Density

What do you observe in the above picture? Why?
Answer: Ice floating in water; Density

Density is a physical property that relates the mass of a substance to its volume. Density is defined as mass per unit volume of a substance. Density is reported as g/ml or g/cc. The mathematical form of density d= m/v. Physical meaning of density refers to the compactness of the substance.

Density of a substance depends on temperature. Specially for liquids and gases, when temperature increases, volume expands and therefore density decreases. For most substances solid state is denser than liquid and liquid is more dense than gas. Water is an exception. Ice is less dense than liquid water. A less dense substance floats on a denser liquid.

Density also depends on pressure. An allotrope of carbon Diamond can be converted to graphite at a very high pressure. Although they contain the same atoms of carbon but they do not share the same density.

If two liquids are mixed together and they are immiscible, liquid with lower density is always on top of liquid with higher density. In other words, substance with higher density always sinks in substance with lower density and vice versa.

Densities of Common Substances

Material	Density (gm/cm^3)
Liquids
Water at 4 C	1.0000
Water at 20 C	0.998
Gasoline	0.70
Mercury	13.6
Milk	1.03
Material	Density (gm/cm^3)
Solids
Magnesium	1.7
Aluminum	2.7
Copper	8.3-9.0
Gold	19.3
Iron	7.8
Lead	11.3
Platinum	21.4
Uranium	18.7
Osmium	22.5
Ice at 0 C	0.92
Material	Density (gm/cm^3)
Gases at STP
Air	0.001293
Carbon dioxide	.001977
Carbon monoxide	0.00125
Hydrogen	0.00009
Helium	0.000178
Nitrogen	0.001251

There are two different ways density can be determined in Lab. 1) dimensional method and 2) displacement method.

In dimensional method, volume of the regularly shaped object is determined applying the standard formula. Mass of the object is determined using analytical balance. Then mass is divided by volume to determine the density.

Example: Determine the density of a unknown metal cube that has side length 3.00cmand mass is 310.672g.

Volume of the metal cube 3.00*3.00*3.00= 27.0 cm³

Density of the metal= 310.671/27.0= 11.5 g/cm³

In displacement method some water is taken in the graduated cylinder and then the irregular shaped object is dropped in the cylinder. Volume of water in the cylinder rises. The difference in volume between initial and final volume of graduated cylinder is the volume of the cylinder.

In the above example, volume of the liquid (96.0-90.0)ml =6.0 ml.
If the mass of the sample 16.9050g, the density of the sample = 16.9050/6.0 ml= 2.8 g/ml.

https://gpb.pbslearningmedia.org/resource/arct15-sci-densitylab/density-lab/

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TRY THIS OUT!

Phet Simulation:

https://phet.colorado.edu/en/simulations/density

Block#1: Styrofoam

Block#2: Wood

Block#3: Ice

Block#4: Aluminum

Block#5: Brick

Activity:

• Select each custom block and record mass, volume and density of each block.
• Click on the “my block” and determine the density.
• Convert the above density in g/cm³. Does the value change?
• Place each one of them in water. What do those blocks do in water?
• Does your observation depend on the mass/volume ratio?
• Would it be different if the liquid in the tank were ethanol instead of water?

Ans: 1) Wood m= 2.00kg, v= 5.00L; d= 0.400kg/L, Brick = 10.00/5.00=2.00kg/L, Ice 4.60/5.00 kg/L, Aluminum= 13.50/5.00= 2.70 Kg/L

2) density of my block 13.50/5.00= 2.70 Kg/L

3) same

4) Some sink and some float

5) Yes, if the mass/volume ratio>1 , sinks, if the ratio<1, float

6) Yes. Ethanol has different density than water. Less dense object floats, denser object sinks.

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Example problem:

1. Calculate the density of Aluminum block with mass 13.4958g and volume 4.98 cm³_.

D= m/v= 13.4958/4.98= 2.71 g/cm³

2. What is the volume of 25 g copper that has density 8.90 g/ml?

Density can be written as conversion factor.

8.90 g/1 ml or 1 ml/8.90 g Since we have to determine volume, volume will be the numerator of the ratio.

1 ml/8.90 g * 25 g = 2.8 ml (lowest sig fig 2)

Click on the right hand side of the screen and mystery metal. Find the mass and volume of the sample by displacement method, determine the density. Can you identify which metal is this?

