10/29 Practice Problems

Problem 1

In your own words, explain what density is and what it tells us about a substance. Why do different substances have different densities?

Problem 2

You have two blocks of the same size and shape. One is made of aluminum and one is made of lead. The lead block feels much heavier. Explain this observation using the concept of density.

Problem 3

Describe the water displacement method for measuring the volume of an irregular solid object (like a rock). Include the steps you would follow and explain why this method works.

Problem 4

What is specific heat? How does water's high specific heat capacity affect Earth's climate and weather patterns? Give at least one example.

Problem 5

Two identical pots of water are heated on a stove. Pot A contains 1 L of water and Pot B contains 2 L of water. Both start at the same temperature and receive the same amount of heat energy. Which pot will have a higher final temperature? Explain your reasoning using the concept of specific heat.

Problem 6

Express 0.000456 in scientific notation with the correct number of significant figures.

Problem 7

How many significant figures are in the measurement 3050.0 g?

Problem 8

Convert 2.5 L to mL.

Problem 9

Convert 350 cm³ to mL.

Problem 10

Convert 75°F to °C. (Show your work and formula.)

Problem 11

Convert 298 K to °C.

Problem 12

Convert 3.5 km to m.

Problem 13

A sample of aluminum has a mass of 54.0 g and a volume of 20.0 cm³. Calculate the density of aluminum.

Problem 14

Calculate \(\Delta T\) (change in temperature) when water is heated from 25°C to 88°C.

Problem 15

How much heat energy is required to raise the temperature of 100 g of water by 15°C? (\(c_{\text{water}} = 4.18\) J/g°C)

Problem 16

A chemist measures the mass of a chemical sample as \(3.45 \times 10^{-3}\) kg. Express this mass in grams using scientific notation.

Problem 17

A student records the length of a pencil as 18.50 cm. She then multiplies this by 2.1 to calculate something. What is the answer with the correct number of significant figures?

Problem 18

A swimming pool contains 85,000 L of water. Convert this volume to mL and express your answer in scientific notation.

Problem 19

A rectangular aquarium measures 50.0 cm long, 30.0 cm wide, and 40.0 cm tall. Calculate the volume in cm³, then convert to liters. (Remember: 1 L = 1000 cm³)

Problem 20

A weather forecast predicts a high temperature of 86°F. The student wants to know if this is warmer than 30°C. Convert 86°F to Celsius and determine which temperature is warmer.

Problem 21

Liquid nitrogen boils at 77 K. Convert this temperature to both Celsius and Fahrenheit. (Hint: Convert K → °C first, then °C → °F)

Problem 22

A marathon runner runs 42.195 km. Convert this distance to meters, then convert to millimeters.

Problem 23

A gold bar has a mass of 386 g and a volume of 20.0 cm³. Calculate the density of gold in g/cm³. Then, determine the volume of a 50.0 g gold nugget with the same density.

Problem 24

An unknown liquid has a density of 0.85 g/mL. If you have 250 mL of this liquid, what is its mass in grams? If this liquid is then poured into a container that can hold 500 cm³, will it overflow?

Problem 25

A 150 g sample of iron (\(c_{\text{iron}} = 0.449\) J/g°C) is heated from 25°C to 125°C. Calculate the amount of heat energy absorbed. If this same amount of heat energy were used to heat 150 g of water (\(c_{\text{water}} = 4.18\) J/g°C) starting at 25°C, what would be the final temperature of the water?

Problem 26

Calculate the molar mass of water (H₂O). (H = 1.01 g/mol, O = 16.00 g/mol)

Problem 27

Calculate the molar mass of carbon dioxide (CO₂). (C = 12.01 g/mol, O = 16.00 g/mol)

Problem 28

Calculate the molar mass of sodium chloride (NaCl). (Na = 22.99 g/mol, Cl = 35.45 g/mol)

Problem 29

Calculate the molar mass of glucose (C₆H₁₂O₆). (C = 12.01 g/mol, H = 1.01 g/mol, O = 16.00 g/mol)

Problem 30

Calculate the molar mass of calcium carbonate (CaCO₃). (Ca = 40.08 g/mol, C = 12.01 g/mol, O = 16.00 g/mol)

Problem 31

How many moles are in 88.0 g of carbon dioxide (CO₂)? (Molar mass of CO₂ = 44.01 g/mol)

Problem 32

How many molecules are in 36.0 g of water (H₂O)? (Molar mass of H₂O = 18.02 g/mol, Avogadro's number = \(6.022 \times 10^{23}\))

Problem 33

A sample contains 117 g of sodium chloride (NaCl). Calculate (a) the number of moles of NaCl and (b) the number of formula units of NaCl in the sample. (Molar mass of NaCl = 58.44 g/mol, Avogadro's number = \(6.022 \times 10^{23}\))

Problem 34

A jewelry manufacturer produces sterling silver earrings. Sterling silver is 92.5% silver by mass. If the manufacturer needs to produce 250 pairs of earrings, and each earring has a mass of 3.2 grams, how many kilograms of pure silver are needed? Express your answer in scientific notation.

Problem 35

A pharmaceutical company produces a cough syrup that is 12% active ingredient by volume. The syrup is sold in 4.0 fluid ounce bottles. If the company manufactures 5000 bottles per day, how many liters of active ingredient are used per day? (1 fluid ounce = 29.57 mL)

Problem 36

A chemist needs to determine the mass of a sample of ethanol (C₂H₅OH). She fills a graduated cylinder to the 50.0 mL mark, then adds an irregular piece of metal. The new volume reading is 65.3 mL. The metal has a density of 7.87 g/cm³. She then removes the metal and fills the cylinder with ethanol to the 50.0 mL mark. What is the mass of the ethanol in grams? (Density of ethanol = 0.789 g/mL, remember: 1 cm³ = 1 mL)

Problem 37

An Olympic-sized swimming pool measures 50.0 meters long, 25.0 meters wide, and 2.00 meters deep. If the pool is filled to 95% capacity with water, what is the mass of the water in pounds? (Density of water = 1.00 g/mL, 1 m = 100 cm, 1 pound = 453.6 g)