Measuring Enthalpy

Introduction

Calorimetry: Calorimetry is the science dedicated to measuring heat changes resulting from chemical reactions or physical processes. It plays a critical role in understanding essential energy transformations within both academic and industrial contexts.

Principles of Calorimetry

Heat Transfer

• Concept Explanation: Heat transfer involves the movement of thermal energy from a warmer object to a cooler one.
• Role in Calorimetry: This process is measured to determine the energy changes involved in reactions.

Specific Heat Capacity

• Definition: Specific heat capacity refers to the amount of heat needed to raise the temperature of 1 gram of a substance by 1°C.
• Significance in Calorimetry: It is vital for calculating energy shifts in reactions.

Conservation of Energy

• Law Explanation: According to this law, energy can neither be created nor destroyed, only transferred or transformed.
• Application in Calorimetry: This principle is demonstrated through equal exchanges of energy between systems and their surroundings.

Heat Capacity Formula

• Introducing Formula: $q = mc\Delta T$
  • q: Heat absorbed or released
  • m: Mass
  • c: Specific heat capacity
  • $\Delta T$: Change in temperature

Worked Example

Determine the final temperature when 100 g of water at 25°C mixes with 100 g of water at 85°C, assuming no heat loss.

Steps:

1. Heat Lost by Hot Water:
   • $q_{\text{hot}} = 100 \times 4.18 \times (85 - T_f)$
2. Heat Gained by Cold Water:
   • $q_{\text{cold}} = 100 \times 4.18 \times (T_f - 25)$
3. Equate for Equilibrium:
   • $100 \times 4.18 \times (85 - T_f) = 100 \times 4.18 \times (T_f - 25)$
   • Solving: $T_f = \frac{85 + 25}{2} = 55°C$

Types of Calorimeters

Overview

• Calorimeter: A device that measures heat changes during chemical reactions.
  • Functions by capturing heat generated in reactions for analysis.

Types of Calorimeters

Type	Conditions	Cost	Applications
Coffee Cup	Constant Pressure	Low	Solution-based reactions (e.g., neutralisation)
Bomb	Constant Volume	High	Combustion analysis, fuel energetics

Coffee Cup Calorimeter

• Detailed Construction: Utilises a polystyrene cup to conserve heat.
• Principle & Operation: Works under constant pressure, making it ideal for fundamental reactions in educational contexts.
  • Example: Calculate energy change in an acid-base neutralisation:
    • Mixing 50 mL of 1M HCl with 50 mL of 1M NaOH raises the temperature from 22°C to 27°C.
    • $\Delta Q = m \cdot c \cdot \Delta T = 100 \times 4.18 \times (27-22) = 2090 \text{ J}$
• Applications: Suitable for educational laboratories.
• Limitations: Not apt for high-temperature reactions.

Bomb Calorimeter

• Advanced Design: Features a sturdy, pressure-sealed chamber.
• Utilisation: Functions at constant volume, ideal for high-precision combustion reaction measurements.
  • Example: Employed to ascertain energy content in fossil fuels.

Calorimetry Calculations

Introduction

• Calorimetry Calculations: Aim to determine enthalpy changes.
• Enthalpy: Represents total heat content, pivotal for comprehending energy flows.

Using $q = mc\Delta T$

• Worked Example:
  • Calculate $q$ for water:
    • Mass: 100g $({\text{Initial}} = 20^\circ C, \text{Final} = 30^\circ C)$
    • $\Delta T = 10^\circ C$
    • $q = 100 \times 4.18 \times 10 = 4180 \text{ J}$

Enthalpy Change Formula

• Formula: $\Delta H = -q / n$
  • Positive $\Delta H$: Endothermic.
  • Negative $\Delta H$: Exothermic.

Practice Problems

• Coffee Cup Calculation: Ascertain $q$ for a 50g metal undergoing a temperature increase from 25°C to 40°C.
  • Solution:
    • Assuming the specific heat capacity of the metal is 0.5 J/g°C
    • $q = m \cdot c \cdot \Delta T = 50 \times 0.5 \times (40-25) = 375 \text{ J}$

Error Analysis in Calorimetry

Common Errors

• Heat Loss: Occurs notably in coffee cup calorimeters, impacting accuracy.
• Incomplete Combustion: Affects precision in bomb calorimeters.
• Measurement Errors: Influence accuracy; a 1°C error might lead to a 5% calculation deviation.

Mitigation Strategies

• Improving Insulation: Use insulation to minimise heat exchange.
• Instrumentation Calibration: Regular device calibration is recommended.

Strategies for Improvement

• Improving Accuracy:

  • Recalibrate equipment and enhance insulation.

• Enhancing Precision:

  • Conduct multiple experimental trials.

• Statistical Analysis Insights:

  • Evaluate mean enthalpy changes and assess consistency.