Energy Measurement and Enthalpy

Calorie

• Definition: The amount of energy required to raise the temperature of one gram of water by one degree Celsius.
• Important Note: This is NOT the calorie commonly associated with food.

Kilocalorie (Food Calorie)

• The calorie we typically think about in the context of food is actually a kilocalorie.
• Representations:
  • Written with a capital C (Calorie).
  • Equivalent to 1,000 little 'c' calories.
• $1 \text{ Calorie (big C)} = 1 \text{ kilocalorie} = 1000 \text{ calories (little c)}$
• Significance: Our bodies require a substantial amount of energy to function, hence the use of kilocalories for measuring food energy.

Joule

• The official scientific unit for energy.
• Relationship to calorie:
  • $1 \text{ calorie (little c)} = 4.18 \text{ joules}$
• Utility: Allows conversion between food calories (kilocalories) and the scientific unit of energy (joules).

Calorie to Kilojoule Conversion Example

• Goal: Convert a 150 Calorie (big C) beverage into kilojoules.
• Relationships/Conversion Factors:
  • $1 \text{ Calorie (big C)} = 1000 \text{ calories (little c)}$
  • $1 \text{ calorie (little c)} = 4.18 \text{ joules}$
  • $1 \text{ kilojoule} = 1000 \text{ joules}$
• Step-by-step Conversion using Dimensional Analysis:
  • Start with 150 Calories (big C).
  • Convert Calories to calories: $150 \text{ Cal} \times \frac{1000 \text{ cal}}{1 \text{ Cal}}$
  • Convert calories to joules: $\frac{1000 \text{ cal}}{1 \text{ Cal}} \times \frac{4.18 \text{ J}}{1 \text{ cal}}$
  • Convert joules to kilojoules: $\frac{4.18 \text{ J}}{1 \text{ cal}} \times \frac{1 \text{ kJ}}{1000 \text{ J}}$
  • Calculation: $\frac{150 \times 1000 \times 4.18}{1 \times 1 \times 1000} = 627 \text{ kJ}$
• Result: A 150 Calorie beverage is equivalent to 627 kilojoules. This is what would be labeled on the product in Europe.

Heat Energy (q)

• Symbol: Represented by the letter 'q' (can be uppercase or lowercase).
• Units: Typically measured in joules, but can also be expressed in kilojoules.
• Scope: Refers to the heat energy of a specific sample or substance.

Enthalpy (ΔH)

• Definition: Energy gained or lost per mole of a substance.
• Significance: Allows comparisons of energy changes, similar to stoichiometry.
• Formula: Represented as delta H ($\Delta H$).
• Units: Measured in kilojoules per mole (kJ/mol).
• Incorporates: Combines heat energy (q) with the amount of substance (moles).

Enthalpy Calculation Example

• Problem: Ten grams of C8H18 releases 480,000 joules of energy. Determine the enthalpy for the reaction.
• Given:
  • Mass of C8H18 = 10 grams
  • Heat energy (q) = -480,000 joules (negative because energy is released)
• Unknown: Enthalpy ($\Delta H$)
• Step 1: Convert joules to kilojoules.
  • $-480,000 \text{ J} \times \frac{1 \text{ kJ}}{1000 \text{ J}} = -480 \text{ kJ}$
• Step 2: Convert grams of C8H18 to moles using molar mass.
  • Molar mass of C8H18: $(8 \times 12.01) + (18 \times 1.01) = 114.26 \text{ g/mol}$
  • $10 \text{ g} \times \frac{1 \text{ mol}}{114.26 \text{ g}} = 0.0875 \text{ mol}$
• Step 3: Calculate enthalpy ($\Delta H$) by dividing kilojoules by moles.<ul> <li>$\Delta H = \frac{-480 \text{ kJ}}{0.0875 \text{ mol}} = -5485.7 \text{ kJ/mol}

Key Takeaway

• Be aware of the difference between the food calorie (kilocalorie) and the scientific calorie when dealing with energy measurements.