Heating Curves and Phase Change Calculations

Heating Curves

• Depict the phase transitions of a substance as heat is added.

Phase Changes

• Heating Curve Stages
  • Stage 1: Solid is heating.
  • Stage 2: Solid to Liquid (Melting).
  • Stage 3: Liquid is heating.
  • Stage 4: Liquid to Gas (Vaporizing).
  • Stage 5: Gas is heating.

Heat of Fusion

• Formula: $Q = m \times H_f$
  • Q = heat/energy (in Joules)
  • m = mass (in grams)
  • $H_f$ = Heat of Fusion (J/g)
  • Energy required to melt one gram of a specific substance at its melting point.

Example 1: Heat of Fusion Calculation

• Problem: How much energy is required to melt 50.3 grams of $H<em>2O$ at 0°C? ($H</em>f$ of $H_2O$ = 334 J/g)
• Solution:
  • $Q = m \times H_f$
  • $Q = 50.3 \times 334$
  • $Q = 16800$ Joules

Heat of Vaporization

• Formula: $Q = m \times H_v$
  • Q = heat/energy (in Joules)
  • m = mass (in grams)
  • $H_v$ = Heat of Vaporization (J/g)
  • Energy required to vaporize one gram of a specific substance at its boiling point.

Example 2: Heat of Vaporization Calculation

• Problem: How much energy is needed to vaporize 50.3 grams of $H<em>2O$ at 100°C? ($H</em>v$ of $H_2O$ = 2260 J/g)
• Solution:
  • $Q = m \times H_v$
  • $Q = 50.3 \times 2260$
  • $Q = 114000$ Joules

Example 3: Multi-Step Calculation

• Problem: How much heat is needed to change 22.0 grams of water from -14.0°C to 77.0°C?

Step-by-Step Calculation

1. Heating the solid (ice) from -14.0°C to 0°C:
   • Formula: $Q = m \times C_{solid} \times \Delta T$
   • $Q = 22.0 \times 2.05 \times (14.0)$
   • $Q = 631$ J
2. Melting the ice at 0°C:
   • Formula: $Q = m \times H_f$
   • $Q = 22.0 \times 334$
   • $Q = 7350$ J
3. Heating the liquid water from 0°C to 77.0°C:
   • Formula: $Q = m \times C_{liquid} \times \Delta T$
   • $Q = 22.0 \times 4.184 \times (77.0)$
   • $Q = 7090$ J

Total Heat Calculation

• Summing the heat from each step:
  • $Q<em>{total} = Q</em>{solid} + Q<em>{melt} + Q</em>{liquid}$
  • $Q_{total} = 631 + 7350 + 7090$
  • $Q_{total} = 15071$ J