1. Solutions Part II
DHS Chemistry
Chapter 15

2. I. Concentrations of Solutions
The concentration of a solution is a measure of the amount of solute that is dissolved in a given quantity of solvent.
Amount of solute vs. amount of water

4. Dilute vs Concentrated
photo by M.Ferrer
Little solute a lot of solute

5. Very Concentrated
Photo by Michael Solorio

6. Less Concentrated
photo by Nicholas Dumlao

7. Concentrated solutions
A concentrated solution is one that contains a high concentration of solute.

8. Dilute solutions
A dilute solution contains a small concentration of solute.

9. Pictorial Representation

10. Pictorial Representation

11. There are several ways to express concentration
There are several ways to express concentration. These include: percent solutions (by volume or mass), molarity, or molality.

12. A. Percent Solutions

13. Percent Solutions % solute = amount of solute _
TOTAL amount of solvent
solution
3 types:
(%m/m) same units
(%v/v) same units
(%m/v) needs to be g/mL

14. How much vinegar is just acetic acid?
5% of vinegar is acetic acid

15. % by volume (% (v/v)) = volume of solute
Percent by Volume
% by volume (% (v/v)) = volume of solute
Volume of solution
units must be the same
(solute + solvent)
Tip: watch out for the wording. You may need to add the volume of the solute and solvent to get the volume of the total solution

16. Percent by Mass
% by mass (% (m/m)) = mass of solute mass of solution
*units must be the same
(solute + solvent)
Tip: watch out for the wording. You may need to add the mass of the solute and solvent to get the volume of the total solution

17. Percent Mass by Volume
% mass by volume (% (m/v) = mass of solute (g) volume of solution (mL)
*units must g/mL

18. ? % = 20 mL alcohol 30.8% 100 65 mL H2O %(v/v) = Volume of solute
Ex 1: 20 mL of alcohol is diluted with water to a total volume of 65 mL. What is the percentage of alcohol, by volume?
%(v/v) = Volume of solute
100 Volume of solution
%(v/v)=
? % =
20 mL alcohol
30.8%
Alcohol by volume
100
65 mL H2O

19. 30.8% of this solution is alcohol. The rest is water.
65 mL alcohol + water
20 mL alcohol
30.8% of this solution is alcohol. The rest is water.

20. Is white gold really gold?
White Gold, 18 Karat Au 75% - Pt or Pd 25%
Solute = platinum or palladium
Solvent = gold

21. 5 grams of my ring isn’t pure gold.
If I had an 18k white gold ring that weighed 20g, how much of the ring isn’t pure gold?
White Gold, 18 Karat Au 75% - Pt or Pd 25%
25% = ?g g
5 grams of my ring isn’t pure gold.

22. Ex 2 : A solution containing 7 g of NaCl in 165 g of solution
Ex 2 : A solution containing 7 g of NaCl in 165 g of solution. What is the percent of NaCl by mass?
158 g of solvent (water)
4.24%
? % NaCl (m/m)=
7 g NaCl
100
165 g solution
Solution = Solute + solvent
Solution = 7 g g

23. Children’s Dose vs Adult Dose
Diphenhydramine hydrochloride
(active ingredient in allergy medicine like Benadryl)

24. How do you feed a child medicine when one tablet is too strong?

25. Liquid dose for children has been diluted to 12
Liquid dose for children has been diluted to 12.5 mg for every 5 mL of medicine

26. What percent by mass of diphenhydramine hydrochloride is in the solution?
Liquid dose for children has been diluted to 12.5mg for every 5mL of medicine
.0125 g = .250% (m/v)
5 mL

27. EX 3: A saline solution containing 3. 5 g of NaCl in 62
EX 3: A saline solution containing 3.5 g of NaCl in 62.5 mL of solution. What is the percent of NaCl, by mass.
5.60%
? % =
3.5 g NaCl
100
62.5 mL solution

28. EX 3: A saline solution containing 3. 5 g of NaCl in 62
EX 3: A saline solution containing 3.5 g of NaCl in 62.5 mL of solution. What is the percent of NaCl, by mass.
5.60%
? % =
3.5 g NaCl
100
62.5 mL solution

29. %(v/v)= 22.3 % = ? mL ethanol 26.8 mL 100 120 mL solution
Ex 4: What volume of ethanol is needed to produce 120 mL of a 22.3% (v/v) ethanol solution?
%(v/v)=
22.3 % =
ethanol by volume (v/v)
? mL ethanol
26.8 mL
100
120 mL solution

30. 2.8 % = 0.750 g glucose 100 26.8 mL ? mL glucose solution
Ex 5: What volume of a 2.8% (m/v) glucose solution would you need to deliver to a patient who needs 750 mg of glucose?
2.8 % =
glucose by volume (m/v)
0.750 g glucose
100
26.8 mL
? mL glucose
solution

31. Practice
If 10 mL of pure acetone is diluted with water to a total solution volume of 200 mL, what is the percent by volume of acetone in the solution?
2. A bottle of hydrogen peroxide is labeled 3.0% (v/v). How many mL of H2O2 are in a mL bottle of this solution?
3. Calculate the grams of solute required to make 250 g of 0.10% MgSO4 (m/m).
4. A solution contains 2.7 g CuSO4 in 75 mL of solution. What is the percent (m/v) of the solution?

