Enthalpy change and constant-pressure heat
Enthalpy change is defined as the difference between final and initial enthalpy:
\[ \Delta H = H_{\text{final}} - H_{\text{initial}}. \]
For reactions carried out at constant pressure (typical open-to-atmosphere laboratory conditions), the enthalpy change equals the heat transferred at constant pressure:
\[ \Delta H = q_p. \]
Sign convention: \(\Delta H < 0\) corresponds to heat released (exothermic); \(\Delta H > 0\) corresponds to heat absorbed (endothermic).
Four standard ways to find enthalpy change
- Calorimetry at constant pressure: heat flow inferred from a measured temperature change and heat capacity, then related to \(\Delta H\).
- Hess’s law: enthalpy changes added for a reaction written as a sum of known reactions.
- Standard enthalpies of formation: \(\Delta H^\circ_{\text{rxn}}\) computed from tabulated \(\Delta H_f^\circ\) values and stoichiometric coefficients.
- Average bond enthalpies: \(\Delta H\) estimated from bonds broken and formed, with an acknowledged approximation.
Calorimetry relationships
A common constant-pressure model relates the heat absorbed by a measured portion of the surroundings (often the solution) to a temperature change:
\[ q_{\text{surr}} = m c \Delta T. \]
Conservation of energy links the reaction heat to the surroundings heat (with the sign change):
\[ q_{\text{rxn}} = -q_{\text{surr}}. \]
A molar enthalpy change uses the amount of limiting reactant (or moles of reaction as written), \(n\):
\[ \Delta H_{\text{rxn}} = \frac{q_{\text{rxn}}}{n}. \]
Hess’s law and reaction algebra
Enthalpy is a state function, so the enthalpy change depends only on initial and final states. When a target reaction is written as a linear combination of known reactions, the enthalpy change follows the same combination.
If a reaction is multiplied by a factor \(k\), its enthalpy change is multiplied by \(k\). If a reaction is reversed, the sign of \(\Delta H\) changes.
Standard enthalpy of reaction from formation enthalpies
At standard conditions, the most widely used calculation route is:
\[ \Delta H^\circ_{\text{rxn}}=\sum \nu\,\Delta H_f^\circ(\text{products})-\sum \nu\,\Delta H_f^\circ(\text{reactants}), \]
where \(\nu\) denotes stoichiometric coefficients in the balanced chemical equation and \(\Delta H_f^\circ\) values are taken from tables for the correct physical states.
Bond enthalpy estimate
Average bond enthalpies support a qualitative-to-semiquantitative estimate:
\[ \Delta H \approx \sum D(\text{bonds broken})-\sum D(\text{bonds formed}). \]
The approximation arises because tabulated bond enthalpies represent averages over many molecules and environments, rather than the exact bonds in a specific compound.
Method comparison table
| Method | Primary inputs | Typical output | Strength | Limitation |
|---|---|---|---|---|
| Calorimetry | \(m\), \(c\) (or calorimeter constant), \(\Delta T\), amount \(n\) | \(\Delta H\) for the experimental process | Direct measurement under the chosen conditions | Heat losses, calibration, incomplete reaction, and side processes can bias results |
| Hess’s law | Thermochemical equations and their \(\Delta H\) values | \(\Delta H\) for a target reaction | Exact within consistent data sets | Availability and consistency of required component reactions |
| Formation enthalpies | Balanced equation, \(\Delta H_f^\circ\) table values, physical states | \(\Delta H^\circ_{\text{rxn}}\) | Standard, systematic route for many reactions | Standard-state definition; nonstandard conditions require additional corrections |
| Bond enthalpies | Bond inventory in reactants and products, average \(D\) values | Estimated \(\Delta H\) | Fast approximation and trend prediction | Lower accuracy; poor for resonance, strong solvation, or unusual bonding environments |
Visualization of \(\Delta H\) on an energy profile
The vertical difference between reactant and product energy levels corresponds to \(\Delta H\). Exothermic profiles place products lower than reactants (\(\Delta H<0\)); endothermic profiles place products higher than reactants (\(\Delta H>0\)).
Common pitfalls
- Balanced-equation consistency: \(\Delta H\) corresponds to the reaction as written; changing stoichiometric coefficients scales \(\Delta H\) by the same factor.
- Physical state mismatch: \(\Delta H_f^\circ\) values depend on state labels (s, l, g, aq); incorrect states change results substantially.
- Sign confusion in calorimetry: \(q_{\text{rxn}}=-q_{\text{surr}}\) reverses the sign relative to the measured temperature change of the surroundings.
- Bond enthalpy overconfidence: average bond enthalpies support estimates and trends, not high-precision thermochemistry.