1. DO NOW…. Which liquid has the highest density?
least dense 1 < 3 < 5 < 2 < 4 most dense 4 2 3 1 5
Coussement, DeSchepper, et al. , Brain Strains Power Puzzles 2002, page 16

2. EXTENSIVE properties - does NOT depend on quantity of matter.
Density is an INTENSIVE property of matter.
- does NOT depend on quantity of matter.
Examples:
color, melting point, boiling point, odor, density
Styrofoam
Brick
Gold
DIFFERENT THAN
EXTENSIVE properties
- depends on
quantity of matter.
- mass, volume, length

3. Density
D = M V D M V
ensity
ass
olume
M = DV
V = M D

4. The heaviest human brain ever recorded had a mass of 2. 3kg
The heaviest human brain ever recorded had a mass of 2.3kg. How many micrograms is that?
2.3 kg 1000 g 1 x 106 µg = 1 kg 1 g
2.3 x µg

5. The density of lead is 11.34 g/cm3. Find the density of lead in kg/m3
11.34 g kg cm cm cm =
cm g m m 1m
11,340 kg m3

6. The average concentration of testosterone in the blood of a male in his twenties is 550 nanograms per deciliter. How many grams per cubic centimeter does this concentration represent?
550 ng g dL L mL =
dL 1 x 10 9 ng L mL 1 cm3
5.5 x g
cm3

7. Density of Some Common Substances
Substance Density
(g / cm3)
Air *
Lithium
Ice
Water
Aluminum
Iron
Lead
Gold
Density of Some Common Substances
*at 0oC and 1 atm pressure

8. Consider Equal Masses Equal masses… …but unequal volumes.
The object with the
larger volume
(aluminum cube) has
the density.
gold
aluminum
smaller
Christopherson Scales
Made in Normal, Illinois USA
Dorin, Demmin, Gabel, Chemistry The Study of Matter , 3rd Edition, 1990, page 71

9. Comparing Densities (g/cm3)
0.25
ice
cork
0.9
Specific gravity
A quantity that is very closely related to density, and which is frequently used in its place, is specific gravity.
Specific gravity is the ratio of the mass of a material to that of an equal volume of water. Because the density of water is about 1.00 g mL–1, the specific gravity is numerically very close to that of the density, but being a ratio, it is dimensionless.
The relationship of specific gravity and buoyancy. Aluminum has a specific gravity greater than that of water and does not float. Ice has a specific gravity slightly less than that of water and floats largely submerged. Cork has a low specific gravity and floats with most of its mass above water. The weight of the ice and cork push down, while a buoyant force lifts the objects upward. The aluminum’s weight is larger than the buoyant force of the water.
Specific gravity is relative to water that is 1.0 g/mL.
Note: 90% of the ice is submerged below the water (its specific gravity is 0.9)
and 25% of the cork is below the water (its specific gravity is 0.25).
water 1.0
aluminum
2.7
Jaffe, New World of Chemistry, 1955, page 66

10. Density Practice Problems
What is the density of carbon dioxide gas if g occupies a volume of 100. mL?
D = M V
0.196 g
100. mL
1.96 x 10-3 g/mL

11. Density Practice Problems
An irregularly shaped stone has a volume of 5.0 mL. The density of the stone is 1.75 g/mL. What is the mass of this stone?
M = D x V
x 5.0 mL
1.75 g mL
8.8g

12. Density Practice Problems
A sample of iron has a mass of 94 g and a density of 7.8 g/cm3. What is the volume of the iron?
V = M D
94 g
7.8 g
cm3
12 cm3

13. How to use in conversion factors?
SI Prefixes
mega- 1,000,000
kilo- 1,000
deci- 1/10
centi- 1/100
milli- 1/1,000
micro- 1/1,000,000
nano- 1/1,000,000,000
→ 1Mg = 1,000,000 g
→ 1kg = 1,000 g
→ 10 dg = 1 g
→ 100 cg = 1 g
→ 1,000 mg = 1 g
→ 1 x 106 µg = 1 g
→ 1 x 109 ng = 1 g
Also know…
1 mL = 1 cm3