32. %(v/v)= ? % = 5.00 % 10 mL acetone 100 200 mL solution
If 10 mL of pure acetone is diluted with water to a total solution volume of 200 mL, what is the percent by volume of acetone in the solution?
%(v/v)=
? % =
5.00 %
10 mL acetone
acetone by volume (v/v)
100
200 mL solution

33. %(v/v)= 3.00 % = ? mL H2O2 12.0 mL 100 400. mL solution
2. A bottle of hydrogen peroxide is labeled 3.0% (v/v). How many mL of H2O2 are in a mL bottle of this solution?
%(v/v)=
3.00 % =
? mL H2O2
12.0 mL
H2O2 by volume (v/v)
100
400. mL solution

34. 3. Calculate the grams of solute required to make 250 g of 0
3. Calculate the grams of solute required to make 250 g of 0.10% MgSO4 (m/m).
%(m/m)=
0.10 % =
? g MgSO4
0.250 g
MgSO4 by volume (v/v)
100
250 g solution

35. 4. A solution contains 2. 7 g CuSO4 in 75 mL of solution
4. A solution contains 2.7 g CuSO4 in mL of solution. What is the percent (m/v) of the solution?
%(m/v)=
3.60 %
? % =
2.7 g CuSO4
CuSO4 by volume (m/v)
100
75 mL solution

36. Practice
If 10 mL of pure acetone is diluted with water to a total solution volume of 200 mL, what is the percent by volume of acetone in the solution?
2. A bottle of hydrogen peroxide is labeled 3.0% (v/v). How many mL of H2O2 are in a mL bottle of this solution?
3. Calculate the grams of solute required to make 250 g of 0.10% MgSO4 (m/m).
4. A solution contains 2.7 g CuSO4 in 75 mL of solution. What is the percent (m/v) of the solution?
5.00% acetone (v/v)
12.0mL H2O2
0.250g MgSO4
3.60% (m/v)

37. B. Molarity

38. Molarity
Molarity (M) is the number of moles of a solute dissolved per liter of solution.

39. Molarity
Molarity is also known as molar concentration and is read as “ __#__ molar” (Ex. a 2M HCl solution is read as two molar HCl”
Note that the volume involved is the total volume of solution, not just the solvent.

40. Molarity Molarity (M) = moles of solute M = mol Liters of solution 1 L
*if given grams, convert if to moles using the molar mass of the substance

41. Why are grams important?
Moles
Grams
Molar mass
___g = 1 mole
You can not directly measure moles, you must calculate the mass in grams first

42. How to Prepare a Solution
To make 1.00 liter of a 1.00 molar (1.0 M) solution:
1) add 1.0 mol of solute to a volumetric flask
2) add about ¼ flask of distilled water. Swirl the flask till the solute is dissolved.
3) slowly add water until the final volume reads 1.00 L

44. Molarity
EX 1. What is the molarity of a solution that contains 8 moles of CaCl2 in 50 mL of solution?
M =
mol
8 mol
160M CaCl2 1 L
0.05 L

45. Molarity
EX 2. How many grams of NaCl are needed to make 500mL of a 0.2 M solution?
.2 M
M =
? mol
.1 mol 1 L
0.5 L
0.1 mol NaCl
g NaCl
=5.84 mol NaCl
1 mol NaCl

46. Using Molarity
Ex 3: A saline solution contains 0.90 g NaCl in exactly 100 mL of solution. What is the molarity of the solution?
Step 1: Calculate # moles
0.90g NaCl x
1 mol NaCl
= mol NaCl
g NaCl
Step 2: mL  L
100 mL x
1 L
= L NaCl
1000 mL

47. 0.154 M ? M M = 0.0154 mol 1 L 0.1 L Ex 3 continued
Step 3: Calculate Molarity
0.154 M
? M
M =
mol 1 L
0.1 L

48. Ex 2: How many grams of solute are present in 562 mL of 0.24 M Na2SO4?
M = mol  mol = M  L L
mol =
0.24M Na2SO4 x .562L
= 0.135mol

