CHE121 Chaper 2 Worked Examples / Extra Questions

On a typical day, a nurse encounters several situations involving measurement. State the name and type of measurement indicated by the units in each of the following:

a. A patient has a temperature of 38.5 °C.

b. A physician orders 1.5 g of cefuroxime for injection.

c. A physician orders 1 L of a sodium chloride solution to be given intravenously.

d. A medication is to be given to a patient every 4 h.

a. A degree Celsius is a unit of temperature.

b. A gram is a unit of mass.

c. A liter is a unit of volume.

d. An hour is a unit of time.

State the names and types of measurements for an infant that is 54.6cm long with a mass of 5.2 kg

A centimeter (cm) is a unit of length. A kilogram (kg) is a unit of mass.

Identify each of the following numbers as measured or exact and give the number of significant figures (SFs) in each of the measured numbers:

a. 0.020 80 kg

b. 5.06 × 10⁴ h

c. 4 chemistry books

d. 85 600 s

a. measured; four SFs

b. measured; three SFs

c. exact

d. measured; three SFs

Identify each of the following numbers as measured or exact, and give the number of significant figures (SFs) in each of the measured numbers:

a. 0.170 L

b. 4 knives

c. 6.3 × 10⁻⁶ s

d. 1 m = 100 cm

a. measured; three SFs

b. exact

c. measured; two SFs

d. exact

Round off or add zeros to each of the following measurements to give three significant figures:

a. 35.7823 m

b. 0.002 621 7 L

c. 3.8268 × 10³ g

d. 8 s

a. 35.8 m

b. 0.002 62 L

c. 3.83 × 10³ g

d. 8.00 s

Round off each of the measurements in to two significant figures:

a. 35.8 m

b. 0.002 62 L

c. 3.83 × 10³ g

d. 8.00 s

a. 36 m

b. 0.0026 L

c. 3.8 × 10³ g

d. 8.0 s

Perform the following calculations with measured numbers. Write each answer with the correct number of significant figures:

a. 56.8 × 0.37

b. (2.075)(0.585) / (8.42)(0.0245)

c. 25.0 / 5.00

Step 1: Determine the number of significant figures in each measured number.

a. 56.8 = 3 SFs; 0.37 = 2 SFs
b. 2.075 = 4 SFs; 0.585 = 3 SFs; 8.42 = 3 SFs; 0.0245 = 3 SFs
c. 25.0 = 3 SFs; 5.00 = 3 SFs

Step 2: Perform the indicated calculation.

a. 21.016
b. 5.88433345
c. 5

Step 3: Round off or add zeros to give the same number of significant figures as the measurement having the fewest significant figures.

a. 21
b. 5.88
c. 5.00

Perform the following calculations with measured numbers, and give the answers with the correct number of significant figures:

a. 45.26 × 0.01088

b. 2.6 ÷ 324

c. 10.00 ÷ 5.00

a. 0.4924
b. 8.0 × 10⁻³
c. 2.0

Perform the following calculations with measured numbers and give each answer with the correct number of decimal places:

a. 104 + 7.8 + 40

b. 153.247 − 14.82

Step 1: Determine the number of decimal places in each measured number.

a. 104 = ones place; 7.8 = tenths place; 40 = tens place
b. 153.247 = thousandths place; 14.82 = hundredths place

Step 2: Perform the indicated calculation.

a. 151.8
b. 138.427

Step 3: Round off or add zeros to give the same number of decimal places as the measured number having the fewest decimal places.

a. 150, rounded off to the tens place
b. 138.43, rounded off to the hundredths place

Perform the following calculations with measured numbers, and give each answer with the correct number of decimal places:

a. 82.45 + 1.245 + 0.000 56

b. 4.259 − 3.8

a. 83.70
b. 0.5

An endoscopic camera has a width of 1 mm. Complete each of the following equalities involving millimeters:

a. 1 m = ___ mm

b. 1 cm = ___ mm

a. 1 m = 1000 mm
b. 1 cm = 10 mm

a. What is the relationship between millimeters and micrometers?

b. What is the relationship between liters and centiliters?

a. 1 mm = 1000 μm (mcm)
b. 1 L = 100 cL

Write the equality and two conversion factors, and identify each number as exact or give the number of significant figures for each of the following:

a. The medication that Greg takes for his high blood pressure contains 40. mg of propranolol in 1 tablet.

b. Cold-water fish such as salmon contains 1.9% omega-3 fatty acids by mass.

c. The U.S. Environmental Protection Agency (EPA) has set the maximum level for mercury in tuna at 0.5 ppm.

a.

