Q: A TA can grade 4 assignments per hour. Each assignment has 12 questions. How many questions can the TA grade in 130 minutes?

$$4 \times 12 \times \frac{130}{60} = 104$$ questions

Q: If the distance between Washington, D.C. and New York City is 224.9 miles, what is this distance in centimeters? (1 mile = 1.609 km, 1 km = 1,000 m, 1 m = 100 cm)

$$224.9 \times 1.609 \times 1,000 \times 100 = 36,202,810 cm$$

Q: The average human body contains approximately 160 fluid ounces of blood. How many quarts of blood does the average human body possess? (1 quart = 2 pints, 1 pint = 2 cups, 1 cup = 8 fluid ounces)

$$160 \div (2 \times 2 \times 8) = 5$$ quarts

Q: Lipitor pills each weigh 2.5 g and contain 4.0% of the active ingredient by mass. If a bottle contains 120 pills, what is the mass in kg of the active ingredient in the bottle?

$$120 \times 2.5 \times 0.04 \div 1000 = 0.012 kg$$

Q: Which of the following is the correct general form for a dimensional analysis conversion?

$$\text{Given Amount} \times \text{Conversion Factor}_1 \times \text{Conversion Factor}_2 = \text{End Amount}$$

Q: A car travels 60 miles per hour. How many kilometers does it travel in 2 hours? (1 mile = 1.609 km)

$$60 \times 2 \times 1.609 = 193.08 km$$

Q: If a patient receives 1.5 L of IV fluid over 6 hours, what is the rate in mL/hour?

$$1.5 \times 1,000 \div 6 = 250 mL/$$hour

Question 1

Which of the following best describes the purpose of dimensional analysis in chemistry?

Accepted Answer

To convert measurements from one unit to another using conversion factors.

Question 2

A TA can grade 4 assignments per hour. Each assignment has 12 questions. How many questions can the TA grade in 130 minutes?

Accepted Answer

$$4 	imes 12 	imes \frac{130}{60} = 104$$ questions

Question 3

If the distance between Washington, D.C. and New York City is 224.9 miles, what is this distance in centimeters? (1 mile = 1.609 km, 1 km = 1,000 m, 1 m = 100 cm)

Accepted Answer

$$224.9 	imes 1.609 	imes 1,000 	imes 100 = 36,202,810 cm$$

Question 4

The average human body contains approximately 160 fluid ounces of blood. How many quarts of blood does the average human body possess? (1 quart = 2 pints, 1 pint = 2 cups, 1 cup = 8 fluid ounces)

Accepted Answer

$$160 \div (2 	imes 2 	imes 8) = 5$$ quarts

Question 5

Lipitor pills each weigh 2.5 g and contain 4.0% of the active ingredient by mass. If a bottle contains 120 pills, what is the mass in kg of the active ingredient in the bottle?

Accepted Answer

$$120 	imes 2.5 	imes 0.04 \div 1000 = 0.012 kg$$

Question 6

Which step should you perform first when solving a dimensional analysis problem?

Accepted Answer

Identify the given amount.

Question 7

If you have 32 inches, how many centimeters is this? (1 inch = 2.54 cm)

Accepted Answer

$$32 	imes 2.54 = 81.28 cm$$

Question 8

A student needs to convert 115 minutes to years. Which of the following conversion factors would NOT be needed?

Accepted Answer

Inches to centimeters

Question 9

Which of the following is the correct general form for a dimensional analysis conversion?

Accepted Answer

$$	ext{Given Amount} 	imes 	ext{Conversion Factor}_1 	imes 	ext{Conversion Factor}_2 = 	ext{End Amount}$$

Question 10

A nurse needs to administer 250 mL of a solution. If 1 cup = 240 mL, how many cups should the nurse use?

Accepted Answer

$$250 \div 240 = 1.04$$ cups

Question 11

Which of the following is a common mistake when performing dimensional analysis?

Accepted Answer

Not canceling out the unwanted units.

Question 12

A patient is prescribed 500 mg of a medication. If each tablet contains 125 mg, how many tablets should the patient take?

Accepted Answer

$$500 \div 125 = 4$$ tablets

Question 13

If a solution contains 0.5 mol of NaCl in 250 mL, what is its concentration in mol/L?

Accepted Answer

$$0.5 \div 0.25 = 2.0$$ mol/L

Question 14

A car travels 60 miles per hour. How many kilometers does it travel in 2 hours? (1 mile = 1.609 km)

Accepted Answer

$$60 	imes 2 	imes 1.609 = 193.08 km$$

Question 15

Which of the following is the correct sequence of steps for dimensional analysis?

Accepted Answer

Identify the given amount, write down conversion factors, connect given amount and conversion factors to isolate the end amount.

Question 16

A recipe calls for 3 cups of flour. If 1 cup = 120 g, how many grams of flour are needed?

Accepted Answer

$$3 	imes 120 = 360 g$$

Question 17

A solution contains 5% (by mass) of glucose. If you have 200 g of solution, how many grams of glucose are present?

Accepted Answer

$$200 	imes 0.05 = 10 g$$

Question 18

If a patient receives 1.5 L of IV fluid over 6 hours, what is the rate in mL/hour?

Accepted Answer

$$1.5 	imes 1,000 \div 6 = 250 mL/$$hour

Question 19

A chemist needs 0.75 mol of a substance. If each container holds 0.25 mol, how many containers are needed?

Accepted Answer

$$0.75 \div 0.25 = 3$$ containers

Question 20

Which of the following is NOT a valid conversion factor for dimensional analysis?

Accepted Answer

1 apple = 2 oranges

Dimensional Analysis and Unit Conversion in GOB Chemistry

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