49. Convert from Moles to Grams
0.135mol Na2SO4 | 142g Na2SO4 = | 1 mol Na2SO4
= 19.2g Na2SO4

50. Practice
A solution has a volume of 2.0 L and contains 36.0 g of glucose. If the molar mass of glucose is 180 g/mol, what is the molarity of the solution? 0.100M glucose
2. How many moles of ammonium nitrate are in 335 mL of M NH4NO3? 0.142mol NH4NO3
3. How many grams of solute are in 250 mL of 2.0 M CaCl2 solution? 55.5gCaCl2
4. Describe how you would prepare 250 mL of a 0.2 M NaOH solution. Need 2.00g NaOH in 250mL of solution

51. Molar mass = 6(12.01g) + 12(1.008g) + 6(15.999g) =
1. A solution has a volume of 2.0 L and contains 36.0 g of glucose. If the molar mass of glucose is 180 g/mol, what is the molarity of the solution?
Molarity = mol L
Glucose = C6H12O6
Molar mass = 6(12.01g) + 12(1.008g) + 6(15.999g) =
Calculate moles:
36.0g C6H12O6 | 1 mol C6H12O6 = mol C6H12O6
| XXX g C6H12O6
Calculate Molarity: XXXmol C6H12O6 = 0.100M glucose
2.0 L

52. C. Dilutions

53. C. Dilutions
You can make a less concentrated solution by diluting it with solvent.
The dilution reduces the grams of solute per unit volume, but the total amount of solute in solution does not change.

54. Diluted Solutions
Before After
Dilutions Dilutions

55. Moles of solute = Molarity x volume
Moles of solute before dilution = Moles of solute after dilution
Moles of solute = Molarity x volume
Dilutions:
M1V1 = M2V2

56. m1 v1 m2 v2 V1 = 20mL of stock solution (2M)(V1) = (0.400M)(100mL)
Ex: How many mL of a stock solution of 2.00 M MgSO4 would you need to prepare mL of M MgSO4?
Stock soln
(2M)(V1) = (0.400M)(100mL)
m1 v m v2
V1 = 20mL of stock solution

57. Ex. 2: Describe how to prepare 100 mL of 0.400M MgSO4 from 2M MgSO4.
(see previous example)
Add 20mL of 2M stock solution in a container and add solvent up to the 100mL mark

58. Practice
1. How many mL of a stock solution of 4.00 M KI would you need to prepare mL of M KI? 47.5mL of 4.00MKI
2. What volume must you dilute to make 50.0 mL of 0.20 M KNO3 from 4.0 M KNO3? 2.5mL of 4M KNO3
3. What is the molarity of a solution formed when you add 200 mL of water to 50 mL of 5.0 M HCl? 1.00M

59. V1 = 47.5mL of 4M stock solution
1. How many mL of a stock solution of 4.00 M KI would you need to prepare mL of M KI?
(4M) (V1) = (0.760M) (250mL)
m1 v m v2
V1 = 47.5mL of 4M stock solution

60. (4M) (V1) = (0.20M) (50mL) m1 v1 m2 v2 V1 = 2.5mL of 4M solution
2. What volume must you dilute to make 50.0 mL of 0.20 M KNO3 from 4.0 M KNO3?
(4M) (V1) = (0.20M) (50mL)
m1 v m v2
V1 = 2.5mL of 4M solution

61. (5.0M) (50mL) = (M2) (250mL) m1 v1 m2 v2 M2 = 1M of solution
3. What is the molarity of a solution formed when you add 200 mL of water to 50 mL of 5.0 M HCl?
(5.0M) (50mL) = (M2) (250mL)
m v m v2
M2 = 1M of solution

62. M2 = 0.0200 M is the concentration of the diluted solution
EX. A chemist starts with 50 mL of a 0.40M NaCl solution and dilutes it to 1000 mL. What is the concentration of the dilute solution?
Stock soln
(0.4 M)(50 mL) = (?M)(1000 mL)
M V M V2
M2 = M is the concentration of the diluted solution
“of a” are key words to help link a Molarity and volume together

63. Practice
What volume of a 3.00M KI stock solution would you use to make L of a M KI solution? L
How many milliliters of a 5.0M H2SO4 stock solution would you need to prepare mL of a 0.25M H2SO4? mL
If you dilute 20.0 mL of a 3.0M solution to make mL of solution, what is the molarity of the dilute solution? 0.600M

64. (3.00M) (V1) = (1.25M) (.300) (5M) (V1 mL) = (0.25M) (100 mL)
Practice 1
(3.00M) (V1) = (1.25M) (.300)
m v m v2
V1 = .125 L of 3M stock solution
Practice 2
(5M) (V1 mL) = (0.25M) (100 mL)
m1 v m v2
V1 = 5.00mL of 5M solution

65. M1 = 0.600M is the new concentration
Practice 3
(3.0M) (20mL) = (M2) (100mL)
m v m v2
M1 = 0.600M is the new concentration