10.3 Thermochemistry & Energy in Chemical Changes

Thermochemistry & Energy in Chemical Changes

Quick Answer: Thermochemistry is the study of heat flow during chemical and physical changes. The PA-CAT Bulletin of Information (rev. 20240815) places thermochemistry in Chemistry Table 5. You must distinguish endo- vs exothermic, apply q = m·c·ΔT, use Hess's law to combine reactions, and estimate ΔH from bond energies.

System, Surroundings, and Energy Flow

The system is the reaction or process under study; the surroundings are everything else. Energy crosses the boundary as heat (q) (driven by a temperature difference) or work (w) (PV work or other mechanical/electrical work). The first law of thermodynamics: ΔU = q + w.

Exothermic vs Endothermic

A reaction mixture that warms its container is exothermic; one that cools it (or must be heated to proceed) is endothermic.

Enthalpy (H) and ΔH

Enthalpy is heat content at constant pressure. ΔH°_rxn = Σ ΔH°_f(products) − Σ ΔH°_f(reactants), using standard enthalpies of formation (elements in their standard states have ΔH°_f = 0). For CH₄ + 2 O₂ → CO₂ + 2 H₂O(l): ΔH° = [−393.5 + 2(−285.8)] − [−74.8 + 0] = −890.3 kJ/mol.

Hess's Law

Hess's law: if a reaction is the sum of two or more steps, its ΔH is the sum of the steps' ΔH values. Rules for manipulating thermochemical equations:

• Reverse a reaction → flip the sign of ΔH.
• Multiply by n → multiply ΔH by n.

Example: find ΔH for C(s) + 2 H₂(g) → CH₄(g) given

1. C(s) + O₂(g) → CO₂(g) ΔH = −393.5 kJ
2. H₂(g) + ½ O₂(g) → H₂O(l) ΔH = −285.8 kJ
3. CH₄(g) + 2 O₂(g) → CO₂(g) + 2 H₂O(l) ΔH = −890.3 kJ

Keep (1): C + O₂ → CO₂, ΔH = −393.5 kJ. Keep (2) ×2: 2 H₂ + O₂ → 2 H₂O, ΔH = 2(−285.8) = −571.6 kJ. Reverse (3): CO₂ + 2 H₂O → CH₄ + 2 O₂, ΔH = +890.3 kJ. Sum: (−393.5) + (−571.6) + 890.3 = 890.3 − 393.5 − 571.6 = −74.8 kJ, the standard enthalpy of formation of methane.

Why this works: enthalpy is a state function, so only the initial and final states matter, not the path. You may therefore combine any thermochemical equations that sum to the target and add their ΔH values. The two recurring PA-CAT errors are (1) forgetting to flip the sign of ΔH when you reverse a reaction, and (2) forgetting to multiply ΔH by the same factor when you scale an equation — using equation 2 twice doubles both the species and the heat (2 × −285.8 = −571.6, not −285.8). Write each manipulated ΔH beside its equation before summing, then cancel species appearing on both sides exactly as in algebra. A quick self-check: if your target is a formation reaction (elements → compound), the result should match the tabulated ΔH°_f; for methane that is −74.8 kJ/mol, so a positive result signals a sign error.

Calorimetry and Heat Capacity

Constant-pressure calorimetry (coffee-cup): q_solution = m · c · ΔT, where m is solution mass, c is specific heat (water = 4.184 J/g·°C), and ΔT = T_final − T_initial. The reaction heat q_rxn = −q_solution.

Worked example: 50.0 g of water rises from 22.0 °C to 28.6 °C when 0.0100 mol of a fuel is burned at constant pressure. Find q_rxn per mole.

1. q_water = (50.0 g)(4.184 J/g·°C)(6.6 °C) = 1381 J = 1.38 kJ absorbed by water.
2. q_rxn = −1.38 kJ for 0.0100 mol → per mole = −1.38 ÷ 0.0100 = −138 kJ/mol (exothermic).

Constant-volume bomb calorimetry measures ΔU directly; convert to ΔH with ΔH = ΔU + Δn_gas·RT, where Δn_gas is the change in moles of gas.

Heat capacity C of an object = m·c; molar heat capacity C_m = c · M.

Bond Energies (Approximate ΔH)

ΔH°_rxn ≈ Σ (bonds broken) − Σ (bonds formed), using average bond dissociation energies (positive values). Breaking bonds is endothermic; forming bonds is exothermic.

Example for H₂ + Cl₂ → 2 HCl: break H–H (436 kJ) + Cl–Cl (243 kJ) = 679 kJ; form 2 H–Cl (2 × 432 = 864 kJ). ΔH ≈ 679 − 864 = −185 kJ for 2 mol HCl, or −92.5 kJ/mol HCl.

Bond energies are averages, so estimates differ from calorimetric ΔH by a few kJ — fine for PA-CAT-style estimation questions.

flowchart LR
    A[Reaction] --> B{Heat flow?}
    B -->|Releases, ΔH<0| C[Exothermic: container warms]
    B -->|Absorbs, ΔH>0| D[Endothermic: container cools]
    C --> E[Calorimetry: q_rxn = -m c ΔT]
    D --> E

Key Constants to Memorize

• Specific heat of water: 4.184 J/g·°C (≈ 4.18).
• Standard heat of formation of H₂O(l): −285.8 kJ/mol; CO₂(g): −393.5 kJ/mol.
• R = 8.314 J/mol·K = 0.0821 L·atm/mol·K.