Thermochemical Equations

Introduction

A thermochemical equation states both what reacts and the enthalpy change for that balanced event. Its ΔH belongs to the stoichiometric equation as written, with specified physical states. Doubling the equation doubles the enthalpy change; reversing it changes the sign. These rules follow from enthalpy being an extensive state-function difference.

Core explanation

Consider H₂(g) + ½O₂(g) → H₂O(l), ΔH = −285.8 kJ for the reaction as written at a stated reference temperature and pressure. One mole of liquid water forms, and approximately 285.8 kJ is released under those conditions. If written with whole-number coefficients, 2H₂(g) + O₂(g) → 2H₂O(l), ΔH doubles to −571.6 kJ. The chemistry is the same, but the stated reaction extent is twice as large.

Reverse the first equation: H₂O(l) → H₂(g) + ½O₂(g). The reverse requires +285.8 kJ under corresponding conditions. The reactant and product states swap, so ΔH reverse = −ΔH forward. If a reaction is multiplied by a factor f, every stoichiometric coefficient and ΔH must be multiplied by f. One must not scale only a single compound while leaving oxygen or energy unchanged.

Physical states are part of the equation. Formation of H₂O(g) has a different enthalpy change from formation of H₂O(l), because vaporization or condensation is an additional energy change. Allotropes matter as well: carbon graphite and carbon diamond are different states with different standard enthalpies. An equation showing “H₂O” without (l) or (g) is incomplete for precise thermochemistry.

The phrase “per mole of reaction” means per occurrence of the balanced equation with its coefficients, not per mole of whichever reactant happens to be present. For 2H₂ + O₂ → 2H₂O, one mole of reaction consumes two moles H₂ and produces two moles H₂O. If a table quotes kJ mol⁻¹, identify the convention—per mole of reaction, per mole fuel, or per mole product—before applying it.

To calculate heat for an actual sample, find the limiting reactant and reaction extent ξ. If the balanced equation consumes ν moles of a limiting species per mole of reaction and the sample consumes n moles of it, ξ = n/ν. Then heat at constant pressure under matching conditions is q p ≈ ξΔ rH. If the reaction is incomplete, use amount actually reacted rather than initial amount.

Thermochemical equations can be combined in Hess's law because enthalpy changes add when the equations add and intermediate species cancel. Accuracy in state labels and scaling is crucial: an intermediate cancels only if it appears in the same physical state on opposite sides.

Step-by-step reasoning

1. Balance the chemical equation and include physical states. 2. Identify the ΔH assigned to that exact direction and scale. 3. Reverse sign if direction reverses; multiply ΔH if coefficients scale. 4. Calculate actual reaction extent from consumed moles. 5. Multiply extent by the stated enthalpy change with matching units.

Visual explanation

Draw one reaction arrow with a −100 kJ label. Under it draw a second arrow with every coefficient doubled and a −200 kJ label. Draw the original arrow reversed with +100 kJ. Put the same liquid/gas phase symbols on matching species to highlight endpoint identity.

Real-world analogy

A recipe lists ingredients and heat use for one batch. Two batches require twice each ingredient and twice the energy; running a reversible bookkeeping process backward changes the energy direction. The analogy works for scaling but chemical reactions may not practically reverse by simply turning equipment around.

Real-world example

A heater burning 0.50 mol of fuel cannot be assigned the heat for “one mole of reaction” until the balanced combustion equation's fuel coefficient is known. If that coefficient is one and combustion is complete, 0.50 mol corresponds to half the tabulated reaction enthalpy magnitude.

Why?

Why does ΔH scale with coefficients? Twice as many moles of the same initial and final substances produce twice the total enthalpy difference. Enthalpy is extensive with the amount of system.

Common misconception

“Changing the coefficient of a reaction leaves ΔH unchanged because ΔH is a state function.” State functions are path-independent, but their total change scales with the amount of material reacting.

Worked example

Given C(s, graphite) + O₂(g) → CO₂(g), ΔH = −393.5 kJ per reaction as written, calculate heat for 0.25 mol C fully burned at constant pressure under matching conditions. The carbon coefficient is one, so ξ = 0.25 mol reaction. q p ≈ 0.25(−393.5) = −98.4 kJ. For the reverse CO₂ → C + O₂, the enthalpy is +393.5 kJ per mole of reverse reaction.

Quick check

1. What happens to ΔH when every coefficient is multiplied by three? Answer: ΔH is multiplied by three for the new equation as written.

Exam focus

Show physical states, coefficient scaling and direction before arithmetic. State whether a value is per mole of fuel, product or balanced reaction extent. Never change an equation without changing its enthalpy consistently.

Advanced insight

Reaction enthalpy can be expressed as a derivative with respect to reaction extent, Δ rH = (∂H/∂ξ) under specified conditions. This formal definition explains why a balanced equation supplies the scale for its quoted molar reaction enthalpy.

Summary

A thermochemical equation ties ΔH to a precise balanced reaction and physical states. Reversing changes the sign; scaling coefficients scales ΔH. Actual sample heat follows from reaction extent and the stated constant-pressure conditions.

Practice questions

1. If A → B has ΔH = +40 kJ, what is ΔH for 2B → 2A? Answer: −80 kJ, because reversal changes sign and doubling scales magnitude. 2. Why does H₂O(l) need a different thermochemical value from H₂O(g)? Answer: They are different product states separated by a phase-change enthalpy. 3. If 0.10 mol of a species with coefficient 2 is consumed, what reaction extent occurs? Answer: 0.050 mol of reaction as written, assuming it is the amount actually consumed.