1. 3.7 Changes of State
Matter undergoes a change of state when it is converted from one state to another state.
Learning Goal Describe the changes of state between solids, liquids, and gases; calculate the energy involved.

2. Melting and Freezing A substance
is melting while it changes from a solid to a liquid at its melting point (mp).
is freezing while it changes from a liquid to a solid at its freezing point (fp).
Water has a freezing (melting) point of 0 °C.
Melting and freezing are reversible processes.

3. Heat of Fusion The heat of fusion
is the amount of heat released when 1 g of liquid freezes (at its freezing point).
is the amount of heat needed to melt 1 g of solid (at its melting point).
For a given amount of substance,
heat released during freezing = heat needed during melting

4. Heat of Fusion Heat of Fusion for Water To melt water,
H2O(s) cal/g (or 334 J/g)  H2O(l)
To freeze water,
H2O(l)  H2O(s) cal/g (or 334 J/g)

5. Guide to Calculations Using a Heat Conversion Factor

6. Study Check
How many joules are needed to melt 32.0 g of ice at 0 °C?

7. Solution
How many joules are needed to melt 32.0 g of ice at 0 °C? STEP 1 State given and needed quantities. STEP 2 Write a plan to convert the given quantity to the needed quantity. grams of H2O(s) joules (to melt)
ANALYZE Given Need
THE PROBLEM g ice
0 °C joules to melt ice
Heat of
Fusion

8. Solution
How many joules are needed to melt 32.0 g of ice at 0 °C? STEP 3 Write the heat conversion factor and any metric factor.
1 g of H2O (s  l) = 334 J

9. Solution
How many joules are needed to melt 32.0 g of ice at 0 °C? STEP 4 Set up the problem and calculate the needed quantity. ×

10. Evaporation, Boiling, and Condensation
Water
evaporates when molecules on the surface gain sufficient energy to form a gas.
condenses when gas molecules lose energy and form a liquid.
During evaporation, molecules of the liquid are converted to gas at the surface of the liquid.

11. Boiling Water When water is boiling,
all the water molecules acquire enough energy to form a gas (vaporize).
bubbles of water vapor appear throughout the liquid.
During boiling, molecules of the liquid are converted to gas throughout the liquid as well as at the surface.

12. Sublimation and Deposition
When sublimation occurs,
the particles on the surface of the solid change directly to a vapor.
there is no change in temperature.
When deposition occurs, gas particles change directly to a solid.
Dry ice undergoes sublimation at –78 °C.
Sublimation and deposition are
reversible processes.
Dry ice sublimes at –78 °C.

13. Sublimation and Deposition
Sublimation is used to prepare freeze-dried foods for long-term storage.
Water vapor will change to solid on contact with a cold surface.
Freeze-dried foods have a long shelf life because they contain no water.

14. Heat of Vaporization The heat of vaporization is the amount of heat
absorbed to change 1 g of liquid to gas at the boiling point.
released when 1 g of gas changes to liquid at the boiling point.
Vaporization and condensation are reversible processes.

15. Heat of Vaporization
The heat of vaporization for water (boiling point 100 °C) is the heat absorbed when 1 g of water changes to steam.
H2O(l) cal/g (or 2260 J/g)  H2O(g)
The heat of condensation for water is the heat released when 1 g of steam changes to water.
H2O(g)  H2O(l) cal/g (or 2260 J/g)

16. Study Check
How many kilojoules (kJ) are released when 50.0 g of steam from a volcano condenses at 100 °C?

17. Solution
How many kilojoules (kJ) are released when 50.0 g of steam from a volcano condenses at 100 °C? STEP 1 State given and needed quantities. STEP 2 Write a plan to convert the given quantity to the needed quantity. grams joules kilojoules of H2O(g)
ANALYZE Given Need
THE PROBLEM g steam
100 °C kilojoules released
Heat of
Condensation
Metric
Factor

18. Solution
How many kilojoules (kJ) are released when 50.0 g of steam from a volcano condenses at 100 °C? STEP 3 Write the heat conversion factor and any metric factor. STEP 4 Set up the problem and calculate the needed quantity.
1 g of H2O (g  l) = 2260 J J = 1 kJ × ×

19. Heating and Cooling Curves
On a heating curve, diagonal lines indicate changes in temperature for a physical state, and horizontal lines (plateaus) indicate changes of state.
A heating curve diagrams the temperature increases and changes of state as heat is added.

