3.12.E: Chemistry, Matter, and Measurement (Exercises)

These are homework exercises to accompany Chapter 1 of the Ball et al. "The Basics of GOB Chemistry" Textmap.

 

The International System of Units

Exercises

1. List four base units.

2. List four derived units.

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

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

5. Complete the following table:

   Unit	Abbreviation
   centiliter
   	ms
   	cm
   	kL
   micrometer

6. Complete the following table:

   Unit	Abbreviation
   microliter
   kilosecond
   	dL
   	ns
   millimeter

7. What are some appropriate units for density?

8. 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 (m²), cubic meter (m³), grams per milliliter (g/mL), milliliters per second (mL/s) answers will vary

3. 1,000; 100

4. 1,000,000; 1,000,000

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

6.

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)

 

Expressing Numbers: Scientific Notation

Exercises

1. Why is scientific notation useful in expressing numbers?

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

3. Express each number in scientific notation.

   1. 0.00064
   2. 5,230,000
   3. −56,200
   4. 0.000000000220
   5. 1.0

4. Express each number in scientific notation.

   1. 678
   2. −1,061
   3. 0.000560
   4. 0.0000003003
   5. 100,000,000

5. Express each number in standard form.

   1. 6.72 × 10⁴
   2. 2.088 × 10⁻⁴
   3. −3 × 10⁶
   4. 9.98 × 10⁻⁷

6. Express each number in standard form.

   1. 9.05 × 10⁵
   2. 1.0 × 10⁻³
   3. 6.022 × 10²³
   4. 8.834 × 10⁻¹²

7. Complete the following table:

   Incorrect Scientific Notation	Correct Scientific Notation
   54.7 × 10^4
   0.0066 × 10^3
   3,078 × 10^0

8. Complete the following table:

   Incorrect Scientific Notation	Correct Scientific Notation
   234.0 × 10^1
   36 × 10^−4
   0.993 × 10^5

Answers

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

2. The power is the number of places a decimal point is moved when going from standard to scientific notation. It is positive if the decimal point is moved to the left; negative if moved to the right.

3.  

   1. 6.4 × 10⁻⁴
   2. 5.23 × 10⁶
   3. −5.62 × 10⁴
   4. 2.20 × 10⁻¹⁰
   5. 1.0 × 10⁰

4.

1. 6.78 × 10²
2. −1.061 × 10³
3. 5.60 × 10⁻⁴
4. 3.003 × 10⁻⁷
5. 1 × 10⁸

5.  

   1. 67,200
   2. 0.0002088
   3. −3,000,000
   4. 0.000000998

6. Express each number in standard form.

1. 905,000
2. 0.0010
3. 602,200,000,000,000,000,000,000
4. 0.000000000008834

7. 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

 

 

Converting Units

Exercises

1. Give the two conversion factors you can construct using each pair of units.

   1. meters and kilometers
   2. liters and microliters
   3. seconds and milliseconds

2. Give the two conversion factors you can construct using each pair of units.

   1. grams and centigrams
   2. millimeters and meters
   3. liters and megaliters

3. How many meters are in 56.2 km?

4. How many seconds are in 209.7 ms?

5. How many microliters are in 44.1 L?

6. How many megagrams are in 90.532 g?

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

8. Convert 3.8 × 10⁵ mm into kilometers. Express your final answer in scientific notation.

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

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

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

12. 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?

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

14. 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

1.  

   1. \(\mathrm{\dfrac{1,000\:m}{1\:km}\,;\:\dfrac{1\:km}{1,000\:m}}\)
   2. \(\mathrm{\dfrac{1,000,000\:\mu L}{1\:L}\,;\:\dfrac{1\:L}{1,000,000\:\mu L}}\)
   3. \(\mathrm{\dfrac{1,000\:ms}{1\:s}\,;\:\dfrac{1\:s}{1,000\:ms}}\)

2.

