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1 This slide show has been prepared under fair use exemption of the U.S. Copyright Law and are restricted from further use.

2 Density & Dimensional Analysis

3 Density - the volume which is occupied by a specific mass of a material, usually given in units of grams per cubic centimeters or grams per milliliter. D = m/v

4 The density of a liquid can be determined by massing the liquid and then measuring the exact volume.

5 The volume of a solid can be difficult to measure, so its density is determined using a different method. The volume is found by measuring the volume of a liquid that the solid displaces. In the example below, the volume of the compound is 17.2 ml Volume of water= 15.0 ml Volume of water + compound = 32.2 ml

6 To solve all math problems in this class you will use the u,k,p,s method. u: unknown k: known p: plan s: solve

7 An aluminum bar with a volume of 35 cm 3 has a mass of 94.5 g. What is the density of aluminum based on this information? u: density Al k: m= 94.5 g; v=35cm 3 p: d= m v s: d = 94.5g = 35cm g/cm 3

8 A glass tube that holds exactly ml is filled with liquid mercury metal whose mass is shown to be g. From these data, what is the density of mercury metal? u: density Hg k: m= g; v= ml p: d= m v s: d = 1020g = 13.6 g/ml 75mL

9 The mass of 155 ml of ethyl alcohol is found to be exactly g. What is the density of ethyl alcohol? u: density of ethyl alcohol k: m= 122.5g; v=155ml p: d= m v s: d = 122.5g = g/ml 155mL

10 A block of ice with a mass of 519.0g is found to occupy a volume of cm 3. What is the density of the ice? u: density H 2 O(s) k: m= g; v=565.8cm 3 p: d= m v s: d = 519.0g = cm g/cm 3

11 Find the density of a sample of silicon which has a volume of 235.7cm 3 and a mass of g. u: density Si k: m= g; v=235.7cm 3 p: d= m v s: d = g = cm g/cm 3

12 A solid cube of impure zinc metal, 3.50 cm on a side, has a density of 6.95g/cm 3. What is the mass of the cube? u: mass of Zn k: d= 6.95g/mL; l(per side)=3.50cm p: d= m volume=l*w*h v s: volume =3.50cm*3.50cm*3.50cm = 42.88cm g = m = cm cm 3 (6.95g)(42.88cm 3 ) = m (cm 3 ) cm 3 cm 3 m = 176 g

13 An irregularly shaped piece of gold (density = 19.3g/cm 3 ) has a mass of 428.4g. What is the volume of this piece of gold? u: volume of Au k: d= 19.3g/mL; m=428.4g p: d= m v s: 19.3g = 428.4g = ml v (19.3g)(v) = ml (428.4g) 19.3g 19.3g 22.2cm 3 Au = v

15 = ***10*** **6.0** E-4

16 What is the density of carbon dioxide gas if g occupies a volume of 100 ml? U: density Carbon dioxide k: mass CO 2 = g; vol. CO 2 =100mL p: d= m v s: d = 0.196g = g/mL 100mL 2 E -3 g/ml

17 A block of wood 3.0 cm on each side has a mass of 27g. What is the density of this block? u: d wood k: m = 27g length = 3.0 cm p: d= m volume = l * w * h v s: volume = 3.0cm * 3.0cm * 3.0cm = 27cm 3 d wood = 27 g = 27 cm g/cm 3

18 An irregularly shaped stone was lowered into a graduated cylinder holding a volume of water equal to 2.0 ml. The height of the water rose to 7.0 ml. If the mass of the stone was 25g. What was its density? u: d stone = k: v 1 =2.0mL; v 2 = 7.0mL; m = 25g p: d= m vol = v 2 v 1 v S: vol = 7.0mL 2.0mL = 5.0mL d = 25 g = 5.0mL 5.0 g/ml

19 A 10.0 cm 3 sample of copper has a mass of 89.6g. What is the density of copper? u: d copper = k: v = 89.6 cm 3 ; m = 10.0g p: d= m v S: d = 89.6g = 10.0 cm g/cm 3

20 Silver has a density of 10.5g/cm 3 and gold has a density of 19.3 g/cm 3. What would have a greater mass, 5 cm 3 of silver or 5cm 3 of gold? u: m Ag, m Au k: v Ag =5cm 3 ; v Au = 5cm 3 ; d = 10.5g/cm 3 p: d= m v S: 10.5 g = m Ag 19.3 g = m Au cm 3 5.0cm 3 cm 3 5.0cm g (5.0cm 3 ) = m Ag (cm 3 ) 19.3g (5.0cm 3 )= m Au (cm 3 ) cm 3 cm 3 cm 3 cm g = m Ag 96.5g = m Au 5 g of gold

21 Five ml of ethanol has a mass of 3.9g, and 5.0mL of benzene has a mass of 4.4g. Which liquid is denser? u: d ethanol, d benzene k: v ethanol =5mL; v benzene = 5mL; m ethanol =3.9g m benzene = 5.0g p: d= m v S: d ethanol = 3.9g d benzene = 4.4 g 5.0mL 5.0mL d ethanol = 0.78g/mL d benzene = 0.88g/mL Benzene is denser

22 A sample of iron has the dimensions of 2cm x 3cm x 2cm. If the mass of this rectangular-shaped object is 94g, what is the density of iron? u: d iron k: m = 94g l=3cm, w=2cm, h=2cm p: d= m volume = l * w * h v s: volume = 3cm * 2cm * 2cm = 12 cm 3 d wood = 94g = 7.8g/cm 3 12 cm 3 8g/cm 3

23 At times you need to convert from one unit to another, but you do not have a formula in which to plug the numbers into. You can use the relationship between any two known units. These are called conversion factors. For example, there are 60 minutes in one hour, so the relationship is 1 hour=60minutes or 1 hour or 60 mins. 60 mins. 1 hour

24 EE Math formulas Dimensional Analysis density Specific heat conversion

25 Other examples of conversion factors are: 1mile = 5 280ft OR 1mile OR 5280 ft 5280 ft 1 mile 11 lbs = 5 kg OR 11 lbs OR 5kg 5 kg 11 lbs

26 A number ### with a unit ### X Must equal 1 but not be the same. For all problems you MUST use Unknown, Known, Plan, Solve (note how this follows the scientific method.)