14. Practice Measuring cm 1 2 3 4 5 4.5 cm cm 1 2 3 4 5 4.54 cm cm 1 2 3 41 2 3 4 5
4.5 cm cm 1 2 3 4 5
4.54 cm
PRACTICE MEASURING
Estimate one digit of uncertainty.
a) 4.5 cm
b) * 4.55 cm
c) 3.0 cm
*4.550 cm is INCORRECT while 4.52 cm or 4.58 cm are CORRECT (although the estimate is poor)
By adding additional numbers to a measurement – you do not make it more precise. The instrument determines how precise it can make a measurement. Remember, you can only add ONE digit of uncertainty to a measurement.
In applying the rules for significant figures, many students lose sight of the fact that the concept of significant figures comes from estimations in measurement. The last digit in a measurement is an estimation.
How could the measurement be affected by the use of several different rulers to measure the red wire?
(Different rulers could yield different readings depending on their precision.)
Why is it important to use the same measuring instrument throughout an experiment?
(Using the same instrument reduces the discrepancies due to manufacturing defects.) cm 1 2 3 4 5
3.0 cm
Timberlake, Chemistry 7th Edition, page 7

15. 20
15.0 mL
15 mL ?
A student reads a graduated cylinder that is marked at mL, as shown in the illustration.
Is this correct? NO
Express the correct reading using scientific notation mL or 1.50 x101 mL 10

16. Scientific Notation Calculating with scientific notation
(8.1 × 104 mol)
Type on your calculator:
5.44 7
8.1 4 EE ÷ EE = =
= 670 g/mol
= 6.7 × 102 g/mol
Courtesy Christy Johannesson

17. Scientific Notation 65,000 kg  6.5 × 104 kg
Converting into scientific notation:
Move decimal until there’s 1 digit to its left. Places moved = exponent.
Large # (>1)  positive exponent Small # (<1)  negative exponent
Only include sig. figs.
Courtesy Christy Johannesson

18. Scientific Notation Practice Problems 2,400,000 g 0.00256 kg
7  10-5 km
6.2  104 mm
2.4  106 g
2.56  10-3 kg km
62,000 mm
Courtesy Christy Johannesson

19. Significant figures: Rules for zeros
Leading zeros are not significant.
Leading zero
0.421
– three significant figures
Captive zeros are significant.
Captive zero
4012
– four significant figures
Trailing zeros are significant, only IF there is a decimal point somewhere in the number.
Trailing zero
114.20
– five significant figures
11,420
– four significant figures

20. Other Ways of Thinking About Significant Figures…
All digits are significant EXCEPT…
Leading zeros
Trailing zeros without a decimal point -- 2,500
Pacific Ocean = “Present” and Atlantic Ocean = “Absent”
(ask about this one in class )
Courtesy Christy Johannesson

21. Significant Figures Calculating with Sig Figs (con’t)
Exact Numbers do not limit the # of sig figs in the answer.
Counting numbers: 12 students
Exact conversions: 1 m = 100 cm
Courtesy Christy Johannesson

22. Significant Figures (13.91g/cm3)(23.3cm3) = 324.103g 324 g
Calculating with Sig Figs
Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer.
(13.91g/cm3)(23.3cm3) = g
3 SF
3 SF
4 SF
324 g
Courtesy Christy Johannesson

23. Significant Figures 18.9 g - 0.84 g  18.1 g 18.06 g
Calculating with Sig Figs
Add/Subtract - The # with the fewest places after the decimal point determines the # of sig figs in the answer.
18.9 g g
 18.1 g
18.06 g
Courtesy Christy Johannesson

24. Significant Figures Practice Problems (15.30 g) ÷ (6.4 mL)
4 SF
2 SF
= g/mL
 2.4 g/mL
2 SF
18.9 g g
 18.1 g
18.06 g
Courtesy Christy Johannesson