1

Chapter 7 Solutions

7.5 Molarity and Dilution

Copyright © 2009 by Pearson Education, Inc.

2

Molarity (M)

Molarity (M)

• is a concentration term for solutions.

• gives the moles of solute in 1 L of solution.

• moles of soluteliter 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 itcontains 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 NaOH1 mole NaOH and 40.0 g NaOH40.0 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 NaHCO3?

1) 0.557 M 2) 1.44 M3) 1.71 M

Learning Check

7

3) 1.71 M 46.8 g NaHCO3 x 1 mole NaHCO3 = 0.557 mole NaHCO3

84.0 g NaHCO3

0.557 mole of NaHCO3 = 1.71 M NaHCO3

0.325 L

Solution

8

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

Learning Check

9

2) 1.53 M34.8 g KNO3 x 1 mole KNO3 = 0.344 mole of KNO3

101.1 g KNO3

M = mole = 0.344 mole KNO3 = 1.53 M L 0.225 LIn one setup:

34.8 g KNO3 x 1 mole KNO3 x 1 = 1.53 M 101.1 g KNO3 0.225 L

Solution

10

Molarity Conversion Factors

The units of molarity are used as conversion factors in calculations with solutions.

Molarity Equality3.5 M HCl 1 L = 3.5 moles of HCl

Written as Conversion Factors3.5 moles HCl and 1 L

1 L 3.5 moles HCl

11

Calculations Using Molarity

How many grams of KCl are needed to prepare 125 mLof 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 g1 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 KCl0.720 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 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

Learning Check

14

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

15

How many milliliters of 2.00 M HNO3 contain 24.0 g of

HNO3?

1) 12.0 mL

2) 83.3 mL

3) 190. mL

Learning Check

16

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

Solution

17

Dilution

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:C1V1 = C2V2

initial diluted

For molarity:M1V1 = M2V2

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:C1= 14.0% (m/v) V1 = 25.0 mL C2= 2.00% (m/v) V2 = ?

Solve dilution equation for unknown and enter values:

C1V1 = C2V2

V2 = V1C1 = (25.0 mL)(14.0%) = 175 mL C2 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:C1= 9.00 %(m/v) V1 = 10.0 mL

C2= ? V2 = 60.0 mL

Solve dilution equation for unknown and enter values:

C1V1 = C2V2

C2 = C1 V1 = (10.0 mL)(9.00%) = 1.50% (m/v)

V2 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 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

24

Learning Check

What is the final volume (mL) of 15.0 mL of a 1.80 MKOH diluted to give a 0.300 M solution?

1) 27.0 mL2) 60.0 mL 3) 90.0 mL

25

Solution

What is the final volume (mL) of 15.0 mL of a 1.80 MKOH 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 mLM2 0.300 M