4.2 Heats of Reaction and Formation

4.2 Heats of Reaction and Formation

Quick Answer: Tabulated standard heats of formation ΔH°_f give ΔH°_rxn = Σ ν_i ΔH°_f,i. Hess’s law lets you add reaction enthalpies along any path between the same states. Temperature shifts ΔH_rxn via heat-capacity differences (Kirchhoff). Exothermic processes need heat removal; endothermic processes need heat supply.

Material balances with reaction (Section 3.2) tell you how many moles form or disappear. Energy balances need how much enthalpy that chemistry releases or absorbs. On UPDA Chemical Domain A, expect conceptual and numerical items that combine stoichiometry with ΔH_rxn—especially for reactors, combustors, and heat-integrated process sketches.

Standard Heat of Formation

The standard enthalpy of formation ΔH°_f of a compound is the enthalpy change for forming 1 mole of that compound from its elements in their standard states at a stated temperature (commonly 25 °C = 298.15 K) and standard pressure (modern tables often 1 bar).

Phase matters. H₂O(l) and H₂O(g) have different ΔH°_f; the difference is related to the enthalpy of vaporization at the standard temperature. Always match the phase in the reaction as written to the table entry.

Why Formation Data Exist

Measuring every industrial reaction’s heat effect directly is impractical. Measuring or computing formation enthalpies for species, then combining them, covers thousands of reactions with a finite database—the engineering approach behind process simulators and handbook calculations.

Heat of Reaction from Formation Data

For a reaction written with stoichiometric coefficients ν_i (negative for reactants, positive for products):

ΔH°_rxn = Σ_i ν_i ΔH°_f,i

Equivalently:

ΔH°_rxn = Σ_products |ν| ΔH°_f − Σ_reactants |ν| ΔH°_f

Units: kJ per mole of reaction as written. If you double the entire reaction equation, you double ΔH_rxn. Always tie the value to the extent of reaction from your material balance:

Q_reaction-related ≈ ξ̇ × ΔH_rxn

(with temperature corrections as needed—see Kirchhoff below).

Worked Example: Formation Route

Reaction at standard conditions (illustrative table values):

CH₄(g) + 2 O₂(g) → CO₂(g) + 2 H₂O(l)

Use these formation enthalpies (kJ/mol), treated as exam-style data:

Calculation:

ΔH°_rxn = [−393.5 + 2(−285.8)] − [−74.8 + 2(0)] = [−393.5 − 571.6] − [−74.8] = −965.1 + 74.8 = −890.3 kJ per mole of CH₄ burned (as written)

Interpretation: Large negative value → strongly exothermic combustion. Cooling duty and metal temperature control dominate design and safety thinking.

If the product were H₂O(g) instead of liquid, ΔH°_rxn would be less negative (roughly by 2 × ΔH_vap of water at the standard T)—a classic “read the phase” trap.

Hess’s Law

Hess’s law: Because enthalpy is a state function, the net ΔH between given reactants and products is independent of path. Any sequence of reactions whose algebraic sum is the desired reaction has ΔH values that sum to ΔH_rxn.

Uses on exams and in plant work:

• Build an unknown reaction from tabulated half-reactions or formation steps
• Combine known industrial reaction heats when a direct table entry is missing
• Reverse a reaction: flip the sign of ΔH

Worked Hess Sketch

Suppose you know:

(1) C(s) + O₂(g) → CO₂(g) ΔH₁ = −393.5 kJ

(2) CO(g) + ½ O₂(g) → CO₂(g) ΔH₂ = −283.0 kJ

Find ΔH for C(s) + ½ O₂(g) → CO(g).

Path: reaction (1) minus reaction (2):

C + O₂ → CO₂ (−393.5) CO₂ → CO + ½ O₂ (+283.0) [reverse of (2)]

Net: C + ½ O₂ → CO ΔH = −393.5 + 283.0 = −110.5 kJ

Same result as using formation data for CO(g) if ΔH°_f(CO) = −110.5 kJ/mol.

Reference States

Energy and enthalpy have no absolute zero in ordinary engineering tables—you always work with differences relative to a reference.

Rule: Never subtract enthalpies taken from different reference systems without converting. On a short MCQ, all numbers usually share one table; if a stem mixes “from formation data” with “from steam tables,” convert carefully or use only differences within one consistent set.