Equality:
1 tablet = 40. mg of propranolol

Conversion factors:
40. mg propranolol / 1 tablet
and
1 tablet / 40. mg propranolol

Significant figures or exact:
The 40. mg is measured: it has two significant figures. The 1 tablet is exact.

b.

Equality:
100 g salmon = 1.9 g omega-3 fatty acids

Conversion factors:
1.9 g omega-3 fatty acids / 100 g salmon
and
100 g salmon / 1.9 g omega-3 fatty acids

Significant figures or exact:
The 1.9 g is measured: it has two significant figures. The 100 g is exact.

c.

Equality:
1 kg tuna = 0.5 mg mercury

Conversion factors:
0.5 mg mercury / 1 kg tuna
and
1 kg tuna / 0.5 mg mercury

Significant figures or exact:
The 0.5 mg is measured: it has one significant figure. The 1 kg is exact.

Write the equality and its corresponding conversion factors, and identify each number as exact or give the number of significant figures for each of the following:

a. Levsin (hyoscyamine), used to treat stomach and bladder problems, is available as drops with 0.125 mg of Levsin per 1 mL of solution.

b. The EPA has set the maximum level of cadmium in rice as 0.4 ppm.

a.

Equality:
1 mL of solution = 0.125 mg of Levsin

Conversion factors:
0.125 mg Levsin / 1 mL solution
and
1 mL solution / 0.125 mg Levsin

Significant figures or exact:
The 0.125 mg is measured: it has three significant figures. The 1 mL is exact.

b.

Equality:
1 kg of rice = 0.4 mg of cadmium

Conversion factors:
0.4 mg cadmium / 1 kg rice
and
1 kg rice / 0.4 mg cadmium

Significant figures or exact:
The 0.4 mg is measured: it has one significant figure. The 1 kg is exact.

Greg’s doctor has ordered a PET scan of his heart. In radiological imaging, dosages of pharmaceuticals are based on body mass. If Greg weighs 164 lb, what is his body mass in kilograms?

Step 1: State the given and needed quantities.

Given: 164 lb
Need: kilograms

Step 2: Write a plan to convert the given unit to the needed unit.

pounds → U.S.–Metric factor → kilograms

Step 3: State the equalities and conversion factors.

1 kg = 2.20 lb

Conversion factors:
2.20 lb / 1 kg
and
1 kg / 2.20 lb

Step 4: Set up the problem to cancel units and calculate the answer.

164 lb × 1 kg / 2.20 lb = 74.5 kg

Answer: 74.5 kg

a. A total of 2500 mL of a boric acid antiseptic solution is prepared from boric acid concentrate. How many quarts of boric acid have been prepared?

b. A vial contains 65 mg of phenobarbital per 1 mL of solution. How many milliliters are needed for an order of 40. mg of phenobarbital?

a. 2.6 qt
b. 0.62 mL

Greg has been diagnosed with diminished thyroid function. His doctor prescribes a dosage of 0.150 mg of Synthroid to be taken once a day. If tablets in stock contain 75 mcg of Synthroid, how many tablets are required to provide the prescribed medication?

Step 1: State the given and needed quantities.

Given: 0.150 mg of Synthroid
Need: number of tablets

Step 2: Write a plan to convert the given unit to the needed unit.

milligrams → metric factor → micrograms → clinical factor → number of tablets

Step 3: State the equalities and conversion factors.

