Thermal Energy Transfer and Phase Changes Study Guide

Energy Dynamics during Phase Transitions:
- Water and various other substances have the capacity to absorb or release energy without undergoing a change in temperature during a phase transition.
- Heat of Fusion ( $H_{fus}$ ): This is defined as the specific amount of energy or heat required to either melt a solid into a liquid or freeze a liquid into a solid.
- Heat of Vaporization ( $H_{vap}$ ): This is defined as the specific amount of energy or heat required to cause a substance to evaporate (transition from liquid to gas) or condense (transition from gas to liquid).

Graphical Representation: The heating curve illustrates the relationship between heat absorbed (x-axis) and temperature in degrees Celsius (^\regular{C}, y-axis).
Temperature Range and States: The curve spans from below -40\,^\regular{C} to above 140\,^\regular{C}.
Plateaus (Constant Temperature):
- Melting Point: Characterized by a horizontal plateau at 0\,^\regular{C} where the substance exists as both solid and liquid (melting).
- Boiling Point: Characterized by a horizontal plateau at 100\,^\regular{C} where the substance exists as both liquid and gas (boiling).
Sloped Regions (Changing Temperature):
- Solid Phase: Below 0\,^\regular{C}.
- Liquid Phase: Between 0\,^\regular{C} and 100\,^\regular{C}.
- Gas Phase: Above 100\,^\regular{C}.

Data for Calculations (Units in $kJ/mol$ ):
- Water ( $H_2O$ ):
  - Heat of Fusion ( $H_{fus}$ ): $6.01\,kJ/mol$
  - Heat of Vaporization ( $H_{vap}$ ): $40.65\,kJ/mol$
- Ammonia ( $NH_3$ ):
  - Heat of Fusion ( $H_{fus}$ ): $5.66\,kJ/mol$
  - Heat of Vaporization ( $H_{vap}$ ): $23.33\,kJ/mol$
- Methanol ( $CH_3OH$ ):
  - Heat of Fusion ( $H_{fus}$ ): $3.22\,kJ/mol$
  - Heat of Vaporization ( $H_{vap}$ ): $35.21\,kJ/mol$
- Nitrogen ( $N_2$ ):
  - Heat of Fusion ( $H_{fus}$ ): $0.71\,kJ/mol$
  - Heat of Vaporization ( $H_{vap}$ ): $5.57\,kJ/mol$
- Oxygen ( $O_2$ ):
  - Heat of Fusion ( $H_{fus}$ ): $0.44\,kJ/mol$
  - Heat of Vaporization ( $H_{vap}$ ): $6.82\,kJ/mol$

Melting or Freezing Calculations:
- $Q = nH_{fus}$
Evaporation or Condensation Calculations:
- $Q = nH_{vap}$
Variable Definitions:
- $Q$ : The amount of energy or heat, measured in kilojoules ( $kJ$ ).
- $n$ : The number of moles of the substance, measured in moles ( $mol$ ).
- $H_{fus}$ : The molar Heat of Fusion, measured in kilojoules per mole ( $kJ/mol$ ). This value is typically found in a data booklet.
- $H_{vap}$ : The molar Heat of Vaporization, measured in kilojoules per mole ( $kJ/mol$ ). This value is typically found in a data booklet.

Example 1: Calculating Energy for Melting Ice
- Scenario: A container holds exactly $360.4\,g$ of ice at 0\,^\regular{C}. The ice melts to form liquid water at 0\,^\regular{C}.
- Objective: Determine how much energy must be added to convert the ice fully to liquid water.
- Relevant Constants: $H_{fus}$ for water is $6.01\,kJ/mol$ . The molar mass of water ( $H_2O$ ) is required to convert grams to moles.
Example 2: Calculating Mass from Vaporization Energy
- Scenario: A beaker releases $110\,kJ$ of energy when converting liquid methanol to vapor methanol at 100\,^\regular{C}.
- Objective: Calculate how much methanol, in grams ( $g$ ), is required for this vaporization process.
- Relevant Constants: $H_{vap}$ for methanol is $35.21\,kJ/mol$ . The molar mass of methanol ( $CH_3OH$ ) is required to convert the resulting moles back to grams.