Density and Significant Figures in Calculations

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Density and Significant Figures in Calculations

• Practice Problems

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1) A block of aluminum occupies a volume of 15.0
mL and weighs 40.5 g. What is its density?

• Given
• Volume 15.0 mL
• Mass 40.5 g
• Density
• Density 40.5 g 2.70 g/mL
• 15.0 mL

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2) Mercury metal is poured into a graduated
cylinder that holds exactly 22.5 mL. The mercury
used to fill the cylinder weighs 306.0 g. From
this information, calculate the density of
mercury.

• Given
• Volume 22.5 mL
• Mass 306.0 g
• Density
• Density 306.0 g 13.6 g/mL
• 22.5 mL

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3) What is the weight of the ethyl alcohol
that exactly fills a 200.0 mL container? The
density of ethyl alcohol is 0.789 g/mL.

• Given
• Volume 200.0 mL
• Density 0.789 g/mL
• Density
• D V M or M D V
• Mass (0.789 g/mL)(200.0mL) 157.8 g
• 
  158 g

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4) A rectangular block of copper metal weighs
1896 g. The dimensions of the block are 8.4 cm by
5.5 cm by 4.6 cm. From this data, what is the
density of copper?

• Given
• Mass 1896 g
• Volume 8.4cm x 5.5cm x 4.6cm 212.52cm3
• 
  210 cm3
• Density
• Density 1896 g 9.028571429 g/cm3
• 210 cm3 9.0
  g/cm3

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5) A flask that weighs 345.8 g is filled with 225
mL of carbon tetrachloride. The weight of the
flask and carbon tetrachloride is found to be
703.55 g. From this information, calculate the
density of carbon tetrachloride.

• Given
• Mass flask/carbon tetrachloride 703.55 g
• Mass flask 345.8g
• Mass carbon tetrachloride 703.6g - 345.8g
  357.8g
• Volume 225 mL
• Density
• Density 357.8 g 1.5902222222 g/mL
• 225 mL
  1.59 g/mL

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6) Calculate the density of sulfuric acid if 35.4
mL of the acid weighs 65.14 g.

• Given
• Volume 35.4 mL
• Mass 65.14 g
• Density
• Density 65.14 g 1.840112994 g/mL
• 35.4 mL
  1.84 g/mL

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7) Find the mass of 250.0 mL of benzene. The
density of benzene is 0.8765 g/mL.

• Given
• Volume 250.0 mL
• Density 0.8765 g/mL
• Density
• D V M or M D V
• Mass (0.8765g/mL)(250.0mL) 219.125g
• 
  219.1g

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8) A block of lead has dimensions of 4.50 cm by
5.20 cm by 6.00 cm. The block weighs 1587 g. From
this information, calculate the density of lead.

• Given
• Mass 1587 g
• Volume 4.50cm x 5.20cm x 6.00cm 140.4cm3
• 
  140. cm3
• Density
• Density 1587 g 11.33571429 g/cm3
• 140. cm3 11.3
  g/cm3

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9) 28.5 g of iron shot is added to a graduated
cylinder containing 45.50 mL of water. The water
level rises to the 49.10 mL mark, From this
information, calculate the density of iron.

• Given
• Mass 28.5 g
• Volume 49.10 mL - 45.50 mL 3.60 mL
• Density
• Density 28.5 g 7.91666666667 g/mL
• 3.60 mL
  7.92 g/mL

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10) What volume of silver metal will weigh
exactly 2500.0 g? The density of silver is 10.5
g/cm3.

• Given
• Mass 2500.0 g
• Density 10.5g/cm3
• Density
• D V M and then V M/D
• Volume 2500.0 g 238.095238095 cm3
• 10.5g/cm3
  238 cm3

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Density Problem Set (2)

• Practice Problems

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1) Iron has a density of 7.87 g/ cm3. What is
the mass of 26.3 g of Fe? The answer is the
mass 26.3 grams but if you assumed there was a
typo.

• Given
• Mass 26.3 g
• Density 7.87 g/cm3
• Density
• V M/D
• Volume 26.3 g 3.34180432020
  cm3
• 7.87g/cm3
  3.34 cm3

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2) If 1.00 km3 of air has a mass of 1.2
billion kg, what is the density of air?

• Given
• Volume 1.00 km3
• Mass 1.2 x 109 kg
• Density
• Density 1.2 x 109 kg 1.2 x 109 kg/km3
• 1.00km3

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3) Aluminum, because of its light density and
strength, has been used for making aircraft. It
has a density of 2.70 g/ cm3. Magnesium has
similar properties and it has a density of 1.74
g/ cm3. What would the difference in mass if
1000 cm3 of magnesium are used instead of 1000
cm3 of aluminum?

• Aluminum Magnesium
• Given Given
• Density 2.70 g/ cm3 Density 1.74
  g/ cm3 Volume 1000 cm3 Volume 1000
  cm3
• Density M Density M
• V V
• M D V M D V
• M (2.70 g/ cm3)(1000 cm3) M (1.74 g/
  cm3)(1000 cm3)
• M 2700 g M 1740 g
• Difference in mass 2700 g - 1740 g 960 g

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4) Find the density of gasoline if 9.00 dm3 have
a mass of 6120 g.

• Given
• Volume 9.00 dm3
• Mass 6120 g
• Density
• Density 6120 g 680 g/dm3
• 9.00 dm3

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5) The density of nitrogen gas is 1.25 g/dm3.
What is the mass of 1 m3 of nitrogen?

