Q: Which of the following correctly converts 14 mm to meters using dimensional analysis?

$$14 \ \text{mm} \times \frac{1 \ \text{m}}{1000 \ \text{mm}} = 0.014 \ \text{m}$$

Q: A patient is prescribed a medication that requires a dose of 35 kg to be converted to grams for accurate measurement. What is the correct mass in grams?

$$35 \ \text{kg} \times \frac{1000 \ \text{g}}{1 \ \text{kg}} = 35000 \ \text{g}$$

Q: A laboratory sample has a volume of 57 $$\text{cm}^3. $$What is this volume in liters?

$$57 \ \text{cm}^3 \times \frac{1 \ \text{mL}}{1 \ \text{cm}^3} \times \frac{1 \ \text{L}}{1000 \ \text{mL}} = 0.057 \ \text{L}$$

Q: A marathon route is measured as 1,250 cm. What is the distance in kilometers?

$$1,250 \ \text{cm} \times \frac{1 \ \text{m}}{100 \ \text{cm}} \times \frac{1 \ \text{km}}{1000 \ \text{m}} = 0.0125 \ \text{km}$$

Q: A car is traveling at a speed of 88 m/min. What is this speed in cm/s?

$$88 \ \text{m/min} \times \frac{100 \ \text{cm}}{1 \ \text{m}} \times \frac{1 \ \text{min}}{60 \ \text{s}} = 146.7 \ \text{cm/s}$$

Q: A particle moves through a gas at a speed of 15 km/s. How far will it travel in 5.5 s?

$$15 \ \text{km/s} \times 5.5 \ \text{s} = 82.5 \ \text{km}$$

Q: A sample contains 0.525 moles of copper. How many atoms of copper are present in the sample?

$$0.525 \ \text{mol} \times 6.02 \times 10$$^{23}$$ \ \text{atoms/mol} = 3.16 \times 10$$^{23}$$ \ \text{atoms}$$

Q: The density of lead is 11.3 g/mL. What is the mass of 45 mL of lead?

$$45 \ \text{mL} \times 11.3 \ \text{g/mL} = 508.5 \ \text{g}$$

Q: A solution of barium nitrate contains 61.2 g per liter. How many grams are present in 2.75 L of this solution?

$$2.75 \ \text{L} \times 61.2 \ \text{g/L} = 168.3 \ \text{g}$$

Q: A sample of seawater contains 0.000245 g of sodium chloride per mL. How much sodium chloride is in 50.0 mL of this solution?

$$50.0 \ \text{mL} \times 0.000245 \ \text{g/mL} = 0.01225 \ \text{g}$$

Question 1

Which of the following correctly converts 14 mm to meters using dimensional analysis?

Accepted Answer

$$14 \ 	ext{mm} 	imes \frac{1 \ 	ext{m}}{1000 \ 	ext{mm}} = 0.014 \ 	ext{m}$$

Question 2

A patient is prescribed a medication that requires a dose of 35 kg to be converted to grams for accurate measurement. What is the correct mass in grams?

Accepted Answer

$$35 \ 	ext{kg} 	imes \frac{1000 \ 	ext{g}}{1 \ 	ext{kg}} = 35000 \ 	ext{g}$$

Question 3

A laboratory sample has a volume of 57 $$	ext{cm}^3. $$What is this volume in liters?

Accepted Answer

$$57 \ 	ext{cm}^3 	imes \frac{1 \ 	ext{mL}}{1 \ 	ext{cm}^3} 	imes \frac{1 \ 	ext{L}}{1000 \ 	ext{mL}} = 0.057 \ 	ext{L}$$

Question 4

A marathon route is measured as 1,250 cm. What is the distance in kilometers?

Accepted Answer

$$1,250 \ 	ext{cm} 	imes \frac{1 \ 	ext{m}}{100 \ 	ext{cm}} 	imes \frac{1 \ 	ext{km}}{1000 \ 	ext{m}} = 0.0125 \ 	ext{km}$$

Question 5

A car is traveling at a speed of 88 m/min. What is this speed in cm/s?

Accepted Answer

$$88 \ 	ext{m/min} 	imes \frac{100 \ 	ext{cm}}{1 \ 	ext{m}} 	imes \frac{1 \ 	ext{min}}{60 \ 	ext{s}} = 146.7 \ 	ext{cm/s}$$

Question 6

A particle moves through a gas at a speed of 15 km/s. How far will it travel in 5.5 s?