Watch the following video:

Dimensional method:

Displacement method

Questions:

1) The given beaker contains 100 ml of water. Draw an illustration for what would be observed in each circumstances when the following liquids were added. a) Hexane 50.0ml d= 0.65 g/ml b) dichloromethane 50.0ml d=1.33 g/ml.

2. Gasoline has a density of about 0.65 g/mL. How much does 36.0 L weigh in pounds?

3. Which one has higher mass?  100 ml of water or 100 ml of Hg?

4. which substance has higher volume?  100 g of gold or 100 f of Copper?  Explain. ( Use the density chart above to answerthe question.

Ans: 1.hexane sinks and dichloromethane floats

2. 51.9 lb
3. With same volume, higher the density means mass means higher the mass. Hg
4. with same mass, higher the density means lower the volume. Gold has higher density than copper. Therefore Copper has greater volume than gold for a given mass.

Combined Dimensional Analysis Practice Problems

1. Convert 3.55 liters into milliliters.

2. Convert 1.64 pounds to grams and milligrams.

3. Convert 7.2 meters to centimeters and inches.

4. Convert 16,450 milligrams to grams and pounds.

5. Convert 12.0 feet into centimeters and meters.

6. Convert 1.500 days into minutes and seconds.

7. The highest temperature recorded in Washington D.C. was 106°F on July 20, 1930. Convert the temperature to °C and K.

8. On the 4^th of July, a sparkler burns at a temperature of 1644K. Convert the temperature to both °C and °

9. I like my steak cooked medium rare – which means it will have an internal temperature of 135° Convert this temperature to °C and K.

10. A student finds a rock on the way to school.  In the laboratory he determines that the volume of the rock is 22.7 cm³, and the mass in 39.943 g.   What is the density of the rock?

11. Calculate the density of a material that has a mass of 52.457 g and a volume of 13.5 cm³.

12. The density of zinc is approximately 7.13 g/mL.

7.13 g Zinc=1 mL Zinc          7.13 g Zinc   =   1   =   1 mL Zinc

          1 mL Zinc                   7.13 g Zinc

a) What is the volume, in cm³, of a 5.00 g piece of zinc?

b) What is the mass of a 45.6 L block of zinc?

13. a) A sample of iron has a volume of 25.0 cm³ has a mass of 174 grams. Calculate the density of iron.

b) What would be the mass of 15.0 of cm³ iron?

c) What would be the volume of 1000. grams of iron?

Ans: 1. 3550ml

2. 744 g and 744000 mg
3. 720 cm and 283 in
4. 16.45g and 0.03627 lb
5. 56.7 cm and 0.567 m
6. 2160 min and 129600 sec
7. 41.1 ⁰C and 314K
8. 1371 ⁰C and 2500.⁰F
9. 57.2 ⁰C and 330K
10. 1.76 g/cm³
11. 3.89 g/cm³
12. a) 0.701 ml
    b) 325000g
13. a) 6.96 g/cm³
    b) 104 g
    c) 144 cm³

Specific Gravity

Relative density, or specific gravity,^[1][2] is the ratio of the density (mass of a unit volume) of a substance to the density of a given reference material. Specific gravity for liquids is nearly always measured with respect to water at its densest (at 4 °C or 39.2 °F); for gases, the reference is air at room temperature (20 °C or 68 °F). The term “relative density” is often preferred in scientific usage.

If a substance’s relative density is less than 1 then it is less dense than the reference; if greater than 1 then it is denser than the reference. If the relative density is exactly 1 then the densities are equal; that is, equal volumes of the two substances have the same mass. If the reference material is water, then a substance with a relative density (or specific gravity) less than 1 will float in water. For example, an ice cube, with a relative density of about 0.91, will float. A substance with a relative density greater than 1 will sink.

Temperature and pressure must be specified for both the sample and the reference. Pressure is nearly always 1 atm (101.325 kPa). Where it is not, it is more usual to specify the density directly. Temperatures for both sample and reference vary from industry to industry. In British brewing practice, the specific gravity, as specified above, is multiplied by 1000.^[3] Specific gravity is commonly used in industry as a simple means of obtaining information about the concentration of solutions of various materials such as brines, sugar solutions (syrups, juices, honeys, brewers wort, must, etc.) and acids.