1. \(\mathrm{\dfrac{1\:g}{100\:cg}\,;\:\dfrac{100\:cg}{1\:g}}\)
2. \(\mathrm{\dfrac{1,000\:mm}{1\:m}\,;\:\dfrac{1\:m}{1,000\:mm}}\)
3. \(\mathrm{\dfrac{1,000,000\:L}{1\:ML}\,;\:\dfrac{1\:ML}{1,000,000\:L}}\)

3. 5.62 × 10⁴ m

4. 2.097 × 10^-1 s

5. 4.41 × 10⁷ µL

6. 9.0532 × 10^-5 g

7. 1.096 × 10¹¹ µg

8. 0.38 km; 3.8 × 10^-1 km

9. 3.009 × 10³ cL

10. 9.904 × 10⁶ µm

11. 0.27 kg

12. 16,300 mL

13. 0.43 L

14. 11,200 mL

 

Other Units - Density

Exercises

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

2. A sample of iron has a volume of 48.2 cm³. Given the density of iron is 7.874 g/cm³,  what is its mass?

3. The volume of hydrogen used by the Hindenburg, the German airship that exploded in New Jersey in 1937, was 2.000 × 10⁸ L. If hydrogen gas has a 

   density of 0.0899 g/L, what mass of hydrogen was used by the airship?

4. The volume of an Olympic-sized swimming pool is 2.50 × 10⁹ cm³. If the pool is filled with alcohol (d = 0.789 g/cm³), what mass of alcohol is in the pool?

5. A typical engagement ring has 0.77 cm³ of gold. What mass of gold is present? (d = 19.3 g/cm³)

6. A typical mercury thermometer has 0.039 mL of mercury in it. What mass of mercury is in the thermometer? (d = 5.43 g/cm³)

7. What is the volume of 100.0 g of lead if lead has a density of 11.34 g/cm³?

8. What is the volume of 255.0 g of uranium if uranium has a density of 19.05 g/cm³?

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

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

11. Which has the greater volume, 100.0 g of iron (d = 7.87 g/cm³) or 75.0 g of gold (d = 19.3 g/cm³)?

12. Which has the greater volume, 100.0 g of hydrogen gas (d = 0.0000899 g/cm³) or 25.0 g of argon gas (d = 0.00178 g/cm³)?

 

Answers

1. 3.04 g/mL

2. 380. g/cm³

3. 1.80 x 10⁷ grams

4. 1.97 x 10⁹ grams

5. 15 grams

6. 0.21 grams

7. 5.249 cm³

8. 13.39 cm³

9. 247 Liters

10. 3.33 Liters

11. 100.0 g of iron

12. 100.0 g hydrogen gas

 

Dosage Calculations

Exercises

1. 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 19-30 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

Chapter Summary

Exercises

1. A sample of urine has a density of 1.105 g/cm³. What is the mass of 0.255 L of this urine?

2. The hardest bone in the body is tooth enamel, which has a density of 2.91 g/cm³. What is the volume, in liters, of 75.9 g of tooth enamel?

3. 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?

4. 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.

1. What is the unit in this quantity?
2. 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.

1. from millimeters to kilometers
2. from kilograms to micrograms
3. from centimeters to micrometers

8. Construct a conversion factor that can convert from one unit to the other in each pair of units.

1. from kilometers to micrometers
2. from decaliters to milliliters
3. 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

11. Approximately how many inches are in 4.76 m?

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

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

14. The average distance between Earth and the sun is 9.3 × 10⁷ mi. How many kilometers is that?

15. Show mathematically that 1 L equals 1 dm³.

16. Show mathematically that 1 L equals 1,000 cm³.

Answers

1. 282 g

2. 26.1 cm³; 0.0261 L

3. 650 mg

4. 30 oz

5.  

   1. people
   2. 2.841 × 10⁸ people

6.

1. pound (lb)
2. 3.48 x 10¹⁰ lbs

7

1. \(\mathrm{\dfrac{1\:km}{10^6\:mm}}\)
2. \(\mathrm{\dfrac{10^9\:\mu g}{1\:kg}}\)
3. \(\mathrm{\dfrac{10^4\:\mu m}{1\:cm}}\)

8. Construct a conversion factor that can convert from one unit to the other in each pair of units.

1. \(\mathrm{\dfrac{10^9\:\mu m}{1\:km}}\)
2. \(\mathrm{\dfrac{100\:mL}{1\:dL}}\)
3. \(\mathrm{\dfrac{10^9\:mg}{1\:Mg}}\)

9. 1.15 g/mL

10. 2.321 g/mL

 

11. 187 in.

 

12. 3.784 L

 

13. 77 kg

 

14. 1.5 × 10⁸ km

 

15. \(\mathrm{1\:L=0.001\:m^3\times\left(\dfrac{1\:dm}{0.1\:m}\right)^3=1\:dm^3}\)

 

16. \(\mathrm{1\:L=0.001\:m^3\times\left(\dfrac{1\:cm}{0.01\:m}\right)^3=1000\:cm^3}\)