Chemical energetics: enthalpy changes, bond energies, Hess’s law, calorimetry

Chemical Energetics (Cambridge AS & A‑Level Chemistry 9701)

1. Enthalpy (ΔH)

• Definition: The heat exchanged with the surroundings when a process occurs at constant pressure. ΔH is a state function – only the initial and final states matter.
• Sign convention
  • Exothermic: ΔH < 0 (heat released to the surroundings).
  • Endothermic: ΔH > 0 (heat absorbed from the surroundings).
• Standard enthalpy change (ΔH°): Measured under the standard state
  • Temperature: 298 K (25 °C)
  • Pressure: 101 kPa (1 atm)
  • All reactants and products at a concentration of 1 mol L⁻¹ (or 1 atm for gases).

1.1 Types of Standard Enthalpy Changes

Symbol	Name	Definition (standard state)	Typical example
ΔH°f	Standard enthalpy of formation	Enthalpy change when 1 mol of a compound is formed from its constituent elements in their standard states.	H₂(g) + ½ O₂(g) → H₂O(l)
ΔH°c	Standard enthalpy of combustion	Enthalpy change when 1 mol of a substance burns completely in excess O₂ under standard conditions.	CH₄(g) + 2 O₂(g) → CO₂(g) + 2 H₂O(l)
ΔH°neut	Standard enthalpy of neutralisation	Enthalpy change when 1 mol of H⁺ reacts with 1 mol of OH⁻ to give liquid water (standard conditions).	HCl(aq) + NaOH(aq) → NaCl(aq) + H₂O(l)
ΔH°r	Standard enthalpy of reaction	Overall enthalpy change for any reaction, calculated from ΔH°f values of reactants and products.	Any balanced equation, e.g. the combustion of propane.

1.2 Example – Standard Enthalpy of Neutralisation

For the reaction HCl(aq) + NaOH(aq) → NaCl(aq) + H₂O(l) the measured heat released is –57 kJ per mole of water formed. Hence, ΔH°neut = –57 kJ mol⁻¹.

2. Bond Energies

• Bond dissociation energy (average bond enthalpy): Energy required to break one mole of a particular bond in the gas phase.
• Values are averages because the energy varies with the molecular environment; they are best used for quick estimates.
• Estimating reaction enthalpy:

  ΔH_rxn ≈ ∑ E_broken − ∑ E_formed

• Limitations
  • Applicable only to gaseous species (bond energies are defined for gas‑phase molecules).
  • Ignores phase changes, hydrogen bonding, resonance and other electronic effects.
  • Provides an approximation; for accurate values use ΔH°_f data or calorimetry.

Bond	Bond energy (kJ mol⁻¹)	Bond	Bond energy (kJ mol⁻¹)
C–C	347	C=O	799
C–H	413	O–H	463
H–H	436	N≡N	945
Cl–Cl	242	O=O	498

3. Hess’s Law

Because enthalpy is a state function, the total ΔH for a reaction is independent of the pathway taken. This allows us to combine known enthalpy changes to obtain the ΔH for a reaction that is difficult to measure directly.

Mathematical form:

ΔH_overall = ∑ ΔH_i

Steps to apply Hess’s Law

1. Write the target reaction clearly.
2. Identify standard enthalpies (ΔH°_f, ΔH°_c, ΔH°_neut, etc.) that are available.
3. Manipulate the known equations (reverse, multiply by a coefficient) so that, when added, unwanted species cancel and the desired reaction remains.
4. Sum the adjusted ΔH values – the result is ΔH° for the target reaction.

4. Calorimetry

4.1 Constant‑pressure (coffee‑cup) calorimeter

At constant pressure the heat exchanged equals the enthalpy change of the reaction:

q_rxn = −q_solution = −m c ΔT

• m – mass of the solution (≈ mass of water, in g).
• c – specific heat capacity of water (4.18 J g⁻¹ K⁻¹).
• ΔT – final temperature − initial temperature (K or °C).

To obtain the molar enthalpy change:

ΔH = q_rxn / n (kJ mol⁻¹)

4.2 Practical considerations

• Determine the calorimeter’s heat capacity (Ccal) by a calibration experiment. Then include it:

  q_total = C_calΔT + m c ΔT

• Use a well‑insulated cup to minimise heat loss; if loss is significant, apply a correction.
• Assume all reactants and products reach the same final temperature.

4.3 Constant‑volume (bomb) calorimeter (optional for A‑Level)

At constant volume the heat exchanged equals the change in internal energy (ΔU):

q_rxn = −C_calΔT = ΔU

For reactions involving gases, ΔH can be obtained from ΔU using:

ΔH = ΔU + Δn_gRT

where Δng is the change in the number of moles of gas.

5. Standard Enthalpies of Formation (ΔH°_f)

ΔH°_f is the enthalpy change for forming 1 mol of a compound from its elements in their standard states. By definition, ΔH°_f = 0 for any element in its standard state.

Compound	ΔH°f (kJ mol⁻¹)	Compound	ΔH°f (kJ mol⁻¹)
H₂O(l)	-285.8	CO₂(g)	-393.5
CH₄(g)	-74.8	NH₃(g)	-46.1
C₂H₆(g)	-84.0	SO₂(g)	-296.8
H₂(g)	0	O₂(g)	0

Using ΔH°_f values, the standard enthalpy change for any reaction is:

ΔH°_rxn = ∑ ΔH°_{f, products} − ∑ ΔH°_{f, reactants}

6. Worked Example – Enthalpy of Combustion of Propane

Reaction (standard conditions)

C₃H₈(g) + 5 O₂(g) → 3 CO₂(g) + 4 H₂O(l)

ΔH°_f values (kJ mol⁻¹)

• ΔH°_f(C₃H₈) = –104.7
• ΔH°_f(O₂) = 0
• ΔH°_f(CO₂) = –393.5
• ΔH°_f(H₂O(l)) = –285.8

Calculation

\[ \Delta H^\circ_{\text{comb}} = [3(-393.5) + 4(-285.8)] - [(-104.7) + 5(0)] \] \[ \Delta H^\circ_{\text{comb}} = (-1180.5 - 1143.2) - (-104.7) = -2323.7 + 104.7 = -2219.0\ \text{kJ mol}^{-1} \]

The combustion of one mole of propane releases 2219 kJ** under standard conditions.

7. Summary Checklist (What to Remember)

• ΔH is measured at constant pressure; ΔU at constant volume.
• Standard state: 298 K, 101 kPa (1 atm), 1 mol L⁻¹ (or 1 atm for gases).
• ΔH°_f values are the basis for calculating any ΔH°_r.
• ΔH°_c and ΔH°_neut are special cases of ΔH°_r.
• Bond‑energy method gives a quick estimate: ΔH ≈ ΣE_broken − ΣE_formed.
• Hess’s law lets you combine known enthalpy changes to find an unknown ΔH.
• In a coffee‑cup calorimeter: q = –m c ΔT; ΔH = q / n.
• For bomb calorimetry: q = –C_calΔT = ΔU; convert to ΔH with ΔH = ΔU + Δn_gRT if required.