For reacting systems, a powerful method is:

1. Cool/heat feeds to a reference T (sensible ± latent).
2. Carry out reaction at reference T with ΔH_rxn(T_ref).
3. Heat/cool products to the actual outlet T.

That path is Hess’s law applied to process temperatures—and it matches how many hand calculations are taught.

Effect of Temperature (Kirchhoff Intuition)

Tabulated ΔH°_rxn is often at 25 °C, while industrial reactors run hot or cold. Kirchhoff’s law (integral form) says:

ΔH_rxn(T₂) ≈ ΔH_rxn(T₁) + ∫_{T₁}^{T₂} ΔC_p dT

where ΔC_p = Σ ν_i C_p,i for the reaction as written.

Intuition for MCQs (no heavy integration required):

Over moderate ranges, a constant ΔC_p estimate ΔH(T₂) ≈ ΔH(T₁) + ΔC_p (T₂ − T₁) is enough for exam reasoning. Large temperature spans or phase changes need piecewise Cp and latent heats.

Exothermic vs Endothermic Process Implications

Sign language caution: Some plant operators say “heat of reaction is 890 kJ/mol” meaning the magnitude of heat released. Exam options may use signed thermo convention. Prefer statements like “ΔH_rxn = −890 kJ/mol (exothermic)” in your reasoning.

Safety and Utilities Link (UPDA-relevant)

• Exothermic oxidation or polymerization → jacket cooling, quench, relief design themes (later safety chapters).
• Endothermic steam reforming-style thinking → fired heaters or heat exchange with hot streams.
• Wrong phase on H₂O in combustion ΔH → wrong fired duty estimate.

Coupling ΔH_rxn to the Open-System Energy Balance

Two equivalent bookkeeping styles:

A. Formation-based enthalpies for every species at its T and phase (includes chemical enthalpy). Then:

Σ ṁ_in ĥ_in − Σ ṁ_out ĥ_out + Q̇ + Ẇ_s ≈ 0

already contains the heat of reaction—no separate ΔH_rxn term.

B. Sensible/latent-only enthalpies plus an explicit reaction term:

Σ ṁ ĥ_sensible + ξ̇ ΔH_rxn + Q̇ + Ẇ_s ≈ 0

(Details of signs depend on how ĥ and ΔH_rxn are defined—stay consistent.)

UPDA items that give “ΔH_rxn = …” usually want style B with a clear extent from the material balance.

Mini Numerical: Extent × Heat of Reaction

Reactor feed converts with extent ξ̇ = 0.25 kmol/h. ΔH_rxn = −120 MJ/kmol at reactor temperature (already corrected). Neglect sensible changes and shaft work for a rough isothermal estimate of heat duty.

Heat that must be removed to hold temperature ≈ −ξ̇ ΔH_rxn wait—careful:

If ΔH_rxn = −120 MJ per kmol of reaction progress, the chemical enthalpy of the reacting mixture drops by 0.25 × 120 = 30 MJ/h when reaction occurs. To keep U/H from falling (isothermal steady reactor), the surroundings must remove about 30 MJ/h (cooling duty ≈ 30 MJ/h).

Common Traps

• Forgetting O₂, N₂, or elements have ΔH°_f = 0 only in standard states—not as atoms in compounds.
• Using liquid water formation data when the reaction produces steam.
• Scaling ΔH_rxn incorrectly vs the stoichiometric equation and the extent.
• Ignoring temperature: using 25 °C ΔH_rxn at 800 °C without even a qualitative Kirchhoff sense when options hinge on it.
• Mixing “kJ/mol of limiting reactant” with “kJ per mole of reaction as written” when coefficients are not 1.

Exam Workflow

1. Write the balanced reaction and identify the basis of ΔH (per mole of what?).
2. Pull ΔH°_f or use Hess steps; watch phases.
3. Multiply by extent from the material balance.
4. Adjust for T if the stem provides Cp data or asks qualitative Kirchhoff reasoning.
5. Classify exo/endo and state the utility consequence (heat removal vs addition).

Section 4.3 puts these ideas into steady heaters, coolers, and mixers with sensible and latent heat—the everyday numerical form of process energy balances on the UPDA Chemical exam.