27 Begin with KNOWN what you want to convert from. Ex: 4 m = cm u: cm k: 4 m p: 1m=100cm s: Known 4m 100 cm 1 m

28 Multiply across the top row and divide by each section on the bottom. 4m 100 cm =4*100cm= 400cm 1 m 1 1 = 400 cm

29 Convert 10 m to Km. U: Km K: 10m P: 1 Km= 1000m S: 10 meters 1 Km = 10 *1 Km 1000 meters 1000 = 0.01 Km

30 How much will it cost to take a trip by car. Where? Miles? Type of car? Miles per gallon? $ per gallon? u: how much does it cost to drive to Myrtle Beach k: 1 Myrtle Beach p: 1 Myrtle Beach = 250 miles; 1 gallon = $2.50; 25 miles =1 gallon

31 u: how much does it cost to drive to Myrtle Beach k:1 Myrtle Beach p :1 Myrtle Beach = 250 miles; 1 gallon = $2.50; 25 miles =1 gallon 1 Myrtle Beach 250 miles 1 gallon $ Myrtle Beach 25 miles 1 gallon = 1 * 250 * 1 * $ = $25

33 1 Exe (E) = Penta (P) = Tetra (T) = Giga (G) = Mega (M) = Kilo (K) = 10 3 (1000) 1 Hecto(H) = 10 2 (100) 1 Deka (D) = 10

34 1 = 10 deci (d) 1 = 100 centi (c) 1 = 1000 milli (m) 1 = 10 6 micro (μ) 1 = 10 9 nano (n) 1 = pico (p)

35 1 Kilo(K) = 10 3 (1000) 1 Hecto(H) = 10 2 (100) 1 Deka (D) = 10 1 = 10 deci (d) 1 = 100 centi (c) 1 = 1000 milli (m)

36 Steps: 1. Start with the original number and unit (your known) 2. Multiply by a unit factor (any two numbers and units that are equal). Place the unit that cancels on the bottom and the new unit on top. 3. Cancel units. 4. Repeat as needed 5. Perform numerical calculations!!!

37 500 ml = L U: L K: 500 ml P: 1 L = 1000mL S: 500mL 1 Kilo(K) = 10 3 (1000) 1 Hecto(H) = 10 2 (100) 1 Deka (D) = 10 1 = 10 deci (d) 1 = 100 centi (c) 1 = 1000 milli (m) 1 L = 500 * 1 L 1000 ml 1000 = 0.5L

38 25 cg = g U: g K: 25 cg P: 1 g= 100cg S: 25 cg 1 Kilo(K) = 10 3 (1000) 1 Hecto(H) = 10 2 (100) 1 Deka (D) = 10 1 = 10 deci (d) 1 = 100 centi (c) 1 = 1000 milli (m) 1 g = 25 * 1g 100 cg 100 = 0.25L

39 400 mg = kg U: kg K: 400 mg P: 1 g= 1000mg; 1000g = 1kg S: 400 mg 1 g 1000 mg 1kg 1000 g = 400 * 1 * 1kg = kg 1 Kilo(K) = 10 3 (1000) 1 Hecto(H) = 10 2 (100) 1 Deka (D) = 10 1 = 10 deci (d) 1 = 100 centi (c) 1 = 1000 milli (m)

40 30 cm = mm U: mm K: 30 cm P: 1 m= 100 cm; 1m = 1000mm S: 30cm 1 m 100 cm = 30 * 1 * 1000mm = 300 mm 1 Kilo(K) = 10 3 (1000) 1 Hecto(H) = 10 2 (100) 1 Deka (D) = 10 1 = 10 deci (d) 1 = 100 centi (c) 1 = 1000 milli (m) 1000mm 1 m

41 3500 sec = hr U: hr K: 3500 secs P: 1 min= 60 s; 60 mins=1 hr S: 3500 s 1 min 60 s = 3500 * 1 * 2hr =0.97 hr 1 hr 60 min

42 2 yrs = secs U: secs K: 2 yrs P: 365 days= 1 yr; 1 day=60mins;1 min=60sec S: 2 yrs 365 days 1 yr = 2 * 365 * 60sec = sec 60 min 1 day 60sec 1 min

43 barrels 42 gal L 1000mL 1 barrel 1 gallon 1L = ml of oil spilled into the Gulf of Mexico 719 trillion 604 billon 411millon 960 thousand gallons

44 sec cg lbs in hr 6. 2 E 24 molecules moles liters moles E 24 molecules liters liters

Density What is density? How do you measure density?

Density What is density? How do you measure density? What is density? Density describes how much mass is in a given volume of a material. Mass: the amount of matter in an object. Volume: the amount of