Chapter 3: Matter and Energy – Changes of State and Associated Energy Calculations

Changes of State

Introduction to Changes of State

Changes of state refer to the physical processes in which matter transitions between solid, liquid, and gaseous forms. These transitions occur at constant temperature and involve the absorption or release of energy.

• Melting and Freezing

• Boiling (Vaporization) and Condensation

• Sublimation and Deposition

Key Point: Each change of state is associated with a specific energy change, either absorbed or released by the substance.

Melting and Freezing

Definitions and Processes

• Melting: The process by which a solid becomes a liquid at its melting point (mp).

• Freezing: The process by which a liquid becomes a solid at its freezing point (fp).

• For water, the melting/freezing point is 0°C.

• Melting and freezing are reversible processes.

Example: Ice (solid water) melts to form liquid water at 0°C; liquid water freezes to form ice at 0°C.

Heat of Fusion

Definition and Calculation

The heat of fusion is the amount of energy required to convert 1 gram of a solid to a liquid at its melting point, or the energy released when 1 gram of liquid solidifies at its freezing point.

• For H2O: 80 cal/g or 334 J/g is needed to melt 1 g of ice at 0°C.

• The same amount of energy is released when 1 g of water freezes at 0°C.

Equations:

• Melting: $\text{H}_2\text{O}(s) + 80\,\text{cal/g} \ (334\,\text{J/g}) \rightarrow \text{H}_2\text{O}(l)$

• Freezing: $\text{H}_2\text{O}(l) \rightarrow \text{H}_2\text{O}(s) + 80\,\text{cal/g} \ (334\,\text{J/g})$

Using Heat of Fusion in Calculations

The heat of fusion can be used as a conversion factor in calculations involving melting or freezing.

• Conversion factors: 80 cal/1 g H2O or 334 J/1 g H2O

• Formula:

$\text{Heat (cal)} = \text{mass (g)} \times 80\,\text{cal/g}$ $\text{Heat (J)} = \text{mass (g)} \times 334\,\text{J/g}$

Example: To melt 32.0 g of ice at 0°C:

• Heat required (J): $32.0\,\text{g} \times 334\,\text{J/g} = 10,688\,\text{J} = 10.7\,\text{kJ}$

Sublimation and Deposition

Direct Solid-Gas Transitions

• Sublimation: The process where a solid changes directly to a gas without passing through the liquid state.

• Deposition: The reverse process, where a gas changes directly to a solid.

• Both processes occur at constant temperature and are reversible.

Example: Dry ice (solid CO2) sublimes at room temperature.

Vaporization, Boiling, and Condensation

Definitions and Processes

• Evaporation: The process where molecules at the surface of a liquid gain enough energy to enter the gas phase.

• Boiling: Occurs when molecules throughout the liquid have enough energy to become gas, forming bubbles within the liquid.

• Condensation: The process where gas molecules lose energy and return to the liquid state.

• Evaporation and condensation are reversible processes.

Example: Water boils at 100°C, forming steam; steam condenses back to liquid water at 100°C.

Heat of Vaporization and Condensation

Definition and Calculation

The heat of vaporization is the energy required to convert 1 gram of liquid to gas at the boiling point. The same amount of energy is released when 1 gram of gas condenses to liquid at the same temperature.

• For H2O: 540 cal/g or 2260 J/g at 100°C.

Equations:

• Vaporization: $\text{H}_2\text{O}(l) + 540\,\text{cal/g} \ (2260\,\text{J/g}) \rightarrow \text{H}_2\text{O}(g)$

• Condensation: $\text{H}_2\text{O}(g) \rightarrow \text{H}_2\text{O}(l) + 540\,\text{cal/g} \ (2260\,\text{J/g})$

Using Heat of Vaporization in Calculations

• Conversion factors: 540 cal/1 g H2O or 2260 J/1 g H2O

• Formula:

$\text{Heat (cal)} = \text{mass (g)} \times 540\,\text{cal/g}$ $\text{Heat (J)} = \text{mass (g)} \times 2260\,\text{J/g}$

Example: To condense 50.0 g of steam at 100°C:

• Heat released (J): $50.0\,\text{g} \times 2260\,\text{J/g} = 113,000\,\text{J} = 113\,\text{kJ}$

Heating and Cooling Curves

Graphical Representation of State Changes

• A heating curve shows temperature changes and phase transitions as heat is added to a substance.

• A cooling curve shows temperature changes and phase transitions as heat is removed.

• Diagonal lines represent temperature changes within a single phase.

• Horizontal (plateau) lines represent phase changes at constant temperature.

Example: On a heating curve for water, the temperature remains constant at 0°C during melting and at 100°C during boiling, even as heat is added.

Interpretation of Heating/Cooling Curves

• Plateau (horizontal line): Indicates a phase change at constant temperature.

• Sloped (diagonal line): Indicates a temperature change within a single phase.

Sample Calculations and Problem Solving

Stepwise Approach to Energy Calculations

• Identify the mass and the type of phase change or temperature change.

• Use appropriate conversion factors (heat of fusion, heat of vaporization, specific heat).

• Set up the calculation using the correct formula.

Example: Calculating the total energy released when steam condenses, cools, and freezes:

1. Condensation: $\text{mass} \times \text{heat of vaporization}$

2. Cooling: $\text{mass} \times \text{specific heat} \times \Delta T$

3. Freezing: $\text{mass} \times \text{heat of fusion}$

Sample Calculation: For 175 g of steam at 100°C condensing, cooling to 0°C, and freezing:

• Condensation: $175\,\text{g} \times 2260\,\text{J/g} = 396,000\,\text{J} = 396\,\text{kJ}$

• Cooling: $175\,\text{g} \times 4.184\,\text{J/g}^\circ\text{C} \times 100^\circ\text{C} = 73,220\,\text{J} = 73.2\,\text{kJ}$

• Freezing: $175\,\text{g} \times 334\,\text{J/g} = 58,450\,\text{J} = 58.5\,\text{kJ}$

• Total heat released: $396 + 73.2 + 58.5 = 528\,\text{kJ}$

Summary Table: Heats of Fusion and Vaporization for Water

Process	Energy Change (per 1 g H2O)	Temperature
Melting (fusion)	+80 cal (334 J)	0°C
Freezing	-80 cal (-334 J)	0°C
Vaporization (boiling)	+540 cal (2260 J)	100°C
Condensation	-540 cal (-2260 J)	100°C

Additional info: Specific heat of liquid water is 4.184 J/g°C, which is used for temperature changes within the liquid phase.