• Given
• Density 1.25 g/dm3
• Density
• DV M
• 1.25 g 1,000 dm3 1m3 1250
  g
• dm3 1m3

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6) Illegal ivory is sometimes detected on the
basis of density. What is the density of a
sample of ivory whose volume is 14.5 cm3 and
whose mass is 26.8 g?

• Given
• Volume 14.5 cm3
• Mass 26.8 g
• Density
• Density 26.8 g 1.848275862 g/ cm3
• 14.5 cm3 1.85 g/ cm3

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7) What is the density of a rectangular piece
of concrete 5.00 cm x 10.0 cm x 23.0 cm having a
mass of 3.22 kg?

• Given
• Volume (5.00cm)(10.0cm)(23.0cm) 1150cm3
• Mass 3.22 kg
• Density
• Density 3.22 g 0.00280 g/ cm3
• 1150 cm3

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8) Vanadium hardens steel. Vanadium steel is
used in armor plate on tanks, for example. If
its density is 5.96 g/cm3, a cubic meter would
have a mass of how many kg?

• Given
• Density 5.96 g/cm3
• Volume 1m3
• D
• D V M
• 5.96 g 1,000,000 cm3 1m3
  5,960,000 g
• cm3 1m3

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9) Hydrogen has a density of 0.089 g/dm3
whereas helium has a density of 0.178 g/dm3,
about twice that of hydrogen. What is the mass
of helium in a 10,000 m3 blimp?

• Given
• Density 0.178 g/dm3
• Volume 10,000m3
• D
• D V M
• 0.178 g 1,000 dm3 10,000m3
  1,780,000 g
• dm3 1m3

M
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10) The diameter of the sun is estimated to
be about 865,000 miles. Astronomers also
estimate its average density to be 1.4 g/cm3.
What is its mass in kilograms? Remember the
volume formula for a sphere.

• Given
• Density 1.4 g/cm3
• Diameter 865,000 mi so Radius 432,500
  mi
• V 4 p r3 4 p (69,604,128,000cm)3
• 3 3
• V 1.41251673 x 1033 cm3
• D M so M DV (1.4 g/cm3)(1.41251673
  x 1033 cm3)
• V M 1.977523422
  x 1033 g
• 432500mi 5280 ft 12 in 2.54cm
  69,604,128,000cm
• 1 mi 1ft
  1 in

R
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• METRIC CONVERSION WORKSHEET
• Answers

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• How many seconds are there in three (3) days?
• 3 days 24 hrs 60 min 60 sec
  2,592,000 sec
• 1 day 1hr 1 min

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• A hydrogen electron moves at 2000 km/sec.
  Convert that to ft/sec.
• 2000 km 1,000m 100 cm 1in
  1ft
• 1km 1m 2.54
  cm 12 in
• 2000km 6561679.79 ft
• Answer 6561679.79 ft/sec

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• 3. 82 F is what in C?
• Given
• Temp. 82 F
• C ( F - 32 ) 5/9
• C ( 82 - 32 ) 5/9
• C (50) 5/9 250/9 27.77777777 C 28 C

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4. Your new living room has the dimensions of 14
ft. by 16 ft. The tile that you want to put down
is on sale, but the store has only 15m2 of tile.
Will this be enough to cover your living room
floor? Given Dimensions 14 ft x 16 ft 14
ft 12 in 2.54 cm 1m
4.2672 m 4.3 m 1ft 1in
100cm 16 ft 12 in 2.54 cm 1m
4.8768 m 4.9 m 1ft
1in 100cm Tile needed (4.3 m)
(4.9 m) 21.07 m2 NO
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5. The density of magnesium is 1.74 g/cc. What
is the volume of a 42g piece of magnesium?
Given Density 1.74 g/cc Mass 42
g D M So V M V
D V 42g 24.13793103 cc 24 cc
1.74 g/cc
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• Convert 876,000,000,000 and .00000000000457 into
  scientific notation.
• 876,000,000,000 8.76 x 1011
• .00000000000457 4.57 x 10-12

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• 7. How many kilometers are in 27.2 miles?
• 27.2 mi 5280 ft 12 in 2.54 cm
  1m 1 km 43.7741568 km
• 1mi 1ft
  1in 100 cm 1,000m
• 43.8 km
• Note The number of significant figures is from
  the 27.2 miles (which has 3 significant figures).
  We usually do not worry about the number of
  significant figures in the conversion units.

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8. The doctor says that I need to give my child
3.5cc of cough medicine. How many tablespoons
will that be? 3.5 cc 1 Tbsp
0.236646382 Tbsp 0.24 Tbsp
14.79cc Note 1 Tbsp 14.79
mL but since cc, cm3, mL are all the same
amount, the conversion can be written as
1 Tbsp 14.79 cc Also the significant
figures were based on the unit to be converted,
3.5 cc which has 2 significant figures.
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9. You have to be 1.4 meters tall to ride the
roller coaster. How many meters tall are you,
and will you be able to ride the roller coaster?
(your height in inches) 2.54 cm 1m
(your height in m)
1in 100cm

compare with 1.4 m
to answer the
question
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• All I have are metric sockets (mm). The bolt
  takes a 1/2 inch socket. What is the closest
  metric socket?
• 0.5 in 2.54 cm 10 mm 12.7 mm
• 1 in 1cm so
  the choice would be the
• 13mm socket

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