State that the transfer of thermal energy during a reaction is called the enthalpy change, $Delta H$, of the reaction. $Delta H$ is negative for exothermic reactions and positive for endothermic reactions

Chemical Energetics – Enthalpy Change (ΔH)

Learning Objective

State that the transfer of thermal energy during a chemical reaction is called the enthalpy change, ΔH, of the reaction. ΔH is negative for exothermic reactions and positive for endothermic reactions.

Key Definitions (Cambridge IGCSE Core)

• Thermal energy: Energy associated with the random motion of particles; perceived as heat.
• System & surroundings: The reacting chemicals constitute the system; everything else is the surroundings. ΔH describes the heat transferred between them.
• Enthalpy (H): Heat content of a substance at constant pressure (standard state: 25 °C, 1 atm).
• Enthalpy change (ΔH): Heat transferred between system and surroundings at constant pressure.
  ΔH = H_products − H_reactants
• Exothermic reaction: Releases heat to the surroundings; ΔH < 0.
• Endothermic reaction: Absorbs heat from the surroundings; ΔH > 0.
• Activation energy (E_a): Minimum energy that reacting particles must possess to form products.
• Bond‑breaking: Endothermic; energy is absorbed to separate atoms.
• Bond‑making: Exothermic; energy is released when atoms form a bond.
• Molar enthalpy of reaction (ΔH_rxn): Enthalpy change per mole of reaction as written (kJ mol⁻¹).
• Standard enthalpy of formation (ΔH_f°): Enthalpy change when 1 mol of a compound is formed from its elements in their standard states (25 °C, 1 atm).
• Hess’s Law: The total ΔH for a reaction is the sum of the ΔH values for any series of steps that lead from reactants to products.

Sign Convention for ΔH

ΔH is calculated from the enthalpies of products and reactants:

\[

\Delta H = H{\text{products}} - H{\text{reactants}}

\]

• If products have lower enthalpy → ΔH is negative → exothermic.
• If products have higher enthalpy → ΔH is positive → endothermic.

Energy‑Profile (Reaction‑Coordinate) Diagram

Bond‑Breaking and Bond‑Making

• Breaking a bond requires energy → positive contribution to ΔH.
• Forming a bond releases energy → negative contribution to ΔH.
• Overall ΔH (bond‑energy method):

  \[

  \Delta H = \sum \text{E(bonds broken)} - \sum \text{E(bonds formed)}

  \]

Worked Example 1 – Bond‑Energy Calculation (Combustion of Methane)

Reaction:

\[

\mathrm{CH4 + 2\,O2 \;\longrightarrow\; CO2 + 2\,H2O}

\]

Energy required to break bonds (reactants)

\[

\begin{aligned}

\text{Broken} &= 4(\text{C–H}) + 2(\text{O=O}) \\

&= 4(413) + 2(498) \\

&= 1652 + 996 \\

&= 2648\;\text{kJ mol}^{-1}

\end{aligned}

\]

Energy released on forming bonds (products)

\[

\begin{aligned}

\text{Formed} &= 2\bigl[2(\text{C=O})\bigr] + 4(\text{O–H}) \\

&= 2\bigl[2(799)\bigr] + 4(463) \\

&= 2(1598) + 1852 \\

&= 3196 + 1852 \\

&= 5048\;\text{kJ mol}^{-1}

\end{aligned}

\]

Overall ΔH (bond‑energy method)

\[

\Delta H = \text{Broken} - \text{Formed}

= 2648 - 5048

= -2400\;\text{kJ mol}^{-1}

\]

Bond‑energy tables give an approximate value; the accepted standard enthalpy of combustion of methane is –890 kJ mol⁻¹ (see Example 2). The discrepancy illustrates that bond‑energy calculations are approximate because they use average bond energies.

Worked Example 2 – Using Standard Enthalpies of Formation (ΔH_f°)

Calculate ΔH for the same combustion of methane using ΔH_f° values (Cambridge Handbook, 25 °C, 1 atm):

\[

\begin{aligned}

\Delta H_{\text{rxn}}^\circ

&= \bigl[\,\Delta Hf^\circ(\text{CO}2) + 2\Delta Hf^\circ(\text{H}2\text{O})\,\bigr] \\

&\qquad - \bigl[\,\Delta Hf^\circ(\text{CH}4) + 2\Delta Hf^\circ(\text{O}2)\,\bigr] \\

&= \bigl[-393.5 + 2(-285.8)\bigr] - \bigl[-74.8 + 2(0)\bigr] \\

&= \bigl[-393.5 - 571.6\bigr] - (-74.8) \\

&= -965.1 + 74.8 \\

&= -890.3\;\text{kJ mol}^{-1}

\end{aligned}

\]

The result (≈ −890 kJ mol⁻¹) matches the tabulated value and demonstrates the reliability of the ΔH_f° method.

