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# Molarity and dilution

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### Molarity and dilution

1. 1. Chapter 8 Solutions <ul><li>8.5 </li></ul><ul><li>Molarity and Dilution </li></ul>Copyright © 2007 by Pearson Education, Inc Publishing as Benjamin Cummings
2. 2. Molarity (M) <ul><li>Molarity (M) </li></ul><ul><li>Is a concentration term for solutions. </li></ul><ul><li>Gives the moles of solute in 1 L solution. </li></ul><ul><li>= moles of solute </li></ul><ul><li> liter of solution </li></ul>
3. 3. Preparing a 1.0 Molar Solution <ul><li>A 1.00 M NaCl solution is prepared </li></ul><ul><li>By weighing out 58.5 g NaCl (1.00 mole) and </li></ul><ul><li>Adding water to make 1.00 liter of solution. </li></ul>Copyright © 2007 by Pearson Education, Inc Publishing as Benjamin Cummings
4. 4. <ul><li>What is the molarity of 0.500 L NaOH solution if it </li></ul><ul><li>contains 6.00 g NaOH? </li></ul><ul><li>STEP 1 Given 6.00 g NaOH in 0.500 L solution </li></ul><ul><li> Need molarity (mole/L) </li></ul><ul><li>STEP 2 Plan g NaOH mole NaOH molarity </li></ul><ul><li> </li></ul>Calculation of Molarity
5. 5. <ul><li>STEP 3 Conversion factors 1 mole NaOH = 40.0 g </li></ul><ul><li>1 mole NaOH and 40.0 g NaOH </li></ul><ul><li>40.0 g NaOH 1 mole NaOH </li></ul><ul><li>STEP 4 Calculate molarity . </li></ul><ul><li>6.00 g NaOH x 1 mole NaOH = 0.150 mole </li></ul><ul><li>40.0 g NaOH </li></ul><ul><li> 0.150 mole = 0.300 mole = 0.300 M NaOH </li></ul><ul><li>0.500 L 1 L </li></ul><ul><li> </li></ul>Calculation of Molarity (cont.)
6. 6. <ul><li>What is the molarity of 325 mL of a solution containing 46.8 g of NaHCO 3 ? </li></ul><ul><li>1) 0.557 M </li></ul><ul><li>2) 1.44 M </li></ul><ul><li>3) 1.71 M </li></ul>Learning Check
7. 7. <ul><li>3) 1.71 M </li></ul><ul><li>46.8 g NaHCO 3 x 1 mole NaHCO 3 = 0.557 mole NaHCO 3 </li></ul><ul><li> 84.0 g NaHCO 3 </li></ul><ul><li>0.557 mole NaHCO 3 = 1.71 M NaHCO 3 </li></ul><ul><li>0.325 L </li></ul>Solution
8. 8. <ul><li>What is the molarity of 225 mL of a KNO 3 solution containing 34.8 g KNO 3 ? </li></ul><ul><li>1) 0.344 M </li></ul><ul><li>2) 1.53 M </li></ul><ul><li>3) 15.5 M </li></ul>Learning Check
9. 9. <ul><li>2) 1.53 M </li></ul><ul><li>34.8 g KNO 3 x 1 mole KNO 3 = 0.344 mole KNO 3 </li></ul><ul><li> 101.1 g KNO 3 </li></ul><ul><li>M = mole = 0.344 mole KNO 3 = 1.53 M </li></ul><ul><li>L 0.225 L </li></ul><ul><li>In one setup </li></ul><ul><li>34.8 g KNO 3 x 1 mole KNO 3 x 1 = 1.53 M </li></ul><ul><li> 101.1 g KNO 3 0.225 L </li></ul>Solution
10. 10. Molarity Conversion Factors <ul><li>The units of molarity are used to write conversion factors for calculations with solutions. </li></ul>TABLE 8.10 Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings
11. 11. Calculations Using Molarity <ul><li>How many grams of KCl are needed to prepare 125 mL </li></ul><ul><li>of a 0.720 M KCl solution? </li></ul><ul><li>STEP 1 Given 125 mL (0.125 L) of 0.720 M KCl </li></ul><ul><li> Need Grams of KCl </li></ul><ul><li>STEP 2 Plan L KCl moles KCl g KCl </li></ul>
12. 12. Calculations Using Molarity <ul><li>STEP 3 Conversion factors </li></ul><ul><li>1 mole KCl = 74.6 g </li></ul><ul><li>1 mole KCl and 74.6 g KCl </li></ul><ul><li>74.6 g KCl 1 mole KCl </li></ul><ul><li>1 L KCl = 0.720 mole KCl </li></ul><ul><li>1 L and 0.720 mole KCl </li></ul><ul><li>0.720 mole KCl 1 L </li></ul><ul><li>STEP 4 Calculate g KCl </li></ul><ul><li>0.125 L x 0.720 mole KCl x 74.6 g KCl = 6.71 g KCl </li></ul><ul><li>1 L 1 mole KCl </li></ul>
