1. Relating mass and volume
Density
Relating mass and volume

2. Which is heavier: 1 pound of lead or 1 pound of feathers?
SAME: Both weigh 1 lb.

3. Which has a greater volume: 1 pound of lead or 1 pound of feathers?

4. Why do the same masses of lead and feathers have such different volumes?
ANSWER: LEAD AND FEATHERS HAVE DIFFERENT DENSITIES. THE DENSITY OF LEAD (11.3 g/ cm3) IS MUCH GREATER DENSITY THAN THE DENSITY OF FEATHERS (≈ g/cm3)

5. What is the formula for density?
(You learned this in 9th grade or middle school)

6. Density Equation and Units
Density = Mass
Volume
Units: mass g
volume mL or cm3
(recall 1 mL = 1 cm3)
density g/mL or g/ cm3
d = m/v

8. D) Impossible to determine
The density of the aluminum cylinder on the left is 2.7 g/mL. What would be the density of two aluminum cylinders?
m = 2.7 g v = 1 mL
m = ? v = ?
A) 1.4 g/mL
B) 2.7 g/mL
C) 5.4 g/mL
D) Impossible to determine

9. The density of the aluminum cylinder on the left is 2. 7 g/mL
The density of the aluminum cylinder on the left is 2.7 g/mL. What would be the density of two aluminum cylinders?
m = 2.7 g v = 1.0 mL
m = 5.4 g v = 2.0 mL
A) 1.4 g/mL
B) 2.7 g/mL
C) 5.4 g/mL
D) Impossible to determine

10. Calculating Density Using Correct Significant Figures
Calculate the density of a piece of wood that has a mass of 5.0 g and a volume of 210 mL to the appropriate number of SF.

11. SIGNIFICANT FIGURE’S RULES FOR CALCULATIONS
CALCULATIONS USING MEASURED VALUES CAN BE NO MORE ACCURATE THAN THE LEAST ACCURATE MEASUREMENT
POINT OF CONFUSION: Definition of “least accurate” is different from addition and subtraction compared to multiplication and division
Least accurate: Addition and Subtraction = Fewest places past decimal
Least accurate: Multiplication and Division = Fewest SF

12. SIG FIGURE’S RULE SUMMARY
COUNTING #’S and Conversion factors – INFINITE
NONZERO DIGIT’S: ALWAYS
ZERO’S:
LEADING : NEVER
CAPTIVE: ALWAYS
TRAILING :SOMETIMES
Decimal present?
YES; SIGNIFICANT
NO; NOT SIGNIFICANT

13. Calculating Density Using Correct Significant Figures
Calculate the density of a piece of wood that has a mass of 5.0 g and a volume of 210 mL to the appropriate number of SF.
Operation is division – round to fewest SF
2 SF
ANS: d = m/v = 5.0 g =
210 mL
0.024 g/mL
(2 SF)
2 SF

14. Determining Density in the Lab using the water displacement method
Explain how the density of an object could be using the following equipment:

15. HW 4-5, #1) Determine the density of Sponge Bob Square Pants to the correct of SF using the volume displacement method
Step #1: Measure the mass to the correct number of SF
ANS: 7.50 g (record screen exactly)
7.50 g

16. Determining the density of Sponge Bob Square Pants to the correct of SF using the volume displacement method
Step #2: Measure the initial and final volume to the correct SF. Important assumption: Assume Sponge Bob does not act like a normal sponge (justified by the fact he wears pants and talks) and does not actually absorb water.

17. Record initial and Final Volumes and calculate ∆V (Final – initial) to the correct number of SF
Volume Final: 52.0 mL
- Volume Initial: 50.0 mL
∆Volume Final: 2.0 mL

18. d = m/v = 7.50 g/ 2.0 mL = 3.75 → 3.8 g/mL (2 SF)
Determining the density of Sponge Bob Square Pants to the correct of SF using the volume displacement method
Step #3: Plug in mass and volume into density equation
d = m/v = g/ 2.0 mL = 3.75 → 3.8 g/mL (2 SF)
Note that unlike a typical sponge that floats, Sponge Bob sinks since has density > 1 g/mL (density of water)

19. Mass vs Volume Gummy Bears
Slope = Δy/ Δx
Slope = Δmass/ Δvolume
Select any two points on line; one easy point to pick is 0,0. Pick a second point of known value or easily read
Slope = / = g/mL

20. 3) All of the cylinders below have the same mass
3) All of the cylinders below have the same mass. What is true about the relationship between volume and density?
Same mass, smaller volume →
(higher or lower) density

21. Homework Problem #4: Eureka!
Density of Gold = 19.3 g/mL
Density of Silver = 10.5 g/mL
Calculate the volume occupied by 500. g of each metal:
d = m/v → dv = m → v = m/d
Gold: v = 500. g / 19.3 g/mL = 25.9 mL
Silver: v = 500. g / 10.5 g/mL = 47.6 mL

22. Homework Problem #4: Archimedes and the gold crown
Archimedes placed an equal mass of pure gold in water and compared the water displaced by the crown. Since the crown displaced more water, it was not pure gold.
Archimedes link

23. HW 4-5, #5 Explain the following observation: Liquid water has a density of 1.0 g/ mL while solid water (ice) has a density of 0.91 g/mL
Link to ice bomb
5a) Water molecules are packed more closely together in liquid than in ice. In ice molecules pack in 6 –membered rings leaving a hole in the center.
5b) No c) Volume expands when water freezes – could burst bottle

24. Applications of Density: Sink vs. Float and identifying a substance
Sink or Float: Which can has a density less than 1 g/mL and which can has density greater than 1 g/mL?
Different materials displace
different volumes
6a)Regular soda has a density greater than 1 (sinks); diet soda density is less than 1 (floats)
Diet(sugar free) soda and soda in water

25. 6b) Which has a higher concentration of “sweet” molecules, regular or diet soda?
Diet Regular
Artificial sweetners produce the same sweet taste at a much lower concentration than sugar

26. HW 4-5 #7 Densities of common objects – which phases tends to have the lowest densities and which phase tends to have the highest densities? Propose an atomic level observation to account for the data.
What do you notice about the relationship between density and volume of different metals with the same mass?

27. Solids have the greatest number of atoms/molecules per volume space; gases have the fewest number of atoms per space. Less dense materials require a larger volume for the same mass of material.