HNO3 2.00 mole HNO3 Molarity factor inverted = 190. mL of HNO3

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

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: C1V1 = C2V2 initial diluted For molarity: M1V1 = M2V2

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

Dilution Calculations with Molarity What is the molarity (M) of a solution prepared by diluting 0.180 L of 0.600 M HNO3 to 0.540 L? Prepare a table: M1= 0.600 M V1 = 0.180 L M2= ? V2 = 0.540 L Solve dilution equation for unknown and enter values: M1V1 = M2V2 M2 = M1V1 = (0.600 M)(0.180 L) = 0.200 M V2 0.540 L

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

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: M1= 1.80 M V1 = 15.0 mL M2= 0.300 M V2 = ? Solve dilution equation for V2 and enter values: M1V1 = M2V2 V2 = M1V1 = (1.80 M)(15.0 mL) = 90.0 mL M2 0.300 M