1. Chemistry: Unit 2 Chapter 3
Problem Solving in Chemistry

2. Three-step Problem Solving Approach
Analyze – determine how you will find the solution
Calculate – perform the calculation, this may involve measurements
Evaluate – does the answer make sense, and did you use correct units and significant digits

3. Ex. What is the mass, in grams, of a piece of lead that has a volume of 19.84 cm3?
Analyze: list the knowns and the unknown.
Volume = cm3 Density = mass/ volume
Density = 11.4 g/cm3 Mass = ?
Calculate: solve for the unknown.
D = m / V so… m = D x V
Mass = cm3 x g/cm3 = g
Evaluate: does the result make sense?
Would a piece of lead that is about the size of an eraser have a mass of 226 grams? Yes!

4. Practice: Solve the following using correct significant figures.
7.823 x = =
123.3
28459

5. Practice What is the mass, in grams of a piece of lead that has a volume of 8.73 cm3?
Knowns
V = 8.73 cm3
D = 11.4 g/cm3
m = VD
Unknowns
m = ?
To solve:
m = (8.73 cm3)(11.4 g/cm3)
m =
g = 99.5 g

6. Practice: What is the volume, in cm3, of a sample of cough syrup that has a mass of 20.0g and a density of 11.4 g/cm3?
Knowns
M = 20.0 g
D = 11.4 g/cm3
V = M / D
Unknowns
V = ?
To Solve
V = g
11.4 g/cm3
V =
1.75 cm3

7. Dimensional Analysis
To convert from one unit to another, we will use a problem solving method called dimensional analysis.
This method uses equalities or conversion factors to change one unit into another.
Example: If someone gives you 32 quarters, how many dollars do you have? How did you know this?

8. How many inches are there in 4 ft?
What did you have to know in order to figure that out?
1 ft = 12 inches
1 ft = 12 inches is a conversion factor. It can be written as a fraction where the numerator and the denominator are equivalent but have different units. For example, we can use the following conversion factors for changing between inches and feet:
12 inches 1 foot
1 foot or 12 inches

9. Some Handy Conversions
Let’s look at a meter stick and list all the conversions we can get from it.
We can say that one meter is equal to…
10 dm
100 cm
1000 mm
Now let’s use those prefixes to figure out how we can modify units for liters.
A liter should contain _____ deciliters
A liter should contain _____ centiliters
A liter should contain _____ milliliters
Hand out metersticks so that students can discuss.

10. Practicing with Dimensional Analysis
70 kg = ____ g
63 cm = ____ mm
2.5 L = _____ mL
1 m2 = _____ cm2
Work out each one with students. Have them list out conversion factors before you begin, then let them arrange them so that units are cancelled.

11. Practice: How many atoms are in 7. 00g of gold. (1 atom of gold = 3
Practice: How many atoms are in 7.00g of gold? (1 atom of gold = x g)
7.00 g gold
1 atom gold
= 2.14 x 1022 atoms gold
3.271 x g gold

12. Bellwork, Thursday, September 12, 2012
Complete the following conversion:
(Show you work using dimensional analysis)
45.00 m = _____________ mm
5.34 x 10-5 L = ______________ mL
7.00 x 105 g = ______________ mg

13. Wednesday’s Homework
Write at least five conversion factors using the following equalities mg = 1 g = 1 ml water = L water
Use a meter stick to fill in the following: _1_meter = ______ cm = _______ km = ______mm
A filled flask that can hold g of water at 4°C can hold only g of ethanol. What is the density of ethanol at 4°C? (hint: water’s density is 1.0 g/mL. You may need to use a proportion!)
If 100 cm = 1 m, how many cm3 are in 1 m3?
Find the mass of a 5.3 mL sample of lead in kilograms if the density of the sample is g/mL.

14. Some dimensional analysis problems require several steps  How many seconds are in 5.0 days?
5.0 days 24 hours 60 min sec = 430,000 sec
1 day 1 hour min
How many students are in a 10 room building if each classroom contains 25 students?
10 rooms 25 students = Students
1 room

15. Convert 423 m/sec to km/min.
An example of this would be the conversion of speed in miles per hour to meters per second.  An object was traveling at 400. m/min. What was its speed in cm/s?
400. m 100 cm min = 667 cm/sec
1 min m sec
Convert 423 m/sec to km/min.
423 m 1 km 60sec = 25.4 km/min
1 sec m min

16. The density of manganese is 7. 21 g/cm3
The density of manganese is 7.21 g/cm3. What is the density of manganese expressed in units of kg/m3?
7.21 g kg cm3 = 7210 kg/m3
1 cm g m3

17. Bellwork: Friday, September 13
A cheetah can run 112 km/h over a 100 m distance. What is this speed in meters per second?
The density of dry air measured at 25oC is 1.19 x 10-3g/cm3. What is the volume of 50.0g of air?

18. Thursday Homework
Which gas is cheaper based on the sales prices below? (show your calculations!) 1 L = gal Gas A: $2.53/gallon Gas B:$0.45/ liter
Set up the equalities for the story and solve Marie Currie wanted to research an unknown radioactive element (Sneezium Sz) that cost $534 per gram. Sneezium has a density of 55.67g/cm3, if Marie needs 0.35 L of Sneezium, how much money should she need? (hint: 1 cm3 = 1 mL and this will be a 4 step problem)

19. Bellwork: Monday, September 16
Earth is approximately 1.5 x 108 km from the sun. How many minutes does it take light to travel from the sun to Earth? The speed of light is 3.0 x 108m/s.
Convert 7.86 g/cm2 to milligrams per square millimeter

20. Bellwork: Tuesday, Septmeber 17
The density of water is 1.0g/mL. How many deciliters will fill a 0.5 L bottle?
Fill in the following table: mg g cg kg
28.3
6.6 x 103
2.8 x 10-4

21. Monday’s Homework Fill-in the following equalities
Anna wants to buy a one carat diamond. One carat equals 200 mg. If a diamond is carat, what is the mass of the diamond in ounces? 1 kg = pounds pound = 16 ounces
The speed of a rocket is measured and found to be m/sec. What is the rocket’s speed in km/hr?
The moon is 250,000 miles away. How many feet is it from earth?
_________ m = 1 km
_________ cL = 1 L
_________ mg = 1 g
_______ sec = 1 min
_______ cm3 = 1 ml
_______ cm3 = 1 m3