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Thermochemistry: Enthalpy, Stoichiometry, and Calorimetry

Introduction to Enthalpy (H)

  • Heat Content (H): The term for the heat contained within a system.
  • Exothermic Reaction: A chemical reaction that releases heat to the surroundings.
    • For an exothermic reaction, the change in heat content (\Delta H) of the system is a negative value. Heat is flowing out of the system.
  • Endothermic Reaction: A chemical reaction that absorbs heat from the surroundings.
    • For an endothermic reaction, the change in heat content (\Delta H) of the system is a positive value. Heat is flowing into the system.

Stoichiometry and Enthalpy Changes

Definition of Stoichiometry

  • Stoichiometry: Any mathematical calculation performed based on the ratios derived from a balanced chemical equation. This includes mole ratios between reactants and products, and also the relationship between reactant/product quantities and the heat change (\Delta H).

Relationship between \Delta H and Amounts

  • The change in heat content (\Delta H) is directly proportional to the amount of reactants consumed (or products formed) and the stoichiometric ratios in the balanced equation.
  • Example Analogy: Driving a car for 30 miles might consume 1 gallon of gas. The amount of work done (distance covered) is proportional to the amount of fuel used.
  • Using Moles: Moles are the preferred unit for reaction calculations because the coefficients in a balanced equation represent mole ratios. If given grams, convert to moles first.

Example: Hydrogen Combustion

Consider the reaction: 2\text{H}2\text{(g)} + \text{O}2\text{(g)} \longrightarrow 2\text{H}*_2\text{O(l)} with a given \Delta H = -483.6 \text{ kJ} . This means when 2 moles of hydrogen react with 1 mole of oxygen to form 2 moles of water, 483.6 \text{ kJ} of heat are *released*.

Proportionality of \Delta H
  • If the reaction amounts are doubled (e.g., 4 moles of H*_2 react), then the heat released will also double (2 \times (-483.6 \text{ kJ}) = -967.2 \text{ kJ}).
  • Sample Calculation: How much heat is released when 4 moles of hydrogen react?
    • Given: For 2 \text{ mol H}*_2, \Delta H = -483.6 \text{ kJ}.
    • Ratio: \frac{-483.6 \text{ kJ}}{2 \text{ mol H}*_2}
    • Calculation: 4 \text{ mol H}2 \times \frac{-483.6 \text{ kJ}}{2 \text{ mol H}2} = -967.2 \text{ kJ}
Stoichiometric Calculation Example (grams to kJ)

  • Problem: If 10 grams of hydrogen react, how much heat would be released?

  • Steps: Convert grams of H2 to moles of H2, then use the stoichiometric ratio (from the balanced equation and given \Delta H) to find the heat released.

    • Molar mass of H*_2: 2 \times 1.008 \text{ g/mol} \approx 2.016 \text{ g/mol}. (For simplicity in lecture examples, 2 \text{ g/mol} is often used).
    • Moles of H2 from 10 \text{ g}: \text{mol H}2 = \frac{10 \text{ g H}2}{2 \text{ g/mol H}2} = 5.0 \text{ mol H}*_2
    • Heat released: 5.0 \text{ mol H}2 \times \frac{-483.6 \text{ kJ}}{2 \text{ mol H}2} = -1209 \text{ kJ} (This aligns with the 1209 \text{ kJ} result sometimes referred to in lecture for a similar calculation).

  • Problem (Alternative): If 5 grams of hydrogen react, how much heat would be released?

    • Moles of H2 from 5 \text{ g}: \frac{5 \text{ g H}2}{2 \text{ g/mol H}2} = 2.5 \text{ mol H}2
    • Heat released: 2.5 \text{ mol H}2 \times \frac{-483.6 \text{ kJ}}{2 \text{ mol H}2} = -604.5 \text{ kJ}

  • The specific calculation for 0.3789 \text{ g Mg} will be revisited in the calorimetry section.

Sign Convention for \Delta H
  • Wording Matters: The phrasing of a question determines whether the negative sign is explicitly required.
    • If a question asks, "How much heat is released?", the negative sign should typically be omitted in the numerical answer, as "released" already implies the exothermic nature. For example, you would state "1209 \text{ kJ} of heat is released," not "-1209 \text{ kJ} of heat is released." However, in calculations for \Delta H$$ itself, the negative sign is always crucial to indicate the direction of heat flow.