13. 13. <ul><li>How many grams of AlCl 3 are needed to prepare </li></ul><ul><li>125 mL of a 0.150 M solution? </li></ul><ul><li>1) 20.0 g AlCl 3 </li></ul><ul><li>2) 16.7g AlCl 3 </li></ul><ul><li>3) 2.50 g AlCl 3 </li></ul>Learning Check
14. 14. Solution <ul><li>3) 2.50 g AlCl 3 </li></ul><ul><li>0.125 L x 0.150 mole x 133.5 g = 2.50 g AlCl 3 </li></ul><ul><li> 1 L 1 mole </li></ul>
15. 15. <ul><li>How many milliliters of 2.00 M HNO 3 contain </li></ul><ul><li>24.0 g HNO 3 ? </li></ul><ul><li>1) 12.0 mL </li></ul><ul><li>2) 83.3 mL </li></ul><ul><li>3) 190. mL </li></ul>Learning Check
16. 16. <ul><li>24.0 g HNO 3 x 1 mole HNO 3 x 1000 mL = </li></ul><ul><li> 63.0 g HNO 3 2.00 moles HNO 3 </li></ul><ul><li> Molarity factor inverted </li></ul><ul><li>= 190. mL HNO 3 </li></ul>Solution
17. 17. Dilution <ul><li>In a dilution, </li></ul><ul><li>Water is added. </li></ul><ul><li>Volume increases. </li></ul><ul><li>Concentration decreases. </li></ul>Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings
18. 18. Initial and Diluted Solutions <ul><li>In the initial and diluted solution, </li></ul><ul><li>The moles of solute are the same. </li></ul><ul><li>The concentrations and volumes are related by the following equations: </li></ul><ul><li>For percent concentration </li></ul><ul><li>C 1 V 1 = C 2 V 2 </li></ul><ul><li>initial diluted </li></ul><ul><li>For molarity </li></ul><ul><li>M 1 V 1 = M 2 V 2 </li></ul><ul><li>initial diluted </li></ul>
19. 19. Dilution Calculations with Percent <ul><li>What volume of a 2.00 %(m/v) HCl solution can be </li></ul><ul><li>prepared by diluting 25.0 mL of 14.0%(m/v) HCl solution? </li></ul><ul><li>Prepare a table: </li></ul><ul><li>C 1 = 14.0 %(m/v) V 1 = 25.0 mL </li></ul><ul><li>C 2 = 2.00%(m/v) V 2 = ? </li></ul><ul><li>Solve dilution equation for unknown and enter values: </li></ul><ul><li>C 1 V 1 = C 2 V 2 </li></ul><ul><li>V 2 = V 1 C 1 = (25.0 mL)(14.0%) = 175 mL </li></ul><ul><li> C 2 2.00% </li></ul>
20. 20. Learning Check <ul><li>What is the percent (%m/v) of a solution prepared </li></ul><ul><li>by diluting 10.0 mL of 9.00% NaOH to 60.0 mL? </li></ul>
21. 21. Solution <ul><li>What is the percent (%m/v) of a solution prepared </li></ul><ul><li>by diluting 10.0 mL of 9.00% NaOH to 60.0 mL? </li></ul><ul><li>Prepare a table: </li></ul><ul><li>C 1 = 9.00 %(m/v) V 1 = 10.0 mL </li></ul><ul><li>C 2 = ? V 2 = 60.0 mL </li></ul><ul><li>Solve dilution equation for unknown and enter values: </li></ul><ul><li>C 1 V 1 = C 2 V 2 </li></ul><ul><li>C 2 = C 1 V 1 = (10.0 mL)(9.00%) = 1.50 %(m/v) </li></ul><ul><li> V 2 60.0 mL </li></ul>
22. 22. Dilution Calculations <ul><li>What is the molarity (M) of a solution prepared </li></ul><ul><li>by diluting 0.180L of 0.600 M HNO 3 to 0.540 L? </li></ul><ul><li>Prepare a table: </li></ul><ul><li>M 1 = 0.600 M V 1 = 0.180 L </li></ul><ul><li>M 2 = ? V 2 = 0.540 L </li></ul><ul><li>Solve dilution equation for unknown and enter values: </li></ul><ul><li>M 1 V 1 = M 2 V 2 </li></ul><ul><li>M 2 = M 1 V 1 = (0.600 M)(0.180 L) = 0.200 M </li></ul><ul><li>V 2 0.540 L </li></ul>
23. 23. Learning Check <ul><li>What is the final volume (mL) of 15.0 mL of a 1.80 M </li></ul><ul><li>KOH diluted to give a 0.300 M solution? </li></ul><ul><li>1) 27.0 mL </li></ul><ul><li>2) 60.0 mL </li></ul><ul><li>3) 90.0 mL </li></ul>
