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

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

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

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 109 µg

The density of lead is 11.34 g/cm3. Find the density of lead in kg/m3 11.34 g 1 kg 100 cm 100 cm 100 cm = cm3 1000 g 1 m 1m 1m 11,340 kg m3

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 1 g 10 dL 1 L 1 mL = dL 1 x 10 9 ng 1 L 1000 mL 1 cm3 5.5 x 10-9 g cm3

Density of Some Common Substances Substance Density (g / cm3) Air 0.0013* Lithium 0.53 Ice 0.917 Water 1.00 Aluminum 2.70 Iron 7.86 Lead 11.4 Gold 19.3 Density of Some Common Substances *at 0oC and 1 atm pressure

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

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

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

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 1.75 g x 5.0 mL mL 8.8 g

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

SI Prefixes mega- 1,000,000 kilo- 1,000 deci- 1/10 centi- 1/100 milli- 1/1,000 micro- 1/1,000,000 Also know… 1 mL = 1 cm3

Practice Measuring cm 1 2 3 4 5 4.5 cm cm 1 2 3 4 5 4.54 cm cm 1 2 3 4 1 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

20 15.0 mL 15 mL ? A student reads a graduated cylinder that is marked at 15.00 mL, as shown in the illustration. Is this correct? NO Express the correct reading using scientific notation. 15.0 mL or 1.50 x101 mL 10

Scientific Notation Calculating with scientific notation (8.1 × 104 mol) Type on your calculator: 5.44 7 8.1 4 EE ÷ EE = = 671.6049383 = 670 g/mol = 6.7 × 102 g/mol Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

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 www.nisd.net/communicationsarts/pages/chem

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 0.00007 km 62,000 mm Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

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

Other Ways of Thinking About Significant Figures… All digits are significant EXCEPT… Leading zeros -- 0.0025 Trailing zeros without a decimal point -- 2,500 Pacific Ocean = “Present” and Atlantic Ocean = “Absent” (ask about this one in class ) Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

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 www.nisd.net/communicationsarts/pages/chem

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) = 324.103g 3 SF 3 SF 4 SF 324 g Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

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 - 0.84 g  18.1 g 18.06 g Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Significant Figures Practice Problems (15.30 g) ÷ (6.4 mL) 4 SF 2 SF = 2.390625 g/mL  2.4 g/mL 2 SF 18.9 g - 0.84 g  18.1 g 18.06 g Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem