3.12.E: Chemistry, Matter, and Measurement (Exercises)
 Page ID
 290723
These are homework exercises to accompany Chapter 1 of the Ball et al. "The Basics of GOB Chemistry" Textmap.
Exercises

List four base units.

List four derived units.

How many meters are in 1 km? How many centimeters are in 1 m?

How many grams are in 1 Mg? How many microliters are in 1 L?

Complete the following table:
Unit Abbreviation centiliter ms cm kL micrometer 
Complete the following table:
Unit Abbreviation microliter kilosecond dL ns millimeter 
What are some appropriate units for density?

A derived unit for velocity, which is the change of position with respect to time, is meters per second (m/s). Give three other derived units for velocity.
Answers
1. second, meter, kilogram, and kelvin (answers will vary)
2. square meter (m^{2}), cubic meter (m^{3}), grams per milliliter (g/mL), milliliters per second (mL/s) answers will vary

1,000; 100

Unit Abbreviation centiliter cL millisecond ms centimeter cm kiloliter kL micrometer µm
Unit  Abbreviation 

microliter  µL 
kilosecond  ks 
deciliter  dL 
nanosecond  ns 
millimeter  mm 
7. grams per liter, grams per milliliter, and kilograms per liter (answers will vary)
8. kilometers per hour; meters per minute; millimeters per second (answers will vary)
Exercises

Why is scientific notation useful in expressing numbers?

What is the relationship between the power and the number of places a decimal point is moved when going from standard to scientific notation?

Express each number in scientific notation.
 0.00064
 5,230,000
 −56,200
 0.000000000220
 1.0

Express each number in scientific notation.
 678
 −1,061
 0.000560
 0.0000003003
 100,000,000

Express each number in standard form.
 6.72 × 10^{4}
 2.088 × 10^{−4}
 −3 × 10^{6}
 9.98 × 10^{−7}

Express each number in standard form.
 9.05 × 10^{5}
 1.0 × 10^{−3}
 6.022 × 10^{23}
 8.834 × 10^{−12}

Complete the following table:
Incorrect Scientific Notation Correct Scientific Notation 54.7 × 10^{4} 0.0066 × 10^{3} 3,078 × 10^{0} 
Complete the following table:
Incorrect Scientific Notation Correct Scientific Notation 234.0 × 10^{1} 36 × 10^{−4} 0.993 × 10^{5}
Answers

Scientific notation is more convenient than listing a large number of zeros.

 6.4 × 10^{−4}
 5.23 × 10^{6}
 −5.62 × 10^{4}
 2.20 × 10^{−10}
 1.0 × 10^{0}
 6.78 × 10^{2}
 −1.061 × 10^{3}
 5.60 × 10^{−4}
 3.003 × 10^{−7}
 1 × 10^{8}

 67,200
 0.0002088
 −3,000,000
 0.000000998
6. Express each number in standard form.
 905,000
 0.0010
 602,200,000,000,000,000,000,000
 0.000000000008834

Incorrect Scientific Notation Correct Scientific Notation 54.7 × 10^{4} 5.47 × 10^{5} 0.0066 × 10^{3} 6.6 × 10^{0} 3,078 × 10^{0} 3.078 × 10^{3}
8.
Incorrect Scientific Notation  Correct Scientific Notation 

234.0 × 10^{1}  2.340 × 10^{3} 
36 × 10^{−4}  3.6 × 10^{−3} 
0.993 × 10^{5}  9.93 × 10^{4} 
Exercises

Give the two conversion factors you can construct using each pair of units.
 meters and kilometers
 liters and microliters
 seconds and milliseconds

Give the two conversion factors you can construct using each pair of units.
 grams and centigrams
 millimeters and meters
 liters and megaliters

How many meters are in 56.2 km?

How many seconds are in 209.7 ms?

How many microliters are in 44.1 L?

How many megagrams are in 90.532 g?

Convert 109.6 kg into micrograms. Express your final answer in scientific notation.

Convert 3.8 × 10^{5} mm into kilometers. Express your final answer in scientific notation.

Convert 3.009 × 10^{−5} ML into centiliters. Express your final answer in scientific notation.

Convert 99.04 dm into micrometers. Express your final answer in scientific notation.

The density of ethyl alcohol is 0.79 g/mL. What is the mass of 340 mL of ethyl alcohol in kilograms? Do a 2step conversion.

The density of a certain fraction of crude oil is 1.209 g/mL. What is the mass of 13,500 mL of this fraction?

The density of ethyl alcohol is 0.79 g/mL. What is the volume of 340 g of ethyl alcohol in liters? Do a 2step conversion.

The density of a certain component of crude oil is 1.209 g/mL. What is the volume of 13,500 g of this component?
Answers

 \(\mathrm{\dfrac{1,000\:m}{1\:km}\,;\:\dfrac{1\:km}{1,000\:m}}\)
 \(\mathrm{\dfrac{1,000,000\:\mu L}{1\:L}\,;\:\dfrac{1\:L}{1,000,000\:\mu L}}\)
 \(\mathrm{\dfrac{1,000\:ms}{1\:s}\,;\:\dfrac{1\:s}{1,000\:ms}}\)
 \(\mathrm{\dfrac{1\:g}{100\:cg}\,;\:\dfrac{100\:cg}{1\:g}}\)
 \(\mathrm{\dfrac{1,000\:mm}{1\:m}\,;\:\dfrac{1\:m}{1,000\:mm}}\)
 \(\mathrm{\dfrac{1,000,000\:L}{1\:ML}\,;\:\dfrac{1\:ML}{1,000,000\:L}}\)

5.62 × 10^{4} m

4.41 × 10^{7} µL

1.096 × 10^{11} µg

3.009 × 10^{3} cL
11. 0.27 kg
12. 16,300 mL
13. 0.43 L
14. 11,200 mL
Exercises

Calculate the density of a mineral if the mass was found to be 760.15 grams and the volume of 0.25 Liters.

A sample of iron has a volume of 48.2 cm^{3}. Given the density of iron is 7.874 g/cm^{3}, what is its mass?

The volume of hydrogen used by the Hindenburg, the German airship that exploded in New Jersey in 1937, was 2.000 × 10^{8} L. If hydrogen gas has a
density of 0.0899 g/L, what mass of hydrogen was used by the airship?

The volume of an Olympicsized swimming pool is 2.50 × 10^{9} cm^{3}. If the pool is filled with alcohol (d = 0.789 g/cm^{3}), what mass of alcohol is in the pool?

A typical engagement ring has 0.77 cm^{3} of gold. What mass of gold is present? (d = 19.3 g/cm^{3})

A typical mercury thermometer has 0.039 mL of mercury in it. What mass of mercury is in the thermometer? (d = 5.43 g/cm^{3})

What is the volume of 100.0 g of lead if lead has a density of 11.34 g/cm^{3}?

What is the volume of 255.0 g of uranium if uranium has a density of 19.05 g/cm^{3}?

What is the volume in liters of 222 g of neon if neon has a density of 0.900 g/L?

What is the volume in liters of 20.5 g of sulfur hexafluoride if sulfur hexafluoride has a density of 6.164 g/L?

Which has the greater volume, 100.0 g of iron (d = 7.87 g/cm^{3}) or 75.0 g of gold (d = 19.3 g/cm^{3})?

