1. Sample Problem 3.1 Classifying Mixtures
Classify each of the following as a pure substance (element or compound) or a mixture (homogeneous or heterogeneous):
a. copper in copper wire
b. a chocolate-chip cookie
c. nitrox, a combination of oxygen and nitrogen used to fill scuba tanks
Solution
a. Copper is an element, which is a pure substance.
b. A chocolate-chip cookie does not have a uniform composition, which makes it a heterogeneous mixture.
c. The gases oxygen and nitrogen have a uniform composition in nitrox, which makes it a homogeneous mixture.
Study Check 3.1
A salad dressing is prepared with oil, vinegar, and chunks of blue cheese. Is this a homogeneous or heterogeneous mixture?
Answer
heterogeneous

2. Sample Problem 3.2 Physical and Chemical Changes
Classify each of the following as a physical or chemical change:
a. A gold ingot is hammered to form gold leaf.
b. Gasoline burns in air.
c. Garlic is chopped into small pieces.
Solution
a. A physical change occurs when the gold ingot changes shape.
b. A chemical change occurs when gasoline burns and forms different substances with new properties.
c. A physical change occurs when the size of the garlic pieces changes.
Study Check 3.2
Classify each of the following as a physical or chemical change:
a. Water freezes on a pond.
b. Gas bubbles form when baking powder is placed in vinegar.
c. A log is cut for firewood.
Answer
a. physical change b. chemical change c. physical change

3. Sample Problem 3.3 Converting from Degrees Celsius to Degrees Fahrenheit
The typical temperature in a hospital room is set at 21 °C. What is that temperature in degrees Fahrenheit?
Solution
Step 1 State the given and needed quantities.
Step 2 Write a temperature equation.
Step 3 Substitute in the known values and calculate the new temperature.
TF =
= 70. °F Answer to the ones place
In the equation, the values of 1.8 and 32 are exact numbers, which do not affect the number of SFs used in the answer.

4. Sample Problem 3.3 Converting from Degrees Celsius to Degrees Fahrenheit
Continued
Study Check 3.3
In the process of making ice cream, rock salt is added to crushed ice to chill the ice cream mixture. If the temperature drops to −11 °C, what is it in degrees Fahrenheit?
Answer
12 °F

5. Sample Problem 3.4 Converting from Degrees Fahrenheit to Degrees Celsius
In a type of cancer treatment called thermotherapy, temperatures as high as 113 °F are used to destroy cancer cells or make them more sensitive to radiation. What is that temperature in degrees Celsius?
Solution
Step 1 State the given and needed quantities.
Step 2 Write a temperature equation.
Step 3 Substitute in the known values and calculate the new temperature.

6. Sample Problem 3.4 Converting from Degrees Fahrenheit to Degrees Celsius
Continued
Study Check 3.4
A child has a temperature of °F. What is this temperature on a Celsius thermometer?
Answer
39.8 °C

7. Sample Problem 3.5 Energy Units
A defibrillator gives a high-energy-shock output of 360 J. What is this quantity of energy in calories?
Solution
Step 1 State the given and needed quantities.
Step 2 Write a plan to convert the given unit to the needed unit.
Step 3 State the equalities and conversion factors.

8. Sample Problem 3.5 Energy Units
Continued
Step 4 Set up the problem to calculate the needed quantity.
Study Check 3.5
When 1.0 g of glucose is metabolized in the body, it produces 3.8 kcal. How many kilojoules are produced?
Answer
16 kJ

9. Sample Problem 3.6 Energy Content for a Food Using Nutrition Facts
The Nutrition Facts label for crackers states that 1 serving contains 19 g of carbohydrate, 4 g of fat, and 2 g of protein. What is the energy from each food type and the total energy, in kilocalories, for one serving of crackers? Round off the kilocalories for each food type to the tens place.
Solution
Step 1 State the given and needed quantities.
Step 2 Use the energy value for each food type and calculate the kcal rounded off to the tens place. Using the energy values for carbohydrate, fat, and protein (see Table 3.7), we can calculate the energy for each type of food.