20. Study Check
1. A plateau (horizontal line) on a heating curve represents A. a temperature change. B. a constant temperature. C. a change of state. 2. A sloped line on a heating curve represents

21. Solution
1. A plateau (horizontal line) on a heating curve represents B. a constant temperature. C. a change of state. 2. A sloped line on a heating curve represents A. a temperature change.

22. Study Check
Use the cooling curve for water to answer each of the following: 1. Water condenses at a temperature of A. 0 °C. B. 50 °C. C. 100 °C. 2. At a temperature of 0 °C, liquid water A. freezes. B. melts. C. changes to a gas. 3. At 40 °C, water is a A. solid. B. liquid. C. gas. 4. When water freezes, heat is A. removed. B. added.

23. Solution
Use the cooling curve for water to answer each of the following: 1. Water condenses at a temperature of C. 100 °C. 2. At a temperature of 0 °C, liquid water A. freezes. 3. At 40 °C, water is a B. liquid. 4. When water freezes, heat is A. removed.

24. Steps on a Cooling Curve
A cooling curve for water illustrates the change in temperature and changes of state as heat is removed.

25. Combining Heat Calculations
Calculate the total heat, in joules, needed to convert 15.0 g of liquid ethanol at 25.0 °C to gas at its boiling point of 78.0 °C. Ethanol has a specific heat of 2.46 J/g °C and a heat of vaporization of 841 J/g. STEP 1 State the given and needed quantities.
ANALYZE Given Need
THE PROBLEM g ethanol
Tinitial = 25.0 °C
Tfinal = 78.0 °C kilojoules heat vaporization, 841 J/g released
specific heat, J/ g °C

26. Combined Heat Calculations
STEP 2 Write a plan to convert the given quantity to the needed quantity. Total heat = joules needed to warm ethanol (25.0 °C to 78.0 °C) + joules to change liquid to gas at 78.0 °C

27. Combined Heat Calculations
STEP 3 Write the heat conversion factor and any metric factor. 

28. Combined Heat Calculations
STEP 4 Set up the problem and calculate the needed quantity. Calculate the temperature change of the liquid. ΔT = 78.0 °C − 25.0 °C = 53.0 °C Calculate heat needed to warm ethanol. × × × ×

29. Combined Heat Calculations
STEP 4 Set up the problem and calculate the needed quantity.
Calculate the heat needed to vaporize ethanol.
Calculate the total energy needed.
Heating ethanol (25.0 °C to 78.0 °C) = J
Changing liquid to gas = J
Total heat needed = J ×

30. Study Check
When a volcano erupts, 175 g of steam at °C is released. How many kilojoules are lost when the steam condenses, then freezes, at 0.0 °C? A. 396 kJ B. 528 kJ C. 133 kJ

31. Solution
When a volcano erupts, 175 g of steam at °C is released. How many kilojoules are lost when the steam condenses, then freezes, at 0.0 °C? STEP 1 State the given and needed quantities.
ANALYZE Given Need
THE PROBLEM g steam at °C
ice, at 0.0 °C kilojoules
heat vaporization, 2260 J/g released
specific heat, J/ g °C
heat fusion, 334 J/g

32. Solution
STEP 2 Write a plan to convert the given quantity to the needed quantity. Use the cooling curve to determine kilojoules released.
Steam at °C
condenses to liquid
100.0 °C
Liquid cools to 0.0 °C
0.0 °C
Liquid turns to solid at 0.0 °C

33. Solution
STEP 3 Write the heat conversion factor and any metric factor.  

34. Solution
STEP 4 Set up the problem and calculate the needed quantity. Calculate the heat released as steam is condensed. Calculate the temperature change of the liquid. ΔT = °C − 0.0 °C = °C ×

35. Solution
STEP 4 Set up the problem and calculate the needed quantity. Calculate the heat released as the liquid is cooled. Calculate the heat released as the liquid freezes. × × ×

36. Solution STEP 4 Set up the problem and calculate the needed quantity.
Calculate the total energy needed. Heat released as steam is condensed = J Heat released as liquid is cooled = J Heat released as liquid freezes = J Total heat needed = J ×
Answer is B.

37. Concept Map