Heating and Cooling Curves in Chemistry

Heating and Cooling Curves

Introduction to Heating and Cooling Curves

Heating and cooling curves are graphical representations of the amount of heat absorbed or released by a substance during phase changes. These curves help visualize how temperature changes as a substance transitions between solid, liquid, and gas phases.

• Heating Curve: Shows temperature increase as heat is added, including plateaus during phase changes.

• Cooling Curve: Shows temperature decrease as heat is removed, with plateaus during phase changes.

Key Concepts

• Temperature remains constant during phase changes (e.g., melting, boiling) because energy is used to break or form intermolecular forces rather than changing kinetic energy.

• Sloped segments: Temperature changes as heat is added or removed; the substance remains in a single phase.

• Plateau segments: Phase changes occur (solid-liquid, liquid-gas); temperature remains constant.

• Endothermic process: Heat is absorbed (e.g., melting, vaporization).

• Exothermic process: Heat is released (e.g., freezing, condensation).

Formulas Used in Heating and Cooling Curves

• Specific Heat Equation:

$q = m c \Delta T$

• q: Heat absorbed or released (J)

• m: Mass (g)

• c: Specific heat capacity (J/g·°C)

• \Delta T: Change in temperature (°C)

• Heat of Fusion (melting/freezing):

$q = m \Delta H_f$

• \Delta H_f: Heat of fusion (J/g)

• Heat of Vaporization (boiling/condensation):

$q = m \Delta H_v$

• \Delta H_v: Heat of vaporization (J/g)

Heating and Cooling Curve Diagrams

• Heating Curve: Temperature increases with time, with flat regions at melting and boiling points.

• Cooling Curve: Temperature decreases with time, with flat regions at freezing and condensation points.

Table: Specific Heats and Heats of Phase Change

Substance	Specific Heat (J/g·°C)	Heat of Fusion (J/g)	Heat of Vaporization (J/g)
Ice	2.1	334	---
Liquid Water	4.18	---	2260
Steam	2.0	---	---

Additional info: Table values are typical for water; other substances have different values.

Example Problem: Calculating Heat for Phase Change

Example: How much energy (kJ) is required to convert 7.64 g acetone (molar mass = 58.08 g/mol) as a liquid at -30°C to a solid at -115°C?

• Use the specific heat of liquid and solid, and the heat of fusion for acetone.

• Calculate energy for each step: cooling liquid, freezing, cooling solid.

Solution Steps:

1. Calculate energy to cool liquid from -30°C to freezing point.

2. Calculate energy for freezing (phase change).

3. Calculate energy to cool solid from freezing point to -115°C.

4. Add all energies for total heat required.

Additional info: Always use correct specific heat and phase change values for the substance in question.

Practice Problem: Heat Added to Ice

Practice: If 31.2 kJ of heat are added to 11.5 g ice cube at -5.0°C, what will be the resulting state and temperature of the substance?

• Calculate energy to warm ice to 0°C.

• Calculate energy to melt ice at 0°C.

• Calculate energy to warm resulting water, if any heat remains.

Answer: 36.82°C, liquid

Summary Table: Steps in Heating/Cooling Curve Calculations

Step	Equation	When to Use
Temperature change (single phase)	$q = m c \Delta T$	Heating/cooling solid, liquid, or gas
Melting/Freezing	$q = m \Delta H_f$	At melting/freezing point
Boiling/Condensation	$q = m \Delta H_v$	At boiling/condensation point