10. Sample Problem 3.6 Energy Content for a Food Using Nutrition Facts
Continued
Step 3 Add the energy for each food type to give the total energy from the food.
Total energy = 80 kcal + 40 kcal + 10 kcal = 130 kcal
Study Check 3.6
a. Using the nutrition values for one serving of crackers in Sample Problem 3.6, calculate the energy, in kilojoules, for each food type. Round off the kilojoules for each food type to the tens place.
b. What is the total energy, in kilojoules, for one serving of crackers?
Answer
a. carbohydrate, 320 kJ; fat, 150 kJ; protein, 30 kJ
b. 500 kJ

11. Sample Problem 3.7 Calculating Heat Loss
During surgery or when a patient has suffered a cardiac arrest or stroke, lowering the body temperature will reduce the amount of oxygen needed by the body. Some methods used to lower body temperature include cooled saline solution, cool water blankets, or cooling caps worn on the head. How many kilojoules are lost when the body temperature of a surgery patient with a blood volume of 5500 mL is cooled from 38.5 °C to 33.2 °C? (Assume that the specific heat and density of blood is the same as for water.)
Step 1 State the given and needed quantities.
Step 2 Calculate the temperature change (ΔT).
ΔT = 38.5 °C – 33.2 °C = 5.3 °C

12. Sample Problem 3.7 Calculating Heat Loss
Continued
Step 3 Write the heat equation and needed conversion factors.
Heat = m × ΔT × SH
Step 4 Substitute in the given values and calculate the heat, making sure units cancel.
Study Check 3.7
How many kilocalories are lost when 560 g of water cools from 67 °C to 22 °C?
Answer
25 kcal

13. Sample Problem 3.8 Heat of Fusion
Ice bag therapy is used by sports trainers to treat muscle injuries. If 260. g of ice are placed in an ice bag, how much heat, in joules, will be absorbed to melt all the ice at 0 °C?
Solution
Step 1 State the given and needed quantities.
Step 2 Write a plan to convert the given quantity to the needed quantity.
Step 3 Write the heat conversion factor and any metric factor.

14. Sample Problem 3.8 Heat of Fusion
Continued
Step 4 Set up the problem and calculate the needed quantity.
Study Check 3.8
In a freezer, 150 g of water at 0 °C is placed in an ice cube tray. How much heat, in kilocalories, must be removed to form ice cubes at 0 °C?
Answer
12 kcal

15. Sample Problem 3.9 Using Heat of Vaporization
In a sauna, 122 g of water is converted to steam at 100 °C. How many kilojoules of heat are needed?
Solution
Step 1 State the given and needed quantities.
Step 2 Write a plan to convert the given quantity to the needed quantity.
Step 3 Write the heat conversion factor and any metric factor.

16. Sample Problem 3.9 Using Heat of Vaporization
Continued
Step 4 Set up the problem and calculate the needed quantity.
Study Check 3.9
When steam from a pan of boiling water reaches a cool window, it condenses. How much heat, in kilojoules, is released when 25.0 g of steam condenses at 100 °C?
Answer
56.5 kJ released

17. Sample Problem 3.10 Using a Cooling Curve
Using the cooling curve for water, identify the state or change of state for water as solid, liquid, gas, condensation, or freezing.
a. at 120 °C b. at 100 °C c. at 40 °C
Solution
a. A temperature of 120 °C occurs on the diagonal line above the boiling (condensation) point, which indicates that water is a gas.
b. A temperature of 100 °C, shown as a horizontal line, indicates that the water vapor is changing to liquid water, or condensing.
c. A temperature of 40 °C occurs on the diagonal line below the boiling point but above the freezing point, which indicates that the water is in the liquid state.
Study Check 3.10
Using the cooling curve for water, identify the state or change of state for water as solid, liquid, gas, condensation, or freezing.
a. at 0 °C b. at –20 °C
Answer
a. freezing b. solid

18. Sample Problem 3.11 Combining Heat Calculations
Charles has increased his activity by doing more exercise. After a session of using small weights, he has a sore arm. An ice bag is filled with 125 g of ice at 0.0 °C. The heat of fusion for ice is 334 J/g. How much heat, in kilojoules, is absorbed to melt the ice, and to raise the temperature of the water to body temperature, 37.0 °C?
Solution
Step 1 State the given and needed quantities.
Step 2 Write a plan to convert the given quantity to the needed quantity.
Total heat = kilojoules needed to melt the ice and heat the water from 0.0 °C (freezing point) to 37.0 °C
Step 3 Write the heat conversion factor and any metric factor.

19. Sample Problem 3.11 Combining Heat Calculations
Continued
Step 4 Set up the problem and calculate the needed quantity.
ΔT = 37.0 °C – 0.0 °C = 37.0 °C
Heat needed to change ice (solid) to water (liquid) at 0.0 °C:
Heat needed to warm water (liquid) from 0.0 °C to water (liquid) at 37.0 °C:
Calculate the total heat:
Melting ice at 0.0 °C kJ
Heating water (0.0 °C to 37.0 °C) kJ
Total heat needed kJ

20. Sample Problem 3.11 Combining Heat Calculations
Continued
Study Check 3.11
How many kilojoules are released when 75.0 g of steam at 100 °C condenses, cools to 0 °C, and freezes at 0 °C? (Hint: The solution will require three energy calculations.)
Answer
226 kJ