2. NOTES: 3.2 - Density

3. What is DENSITY and how is it determined? DENSITY = the ratio of the mass of an object to its volume Density = Mass Volume The density of a substance changes with temperature

4. Example: 38.6 g of gold was placed in a graduated cylinder and displaced 2.00 mL of water. What is the density of gold? DENSITY ==

5. Example: 38.6 g of gold was placed in a graduated cylinder and displaced 2.00 mL of water. What is the density of gold? DENSITY =38.6 g=19.3 g/mL 2.00 mL

6. Example: What is the mass of 10. mL of a liquid that has a density of 3.76 g/mL? D = m / V m = D ● V m = m = (correct # of sig. figs.)

7. Example: What is the mass of 10. mL of a liquid that has a density of 3.76 g/mL? D = m / V m = D ● V m = (3.76 g/mL)(10. mL) m = 37.6 g m = 38 g (correct # of sig. figs.)

8. EXAMPLE: The density of ethanol is 0.789 g/cm 3. Calculate the volume, in liters, of a sample of ethanol that has a mass of 7.72 kg.

9. **mass = 7.72 kg = 7720 g D=m / V

10. EXAMPLE: The density of ethanol is 0.789 g/cm 3. Calculate the volume, in liters, of a sample of ethanol that has a mass of 7.72 kg. 0.789 g/cm 3 =7720 g / V V= 7720 g =9,780 mL =9.78 L 0.789 g/cm 3

11. NOTES: 3.3 – Dimensional Analysis

12. Performing these conversions is a lot like going on a road trip.

13. Let’s say you want to travel from Oracle Jct. to Casa Grande... You must travel through Tucson… a two part trip.

14. Rule: You must stay on the roads

15. OK…Lets talk about making maps and solving conversion problems. The method we use is called the “Factor-Label” method, a.k.a. DIMENSIONAL ANALYSIS.

16. gallons kildurkins For example: given 1 kildurkin = 18 gallons This is our map.

17. gallons kildurkins For example: given 1 kildurkin = 18 gallons How many kildurkins is 14 gallons? 1 kildurkin 18 gallons 14 gallons = 0.78 kildurkins

18. General Format... going to coming from given

19. gallons kildurkins Also given: 2 farkins = 1 kildurkin farkins Let’s expand the map...

20. gallons kildurkins Also given: 1 hogshead = 63 gallons farkins hogshead 1 barrel = 3.3 bushels bushel barrel 1 bushel = 8 gallons

21. gallons kildurkins farkins hogshead bushel barrel How many hogsheads are 14 barrels? Given: Start Here Finish Here The trip will require 3 transitions 1 2 3

22. gallons hogshead bushel barrel How many hogsheads are 14 barrels? 1 2 3 Given 14 barrels3.3 bushels 1 barrel 8 gallons 1 bushel 1 hogshead 63 gallons = 5.9 hogsheads

23. gallons kildurkins farkins hogshead bushel barrel Now you try one: How many farkins is 3.00 bushels? Start Here End Here This will require 3 conversions.

24. bushelsgallonskildurkins farkins 3.00 bushels 8 gallons 1 bushel 1 kildurkin 18 gallons 2 farkins 1 kildurkin = 2.67 farkins

25. Use dimensional analysis when converting between units. Ex: How many inches are in 1500 meters?

26. **Now let’s revisit the same density problem from earlier but solve it with DIMENSIONAL ANALYSIS.

27. EXAMPLE: The density of ethanol is 0.789 g/cm 3. Calculate the volume, in liters, of a sample of ethanol that has a mass of 7.72 kg.

29. Example: If the density of Al is 2.71 g/cm 3, what is the density of Al in kg/m 3 ?

30. Example: If the density of Al is 2.71 g/cm 3, what is the density of Al in kg/m 3 ?