Which has the greater volume, 100.0 g of hydrogen gas (d = 0.0000899 g/cm^{3}) or 25.0 g of argon gas (d = 0.00178 g/cm^{3})?
Answers
1. 3.04 g/mL
2. 380. g/cm^{3}
3. 1.80 x 10^{7} grams
4. 1.97 x 10^{9} grams
5. 15 grams
6. 0.21 grams
7. 5.249 cm^{3}
8. 13.39 cm^{3}
9. 247 Liters
10. 3.33 Liters
11. 100.0 g of iron
12. 100.0 g hydrogen gas
Dosage Calculations
Exercises
 Vitamin C tablets can come in 500 mg tablets. How many of these tablets are needed to obtain 10 g of vitamin C?
2. A tablet of penicillin contains 250 mg of the antibacterial drug. A prescription contains 44 tablets. What is the total mass of penicillin in the prescription?
3. The recommended daily allowance (RDA) for magnesium for 1930 yrs old+ men is 400 mg. Magnesium supplements come in 200 mg capsules. How many capsules need to be taken to meet RDA?
4. A 175 lb patient is to undergo surgery and will be given an intravenous anesthetic. The safe dosage of anesthetic is up 12 mg/kg of body weight. Determine the maximum dose of anesthetic that should be used. (Hint: 2.2 lbs = 1 kg)
5. The safe dosage of an IV antibiotic for children weighing more than 2.0kg is 60.mg per kilogram of body weight. How many mg should be administered to a child weighing 16 kg?
6. A drug dose of 1.5 mg/kg is ordered for a child weighing 70.4 lbs. How many mg of the drug should be administered? If the drug is available as 60 mg/2 mL. How many mL must the nurse administer?
Answers
1. 20 tablets
2. 11,000 mg; 11 g
3. 2 tablets
4. 955 mg
5. 960 mg
6. 48 mg; 1.6 mL
Exercises

A sample of urine has a density of 1.105 g/cm^{3}. What is the mass of 0.255 L of this urine?

The hardest bone in the body is tooth enamel, which has a density of 2.91 g/cm^{3}. What is the volume, in liters, of 75.9 g of tooth enamel?

Some brands of aspirin have 81 mg of aspirin in each tablet. If a person takes 8 tablets per day, how many grams of aspirin is that person consuming every day?

The US government has a recommended daily intake (RDI) of 5 µg of vitamin D per day. (The name recommended daily allowance was changed to RDI in 1997.) If milk contains 1.2 µg per 8 oz glass, how many ounces of milk are needed to supply the RDI of vitamin D?
5. The population of the United States, according to the 2000 census, was 281.4 million people.
a. What is the unit in this quantity?
b. Express this quantity in proper scientific notation.
6. The United States produces 34,800,000,000 lb of sugar each year, and much of it is exported to other countries.
 What is the unit in this quantity?
 Express this quantity in proper scientific notation.
7. Construct a conversion factor that can convert from one unit to the other in each pair of units.
 from millimeters to kilometers
 from kilograms to micrograms
 from centimeters to micrometers
8. Construct a conversion factor that can convert from one unit to the other in each pair of units.
 from kilometers to micrometers
 from decaliters to milliliters
 from megagrams to milligrams
9. What is the density of a dextrose solution if 355 mL of the solution has a mass of 406.9 g?
10. What is the density of a dental amalgam (an alloy used to fill cavities) if 1.005 kg of the material has a volume of 433 mL? Express your final answer in grams per milliliter.
For Exercises 11–16, see the accompanying table for the relationships between English and SI units.
1 m ≈ 39.36 in. ≈ 3.28 ft ≈ 1.09 yd 
1 in. ≈ 2.54 cm 
1 km ≈ 0.62 mi 
1 kg ≈ 2.20 lb 
1 lb ≈ 454 g 
1 L ≈ 1.06 qt 
1 qt ≈ 0.946 L 

Approximately how many inches are in 4.76 m?

Approximately how many liters are in 1 gal, which is exactly 4 qt?

Approximately how many kilograms are in a person who weighs 170 lb?

The average distance between Earth and the sun is 9.3 × 10^{7} mi. How many kilometers is that?

Show mathematically that 1 L equals 1 dm^{3}.

Show mathematically that 1 L equals 1,000 cm^{3}.
Answers

282 g

650 mg

 people
 2.841 × 10^{8} people
 pound (lb)
 3.48 x 10^{10} lbs
7
 \(\mathrm{\dfrac{1\:km}{10^6\:mm}}\)
 \(\mathrm{\dfrac{10^9\:\mu g}{1\:kg}}\)
 \(\mathrm{\dfrac{10^4\:\mu m}{1\:cm}}\)
8. Construct a conversion factor that can convert from one unit to the other in each pair of units.
 \(\mathrm{\dfrac{10^9\:\mu m}{1\:km}}\)
 \(\mathrm{\dfrac{100\:mL}{1\:dL}}\)
 \(\mathrm{\dfrac{10^9\:mg}{1\:Mg}}\)
9. 1.15 g/mL