Calorimetry – Relating Heat (q) to ΔH

At constant pressure, the heat exchanged with the surroundings equals the enthalpy change of the system:

\[

qp = \Delta H{\text{rxn}}

\]

For a simple coffee‑cup calorimeter (no calorimeter constant), heat is calculated by:

\[

q = m\,c\,\Delta T

\]

• m = mass of the solution (kg) – often taken as the mass of water because density ≈ 1 g mL⁻¹.
• c = specific heat capacity (≈ 4.18 kJ kg⁻¹ K⁻¹ for water).
• ΔT = final temperature – initial temperature (K or °C).

Sign convention

• Exothermic reaction: system loses heat → q (and ΔH) is negative.
• Endothermic reaction: system gains heat → q (and ΔH) is positive.

Calorimeter constant (C_cal) (optional for more accurate work):

\[

q{\text{total}} = (m\,c + C{\text{cal}})\,\Delta T

\]

where C_cal (kJ K⁻¹) is determined by a calibration experiment (e.g., mixing known masses of hot and cold water).

Typical Exothermic and Endothermic Reactions (Cambridge Core)

How to Determine the Sign of ΔH

1. Observe the temperature change of the surroundings

   • Temperature rises → exothermic (ΔH < 0).
   • Temperature falls → endothermic (ΔH > 0).

2. Carry out a calorimetry experiment

   1. Measure the mass of the solution (or reactants).
   2. Record the initial temperature, then the temperature after the reaction.
   3. Calculate q = (m c + C_cal) ΔT.

   • q negative → exothermic; q positive → endothermic.

3. Relate q to ΔH (at constant pressure, q = ΔH).

Common Misconceptions (Cambridge Core)

• “Heat is produced” vs “heat is transferred”: Reactions do not create heat; they transfer thermal energy between system and surroundings.
• All combustion reactions are exothermic: True, but the magnitude of ΔH varies with the fuel and the amount of oxygen.
• Endothermic reactions are “cold”: They absorb heat, making the surroundings feel cooler, but the reaction mixture itself is not inherently cold.
• ΔH is the same as temperature change: ΔH is a measure of heat transferred; temperature change also depends on mass, specific heat capacity, and calorimeter constant.

Suggested Classroom Activities (IGCSE Practical Skills)

1. Temperature‑change investigation

   • Dissolve NaOH (exothermic) and NH₄NO₃ (endothermic) in separate beakers of water. Record ΔT with a digital thermometer.
   • Calculate q and ΔH for each using q = m c ΔT.

2. Coffee‑cup calorimetry

   • Neutralise 50 mL of 1.0 M HCl with 50 mL of 1.0 M NaOH in a polystyrene cup.
   • Measure the temperature change, calculate q, and compare the experimental ΔH (≈ −57 kJ mol⁻¹) with the literature value.

3. Hess’s Law demonstration

   • Use tabulated ΔH_f° values to calculate ΔH for the combustion of methane (Example 2).
   • Then repeat the calculation using bond‑energy data (Example 1) and discuss the differences.

4. Real‑world applications

   • Hand warmers – exothermic crystallisation of supersaturated sodium acetate.
   • Instant cold packs – endothermic dissolution of ammonium nitrate.

Quick Reference – Energy‑Profile Diagram (Exothermic vs. Endothermic)

Summary Checklist (for Revision)

• ΔH = H_products − H_reactants (constant pressure).
• ΔH < 0 → exothermic; ΔH > 0 → endothermic.
• Activation energy (E_a) is the height of the energy barrier.
• Bond‑breaking = +, bond‑making = –; overall ΔH = Σ(broken) − Σ(formed).
• Use ΔH_f° values and Hess’s Law for accurate calculations.
• q = m c ΔT (add calorimeter constant if required); at constant pressure, q = ΔH.
• Observe temperature change of surroundings to decide sign of ΔH.