24. 24. Solution <ul><li>What is the final volume (mL) of 15.0 mL of a 1.80 M </li></ul><ul><li>KOH diluted to give a 0.300 M solution? </li></ul><ul><li>Prepare a table: </li></ul><ul><li>M 1 = 1.80 M V 1 = 15.0 mL </li></ul><ul><li>M 2 = 0.300 M V 2 = ? </li></ul><ul><li>Solve dilution equation for V 2 and enter values: </li></ul><ul><li>M 1 V 1 = M 2 V 2 </li></ul><ul><li>V 2 = M 1 V 1 = (1.80 M)(15.0 mL) = 90.0 mL </li></ul><ul><li>M 2 0.300 M </li></ul>
25. 25. Molarity in Chemical Reactions <ul><li>In a chemical reaction, </li></ul><ul><li>The volume and molarity of a solution are used to determine the moles of a reactant or product. </li></ul><ul><li>molarity ( mole ) x volume (L) = moles </li></ul><ul><li>1 L </li></ul><ul><li>If molarity (mole/L) and moles are given, the volume (L) can be determined </li></ul><ul><li>moles x 1 L = volume (L) </li></ul><ul><ul><li>moles </li></ul></ul>
26. 26. Using Molarity of Reactants <ul><li>How many mL of 3.00 M HCl are needed to completely </li></ul><ul><li>react with 4.85 g CaCO 3 ? </li></ul><ul><li>2HCl( aq ) + CaCO 3 ( s ) CaCl 2 ( aq ) + CO 2 ( g ) + H 2 O( l ) </li></ul><ul><li>STEP 1 Given 3.00 M HCl; 4.85 g CaCO 3 </li></ul><ul><li> Need volume in mL </li></ul><ul><li>STEP 2 Plan </li></ul><ul><li>g CaCO 3 mole CaCO 3 mole HCl mL HCl </li></ul>
27. 27. Using Molarity of Reactants (cont.) <ul><li>2HCl( aq ) + CaCO 3 ( s ) CaCl 2 ( aq ) + CO 2 ( g ) + H 2 O( l ) </li></ul><ul><li>STEP 3 Equalitites </li></ul><ul><li>1 mole CaCO 3 = 100.1 g; 1 mole CaCO 3 = 2 mole HCl </li></ul><ul><li>1000 mL HCl = 3.00 mole HCl </li></ul><ul><li>STEP 4 Set Up </li></ul><ul><li>4.85 g CaCO 3 x 1 mole CaCO 3 x 2 mole HCl x 1000 mL HCl </li></ul><ul><li> 100.1 g CaCO 3 1 mole CaCO 3 3.00 mole HCl </li></ul><ul><li>= 32.3 mL HCl required </li></ul>
28. 28. Learning Check <ul><li>How many mL of a 0.150 M Na 2 S solution are needed to </li></ul><ul><li>completely react 18.5 mL of 0.225 M NiCl 2 solution? </li></ul><ul><li>NiCl 2 ( aq ) + Na 2 S( aq ) NiS( s ) + 2NaCl( aq ) </li></ul><ul><li>1) 4.16 mL </li></ul><ul><li>2) 6.24 mL </li></ul><ul><li>3) 27.8 mL </li></ul>
29. 29. Solution <ul><li>3) 27.8 mL </li></ul><ul><li>0.0185 L x 0.225 mole NiCl 2 x 1 mole Na 2 S x 1000 mL </li></ul><ul><li>1 L 1 mole NiCl 2 0.150 mole Na 2 S </li></ul><ul><li>= 27.8 mL Na 2 S solution </li></ul>
30. 30. Learning Check <ul><li>If 22.8 mL of 0.100 M MgCl 2 is needed to completely </li></ul><ul><li>react 15.0 mL of AgNO 3 solution, what is the molarity of </li></ul><ul><li>the AgNO 3 solution? </li></ul><ul><li>MgCl 2 ( aq ) + 2AgNO 3 ( aq ) 2AgCl( s ) + Mg(NO 3 ) 2 ( aq) </li></ul><ul><li>1) 0.0760 M </li></ul><ul><li>2) 0.152 M </li></ul><ul><li>3) 0.304 M </li></ul>
31. 31. Solution <ul><li>3) 0.304 M AgNO 3 </li></ul><ul><li>0.0228 L x 0.100 mole MgCl 2 x 2 moles AgNO 3 x 1 </li></ul><ul><li>1 L 1 mole MgCl 2 0.0150 L </li></ul><ul><li>= 0.304 mole/L = 0.304 M AgNO 3 </li></ul>
32. 32. Learning Check <ul><li>How many liters of H 2 gas at STP are produced </li></ul><ul><li>when Zn react with 125 mL of 6.00 M HCl? </li></ul><ul><li>Zn( s ) + 2HCl( aq ) ZnCl 2 ( aq ) + H 2 ( g) </li></ul><ul><li>1) 4.20 L H 2 </li></ul><ul><li>2) 8.40 L H 2 </li></ul><ul><li>3) 16.8 L H 2 </li></ul>
33. 33. Solution <ul><li>2) 8.40 L H 2 gas </li></ul><ul><li>0.125 L x 6.00 moles HCl x 1 mole H 2 x 22.4 L </li></ul><ul><li>1 L 2 moles HCl 1 mole H 2 </li></ul><ul><li>= 8.40 L H 2 gas </li></ul>