1 mg = 1000 mcg
1 tablet = 75 mcg of Synthroid

Conversion factors:
1000 mcg / 1 mg
and
1 tablet / 75 mcg Synthroid

Step 4: Set up the problem to cancel units and calculate the answer.

0.150 mg × 1000 mcg / 1 mg × 1 tablet / 75 mcg = 2 tablets

Answer: 2 tablets

a. A bottle contains 120 mL of cough syrup. If one teaspoon (5 mL) is given four times a day, how many days will elapse before a refill is needed?

b. A patient is given a solution containing 0.625 g of calcium carbonate. If the calcium carbonate solution contains 1250 mg per 5 mL, how many milliliters of the solution were given to the patient?

a. 6 days
b. 2.5 mL

A person who exercises regularly has 16% body fat by mass. If this person weighs 155 lb, what is the mass, in kilograms, of body fat?

Step 1: State the given and needed quantities.

Given: 155 lb body weight
Need: kilograms of body fat

Step 2: Write a plan to convert the given unit to the needed unit.

pounds of body weight → U.S.–Metric factor → kilograms of body mass → Percentage factor → kilograms of body fat

Step 3: State the equalities and conversion factors.

1 kg of body mass = 2.20 lb of body weight
100 kg of body mass = 16 kg of body fat

Conversion factors:
1 kg body mass / 2.20 lb body weight
and
16 kg body fat / 100 kg body mass

Step 4: Set up the problem to cancel units and calculate the answer.

155 lb body weight × 1 kg body mass / 2.20 lb body weight × 16 kg body fat / 100 kg body mass = 11 kg of body fat

Answer: 11 kg of body fat

a. A package contains 1.33 lb of ground round. If it contains 15% fat, how many grams of fat are in the ground round?

b. A cream contains 4.0% (by mass) lidocaine to relieve back pain. If a patient uses 12 grams of cream, how many milligrams of lidocaine are used?

a. 91 g of fat
b. 480 mg

High-density lipoprotein (HDL) is a type of cholesterol, sometimes called “good cholesterol,” that is measured in a routine blood test. If a 0.258-g sample of HDL has a volume of 0.215 mL, what is the density, in grams per milliliter, of the HDL sample?

Step 1: State the given and needed quantities.

Given: mass = 0.258 g; volume = 0.215 mL
Need: density in g/mL

Step 2: Write the density expression.

Density = mass / volume

Step 3: Express mass in grams and volume in milliliters.

Mass of HDL sample = 0.258 g
Volume of HDL sample = 0.215 mL

Step 4: Substitute mass and volume into the density expression and calculate the density.

Density = 0.258 g / 0.215 mL = 1.20 g/mL

Answer: 1.20 g/mL

a. Low-density lipoprotein (LDL), sometimes called “bad cholesterol,” is also measured in a routine blood test. If a 0.380-g sample of LDL has a volume of 0.362 mL, what is the density, in grams per milliliter, of the LDL sample?

b. Osteoporosis is a condition in which bone deteriorates to cause a decreased bone mass. If a bone sample has a mass of 2.15 g and a volume of 1.40 cm³, what is its density in grams per cubic centimeter?

a. 1.05 g/mL
b. 1.54 g/cm³

Greg has a blood volume of 5.9 qt. If the density of blood is 1.06 g/mL, what is the mass, in grams, of Greg’s blood?

Step 1: State the given and needed quantities.

Given: 5.9 qt of blood
Need: grams of blood

Step 2: Write a plan to calculate the needed quantity.

quarts → U.S.–Metric factor → milliliters → Density factor → grams

Step 3: Write the equalities and their conversion factors including density.

1 qt = 946 mL
1 mL of blood = 1.06 g of blood

Conversion factors:
946 mL / 1 qt
and
1.06 g blood / 1 mL blood

Step 4: Set up the problem to calculate the needed quantity.

5.9 qt × 946 mL / 1 qt × 1.06 g blood / 1 mL blood = 5.9 × 10³ g blood

Answer: 5.9 × 10³ g blood

During surgery, a patient receives 3.0 pt of blood. How many kilograms of blood (density = 1.06 g/mL) were needed for the transfusion?