Accepted Answer

$$15 \ 	ext{km/s} 	imes 5.5 \ 	ext{s} = 82.5 \ 	ext{km}$$

Question 7

A sample contains 0.525 moles of copper. How many atoms of copper are present in the sample?

Accepted Answer

$$0.525 \ 	ext{mol} 	imes 6.02 	imes 10$$^{23}$$ \ 	ext{atoms/mol} = 3.16 	imes 10$$^{23}$$ \ 	ext{atoms}$$

Question 8

The density of lead is 11.3 g/mL. What is the mass of 45 mL of lead?

Accepted Answer

$$45 \ 	ext{mL} 	imes 11.3 \ 	ext{g/mL} = 508.5 \ 	ext{g}$$

Question 9

A solution of barium nitrate contains 61.2 g per liter. How many grams are present in 2.75 L of this solution?

Accepted Answer

$$2.75 \ 	ext{L} 	imes 61.2 \ 	ext{g/L} = 168.3 \ 	ext{g}$$

Question 10

A sample of seawater contains 0.000245 g of sodium chloride per mL. How much sodium chloride is in 50.0 mL of this solution?

Accepted Answer

$$50.0 \ 	ext{mL} 	imes 0.000245 \ 	ext{g/mL} = 0.01225 \ 	ext{g}$$

Question 11

A chemist needs to prepare 0.250 L of a solution from a stock solution that contains 61.2 g/L of barium nitrate. How many grams of barium nitrate are needed?

Accepted Answer

$$0.250 \ 	ext{L} 	imes 61.2 \ 	ext{g/L} = 15.3 \ 	ext{g}$$

Question 12

A patient receives an intravenous solution at a rate of 88 m/min. If the infusion lasts for 30 seconds, how many centimeters of tubing does the solution travel through?

Accepted Answer

$$88 \ 	ext{m/min} 	imes \frac{1 \ 	ext{min}}{60 \ 	ext{s}} 	imes 30 \ 	ext{s} 	imes \frac{100 \ 	ext{cm}}{1 \ 	ext{m}} = 4,400 \ 	ext{cm}$$

Question 13

A gold bar has a volume of 250 $$	ext{cm}^3$$ and a density of 19.3 g/mL. What is its mass in kilograms?

Accepted Answer

$$250 \ 	ext{cm}^3 	imes \frac{1 \ 	ext{mL}}{1 \ 	ext{cm}^3} 	imes 19.3 \ 	ext{g/mL} 	imes \frac{1 \ 	ext{kg}}{1000 \ 	ext{g}} = 4.825 \ 	ext{kg}$$

Question 14

A solution contains 0.000245 g/mL of sodium chloride. How many milligrams of sodium chloride are in 100 mL of this solution?

Accepted Answer

$$100 \ 	ext{mL} 	imes 0.000245 \ 	ext{g/mL} 	imes \frac{1000 \ 	ext{mg}}{1 \ 	ext{g}} = 24.5 \ 	ext{mg}$$

Question 15

A chemist needs to convert 0.75 L to $$	ext{cm}^3$$ for a reaction. What is the correct volume?

Accepted Answer

$$0.75 \ 	ext{L} 	imes \frac{1000 \ 	ext{mL}}{1 \ 	ext{L}} 	imes \frac{1 \ 	ext{cm}^3}{1 \ 	ext{mL}} = 750 \ 	ext{cm}^3$$

Question 16

A sample contains 2.00 moles of a substance. How many particles are present, using Avogadro's number?

Accepted Answer

$$2.00 \ 	ext{mol} 	imes 6.02 	imes 10$$^{23}$$ \ 	ext{particles/mol} = 1.20 	imes 10$$^{24}$$ \ 	ext{particles}$$

Question 17

A nurse needs to administer 0.500 L of saline solution. How many milliliters is this?

Accepted Answer

$$0.500 \ 	ext{L} 	imes \frac{1000 \ 	ext{mL}}{1 \ 	ext{L}} = 500 \ 	ext{mL}$$

Question 18

A solution contains 0.000245 g/mL of sodium chloride. If a patient receives 250 mL, how many grams of sodium chloride does the patient receive?

Accepted Answer

$$250 \ 	ext{mL} 	imes 0.000245 \ 	ext{g/mL} = 0.06125 \ 	ext{g}$$

Step-by-Step Guidance for Dimensional Analysis and Basic Chemistry Calculations

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