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Use dimensional analysis and the proper conversion factors to solve each of the following problems.
Show all your work and factor-label set-up.
____
1. The density of acetic acid is 1.05 g/mL. What is the volume of 327 g of acetic acid? 3.11 ! 102 mL
____
2. The density of liquid mercury is 13.5 g/cm3. What mass of mercury will fill a 0.500 L container? 6.75 !
103 g
____
3. When 24 copper pennies are submerged in water, the pennies displace 8.26 cm3 of water. If the combined
mass of the pennies is 73.86 g, what is the density of copper? 8.94 g/cm3
____
4. You can identify a metal by carefully determining its density. A 8.44 g piece of an unknown metal is 1.25
cm long, 2.50 cm wide, and 1.00 cm thick. What is a possible identity of the element?
a. nickel, 8.90 g/cm3
b. *aluminum, 2.70 g/cm3
c. titanium, 4.54 g/cm3
d. zirconium, 6.51 g/cm3
e. chromium, 7.20 g/cm3
____
5. You can identify a metal by carefully determining its density. A 2.166 g piece of an unknown metal is
1.50 cm long, 0.550 cm wide, and 0.250 cm thick. What is a possible identity of the element?
a. *silver, 10.5 g/cm3
b. iridium, 22.4 g/cm3
c. platinum, 21.4 g/cm3
d. palladium, 12.0 g/cm3
e. none of the above
____
6. A cube of iron has a mass of 29.31 g. If each side of the cube has dimensions of 1.55 cm, what is the
density of iron? 7.87 g/cm3
____
7. At 0 °C, a bottle contains 325 mL of water in its liquid state. What is the volume of the water after it
freezes (at 0 °C)? The densities of liquid water and ice at 0 °C are 1.000 g/mL and 0.917 g/mL,
respectively. 354 mL
____
8. The boiling point of liquid helium is 4 K. What is this temperature in Celsius? -269 °C
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9. The temperature required to melt NaCl is 528 °C. What is this temperature in Kelvin? 801 K
____ 10. Which of the following is the greatest mass?
a. 2.3 ! 109 pg
b. 1.5 ! 108 ng
c. 6.6 ! 105 µg
d. *8.4 ! 102 mg
e. 3.0 ! 10-1 g
____ 11. The radius of a helium atom is 31 pm. What is the radius in nanometers? 3.1 ! 10-2 nm
____ 12. The wavelength of light emitted from a green laser pointer is 5.32 ! 102 nm. What is the wavelength in
meters? 5.32 ! 10-7 m
____ 13. A cylinder has a radius of 5.08 cm and a height of 125 cm. Calculate the volume of the cylinder in liters.
(Vcyl=!r2h) 10.1 L
____ 14. The dimensions of a box are 12 inch by 11 inch by 5.5 inch. Calculate the volume of the box in cm3.
There is 2.54 cm per inch. 1.2 ! 104 cm3
____ 15. If the fuel efficiency of an automobile is 27 miles per gallon, what is its fuel efficiency in kilometers per
liter? (1 km = 0.621 mile, 1.000 L = 1.057 quarts, 4 quarts = 1 gallon) 11 km/L
____ 16. Barium sulfate (BaSO4) is relatively insoluble in water. At 25 °C, only 244 mg will dissolve in 1.0 liter of
water. What volume of water is needed to dissolve 2.0 g of barium sulfate? 8.2 L
____ 17. At 25 °C, the density of oxygen in air is 0.275 g/L. What volume is occupied by 25 kg of oxygen at 25
°C? 9.1 ! 104 L
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____ 18. Which method is correct for determining the liters of gas required to fill an automobile's 15 gallon tank?
(1.000 L = 1.057 quarts, 4 quarts = 1 gallon)
ÊÁ 1 gallon ˆ˜ ÊÁ 1.057 quarts ˆ˜
˜˜ ÁÁ
˜˜ =
a. 15 gallons ÁÁÁÁ
˜˜ ÁÁ
˜˜
4
quarts
1
liter
Ë
¯Ë
¯
ÊÁ
b. 15 gallons ÁÁÁÁ
Ë
ÊÁ
c. 15 gallons ÁÁÁÁ
Ë
ˆ˜ ÊÁ
ˆ˜
1 liter
˜˜ ÁÁ
˜
˜˜ ÁÁ 1.057 quarts ˜˜˜ =
¯
¯Ë
ˆ
Ê
ˆ˜
4 quarts ˜˜˜ ÁÁÁ
1 liter
˜˜ =
˜
Á
1 gallon ˜¯ ÁË 1.057 quarts ˜˜¯
4 quarts ˆ˜˜˜ ÊÁÁÁ 1.057 quarts ˆ˜˜˜
˜˜ =
1 gallon ˜˜¯ ÁÁË
1 liter
¯
1 gallon
4 quarts
ÊÁ
d. 15 gallons ÁÁÁÁ
Ë
e. none of the above
____ 19. An electronic balance is used to determine that a sample has a mass of 25.7171 g. If the balance's
precision is ±0.1 mg, what is the correct number of significant figures for this measurement? 6
____ 20. Convert 5.000 ! 10-2 meters to millimeters and express the answer in standard notation using the correct
number of significant figures. 50.00 mm
____ 21. What is the correct answer to the following expression: (72.61 - 68.59) ! 18.76? Follow order of
operations. 75.4
____ 22. What is the correct answer to the following expression: (18 + 95) ! 0.077351? 8.74
____ 23. What is the correct answer to the following expression: 2.97 ! 10-5 + 6.13 ! 10-3? 6.16 ! 10-3
____ 24. Express 0.38300 in exponential notation.
____ 25. What mass of zinc (in kg) is in a 3.50 kg roll of tin foil that is 92.5% tin & 7.5% zinc? 0.26 kg
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