Chem 162 - Ch 9 - Thermochemistry (Heating curves)

Introduction to Heating Curves

• Heating curves are graphs that demonstrate how a substance changes temperature and phase when heat is added or removed.

• Calculating the total energy for a temperature or phase change involves separate steps for temperature changes and phase changes.

Phases of Matter

• The three phases of matter discussed:

  • Solids

  • Liquids

  • Gases

• Heat of Fusion (ΔH_Fus): Amount of heat needed to change from solid to liquid (endothermic) and vice versa (exothermic).

• Heat of Vaporization: Amount of heat needed to change from liquid to gas (endothermic) and vice versa (exothermic).

• Cooling Effect of Sweating: Evaporation of sweat cools skin by removing heat.

Sublimation and Deposition

• Sublimation: Direct transition from solid to gas (ΔH_Subl = ΔH_Fus + ΔH_Vap).

• Deposition: Direct transition from gas to solid (ΔH_Dep = ΔH_Vap + ΔH_Fus).

Heating Curve for Ethanol (C2H5OH)

• Example problem: Calculate energy required to change 100.0 g of ethanol from -150.0°C to 150.0°C.

• Key Value Points:

  • Melting Point (MP): -114.0°C

  • Boiling Point (BP): 78.0°C

  • Heat of Fusion: 4.60 kJ/mol

  • Heat of Vaporization: 43.5 kJ/mol

Specific Heats for Ethanol

• Specific heat (solid): 2.419 J/g°C

• Specific heat (liquid): 2.46 J/g°C

• Specific heat (gas): 1.70 J/g°C

Drawing the Heating Curve

• Generally consists of five steps along the temperature scale from -150°C to 150°C.

• Points of interest are critical temperatures (melting and boiling points) where phase changes occur.

Steps of the Heating Curve Calculation

1. Step One: Solid Heating

   • Heating solid from -150°C to -114°C (MP).

   • Formula: Q = mass × specific heat × ΔT.

   • Calculation:

     • Q = 100 g × 2.419 J/g°C × 36°C = 8,708.4 J (or 8.7084 kJ).

2. Step Two: Fusion

   • Phase change from solid to liquid at -114°C.

   • Formula: Q = n × ΔH_Fus.

   • Convert: 100 g of ethanol = 2.171 moles.

   • Calculation:

     • Q = 2.171 moles × 4.60 kJ/mol ≈ 9.982 kJ.

3. Step Three: Liquid Heating

   • Heating liquid ethanol from -114°C to 78°C (BP).

   • Formula: Q = mass × specific heat × ΔT.

   • Calculation:

     • Q = 100.0 g × 2.46 J/g°C × 192°C = 47,230 J (or 47.230 kJ).

4. Step Four: Vaporization

   • Phase change from liquid to gas at 78°C.

   • Formula: Q = n × ΔH_Vap.

   • Calculation:

     • Q = 2.171 moles × 43.5 kJ/mol ≈ 94.44 kJ.

5. Step Five: Gas Heating

   • Heating gas from 78°C to 150°C.

   • Formula: Q = mass × specific heat × ΔT.

   • Calculation:

     • Q = 100.0 g × 1.70 J/g°C × 72°C = 12,240 J (or 12.240 kJ).

Total Energy Calculation

• Final energy calculation involves summing all energy changes from steps one through five:

  • Total Energy = 8.7084 kJ (Step 1) + 9.982 kJ (Step 2) + 47.230 kJ (Step 3) + 94.44 kJ (Step 4) + 12.240 kJ (Step 5) = 172.6 kJ.

• Reminder: Pay attention to units (joules vs kilojoules) and significant figures while calculating.

Conclusion and Review

• Students should practice similar problems independently to reinforce understanding of heating curves and calculations.

• Be aware that not all heating curves contain the same number of steps; some might have fewer based on the initial and final state of the substance.