§ C-13 Thermochemistry, Hess’s Law & Calorimetric Enthalpy Determination ΔH (Grade 9–11 · Thermochemistry)
Measuring heat effects of exo- and endothermic reactions Q = (m·c + C_cal)ΔT = −ν·ΔH and Hess’s Law enthalpy diagram. The heat of a chemical reaction at constant pressure equals the enthalpy change ΔH and depends solely on the initial and final states (Hess’s Law).
Theory Summary & Scientific Mechanism
Thermochemistry quantifies the heat exchanged during chemical reactions. At constant pressure, the heat of reaction equals the change in enthalpy Δ H = Hₚroducts - Hᵣeactants. In an exothermic reaction (Δ H 0 into the surroundings (e.g., strong acid-base neutralization H⁺ + OH⁻ → H₂O, Δ H^° = -57.3 kJ/mol). In an endothermic process (Δ H > 0), heat is absorbed from the solution (e.g., dissolution of NH₄NO₃, Δ H^° = +25.7 kJ/mol).
In an insulated calorimeter, the heat balance yields Δ H = -(Q_cal)/(ν) = -((mₛol cₚ + C_cal)Δ T)/(ν), where cₚ ≈ 4.184 J/(g·K) is the specific heat capacity of the aqueous solution and C_cal is the calorimeter constant.
Hess’s Law states that because enthalpy H is a state function, the overall enthalpy change Δ H^°ᵣxn of a reaction is independent of the pathway or number of intermediate steps: Δ H^°ᵣxn = ∑ νᵢ Δ H^°_f,prod - ∑ νⱼ Δ H^°_f,react.
Everyday Analogy
A chemical hand-warmer releases heat in an exothermic reaction (Δ H 0, temperature drops)!
Interactive Question & Derivation
When reactants are mixed in an insulated calorimeter, the aqueous solution temperature rises by Δ T = +6.5 K. What can be concluded about the heat effect Q and reaction enthalpy change Δ H?
- A: The reaction is exothermic: the chemical system releases heat into the solution (Q > 0), so its enthalpy decreases (Δ H = -Q/ν < 0)
- B: The reaction is endothermic (Δ H > 0), absorbing cold from the surroundings
- C: The enthalpy change is zero (Δ H = 0) because the calorimeter is thermally insulated
Study Hint: If the calorimeter temperature rises (Δ T > 0), the reaction releases heat Q > 0 into the solution (exothermic), meaning the chemical system’s enthalpy decreases: Δ H = -Q/ν < 0.
Proof & Explanation: In an adiabatic calorimeter, heat Q released by an exothermic reaction (Δ H 0). Conversely, endothermic dissolution of NH₄NO₃ (Δ H > 0) absorbs thermal energy from the water, cooling the solution (Δ T < 0).
Key Equations & 3D Simulation Parameters
Δ H = -(Q_cal)/(ν) = -((mₛol cₚ + C_cal) (T_final - Tᵢnit))/(ν)
- Reaction (1=HCl+NaOH exo, 2=NH₄NO₃ endo, 3=Mg+2HCl strong exo): 1 … 3 (default: 1)
- Reactant molar amount ν: 0.02 … 0.25 mol (default: 0.1 mol)
- Calorimeter aqueous solution mass m: 100 … 400 g (default: 200 g)
- Calorimeter vessel heat capacity C_cal: 10 … 120 J/K (default: 45 J/K)