Step 1: State the given and needed quantities.

Given:

3.0 pt blood

Need:

kg blood

Step 2: Write a plan to calculate the needed quantity.

pt to mL to g to kg

Step 3: State the equalities and conversion factors.

Volume equality:

1 pt = 473 mL

Density equality:

1.06 g = 1 mL

Mass equality:

1000 g = 1 kg

Conversion factors:

473 mL / 1 pt

1.06 g / 1 mL

1 kg / 1000 g

Step 4: Set up the problem to cancel units and calculate the answer.

3.0 pt × (473 mL / 1 pt) × (1.06 g / 1 mL) × (1 kg / 1000 g)

= 1.50414 kg

Rounded to 2 significant figures:

1.5 kg

Answer: 1.5 kg

A woman receives 1280 g of type A blood. If the blood has a density of 1.06 g/mL, how many liters of blood did she receive?

1.21 L

Which of the following is a unit of mass?

a) kilogram (kg)
b) milliliter (mL)
c) Kelvin (K)
d) centimeter (cm)

kilogram (kg)

One cubic centimeter (cc) is the same as a milliliter (mL) and is a unit of _____.

a) Length
b) Mass
c) Volume
d) Time

c) Volume

Which number contains a zero that is not significant?

a) 407
b) 12.00
c) 1.740
d) 0.0713

d) 0.0713

The number of significant figures in 2.0045 L is _______.

a) 1
b) 3
c) 4
d) 5

d) 5

Answer the following equation using the proper number of significant figures:

15 + 10.2 + 0.2 =

a) 25
b) 25.2
c) 25.4
d) 26

a) 25

Answer the following equation using the proper number of significant figures:

4.7 × 834.78 =

a) 4000
b) 3923
c) 3920
d) 3900

d) 3900

How many grams are in 1.0 kg?

a) 10
b) 100
c) 1000
d) 10 000

c) 1000

How many millimeters are in 100 cm?

a) 10
b) 100
c) 1000
d) 10 000

c) 1000

A student’s height is 5 feet, 9 inches. There are 2.54 inches in one centimeter. What is the student’s height in centimeters?

a) 175 cm
b) 27 cm
c) 270 cm
d) 1750 cm

a) 175 cm

An antibiotic dosage of 500 mg is ordered. If the antibiotic is supplied in liquid form as 250 mg in 5.0 mL, the number of milliliters (mL) given is _______.

a) 5
b) 10
c) 15
d) 25

b) 10

If the density of a substance is 8 g/mL, what volume would 40 g of the substance occupy?

a) 0.5 mL
b) 2 mL
c) 5 mL
d) 20 mL

c) 5 mL

A total of 0.50 lb of glass marbles is added to 425 mL of water. The water level rises to a volume of 528 mL. The density (g/mL) of the glass marbles is ______.

a) 2.20 g/mL
b) 3.75 g/mL
c) 4.25 g/mL
d) 5.00 g/mL

a) 2.20 g/mL

The volume of a rock weighing 1.075 kg is 334.5 mL. What is the density of the rock?

a) 3.214 × 10⁻³ g/mL
b) 0.3112 g/mL
c) 3.214 g/mL
d) 311.2 g/mL

c) 3.214 g/mL

What mass of mercury occupies 20.4 mL if it has a density of 13.6 g/mL?

a) 0.667 g
b) 1.50 g
c) 27.7 g
d) 277 g

d) 277 g

What is the specific gravity of a solution that has a mass of 15.2 g and a volume of 25.0 mL?

a) 0.608 g/mL
b) 0.608
c) 1.64 g/mL
d) 1.64

b) 0.608

The density of water is 1.00 g/mL. What is the mass, in grams, of 3.5 L of water?

a) 3.5 g
b) 35 g
c) 350 g
d) 3500 g

d) 3500 g

Ethanol has a density of 0.79 g/mL. What volume is occupied by 65.0 g of ethanol?

a) 65 mL
b) 82 mL
c) 51 mL
d) 79 mL

b) 82 mL