Thermochemistry

🟢 Lite — Quick Review (1h–1d)

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Thermochemistry — Key Facts for MDCAT

Key Definitions:

• System: The part of the universe being studied
• Surroundings: Everything else
• Internal Energy (U): Sum of kinetic and potential energies of all particles in the system
• Heat (q): Energy transferred due to temperature difference
• Work (w): Energy transferred when a force acts over a distance; for gases: $w = -P\Delta V$

First Law of Thermodynamics: $$\Delta U = q + w$$ Energy can neither be created nor destroyed. If a system absorbs heat (+q) or has work done on it (+w), its internal energy increases.

Enthalpy (H): $$H = U + PV$$ At constant pressure: $\Delta H = q_p$ (heat absorbed at constant pressure) For exothermic reactions: $\Delta H < 0$ (heat released to surroundings) For endothermic reactions: $\Delta H > 0$ (heat absorbed from surroundings)

** Hess’s Law of Constant Heat Summation:** The total enthalpy change of a reaction is independent of the route taken. This means you can add thermochemical equations to find $\Delta H$ for a target reaction.

Bond Enthalpy: Energy required to break one mole of a particular bond in gaseous molecules (in kJ/mol). Bond formation releases energy; bond breaking absorbs energy. $$\Delta H_{reaction} = \sum(\text{bonds broken}) - \sum(\text{bonds formed})$$

⚡ Exam tip: For calorimetry problems, $q = mc\Delta T$ where $m$ = mass, $c$ = specific heat capacity, $\Delta T$ = temperature change. If the calorimeter is constant pressure (open to atmosphere), $q_{reaction} = -\Delta H_{combustion}$. Always check the sign — if the temperature rises, the reaction is exothermic ($\Delta H < 0$).

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students who want genuine understanding.

Thermochemistry — Complete Study Guide

Types of Thermochemical Reactions:

• Exothermic: Heat flows out of the system (surroundings get hotter). Examples: combustion, neutralisation, most decomposition reactions.

  • $\Delta H < 0$, $\Delta U = \Delta H - P\Delta V$
  • For reactions with $\Delta n_g = 0$: $\Delta H \approx \Delta U$
  • For reactions with $\Delta n_g > 0$: $\Delta U > \Delta H$

• Endothermic: Heat flows into the system (surroundings get cooler). Examples: photosynthesis, thermal decomposition, dissolution of ammonium nitrate.

  • $\Delta H > 0$

Relationship Between $\Delta H$ and $\Delta U$: $$\Delta H = \Delta U + \Delta n_g RT$$ Where $\Delta n_g$ = moles of gaseous products − moles of gaseous reactants, $R = 8.314$ J/(mol·K), $T$ in Kelvin.

Example: $2H_2(g) + O_2(g) \rightarrow 2H_2O(l)$ $\Delta n_g = 0 - 3 = -3$, so $\Delta U = \Delta H + 3RT$

Thermochemical Equations: Always include the physical state and the $\Delta H$ value. $$N_2(g) + 3H_2(g) \rightarrow 2NH_3(g) \quad \Delta H = -92.4 \text{ kJ/mol}$$ The coefficient 2 (for NH$_3$) is stoichiometric — if we write 1 mol NH$_3$, $\Delta H = -46.2$ kJ/mol.

Standard Enthalpy of Formation ($\Delta H_f^\circ$): Enthalpy change when 1 mole of compound is formed from its constituent elements in their standard states (1 atm, 298 K). $\Delta H_f^\circ$ of an element in its standard state = 0.

Using enthalpies of formation: $$\Delta H_{reaction}^\circ = \sum \Delta H_f^\circ (\text{products}) - \sum \Delta H_f^\circ (\text{reactants})$$

Born-Haber Cycle (Lattice Energy): For ionic compounds like NaCl: $$\Delta H_f^\circ = \Delta H_{sub} + \frac{1}{2}\Delta H_{diss} + I_{Na} + E_{Cl} + U_{lattice}$$ Where: sublimation energy of Na + ½ bond dissociation of Cl$_2$ + ionisation energy of Na + electron affinity of Cl + lattice energy (exothermic, negative value).

⚡ Common mistakes: Forgetting to include the sign when using Hess’s law — if a step is reversed, $\Delta H$ changes sign. Confusing specific heat capacity (c, J/g·K) with heat capacity (C, J/K). In Born-Haber cycles, lattice energy is exothermic (negative) but is subtracted — students often get the sign wrong.

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Thermochemistry — Advanced Notes

Calorimetry: A bomb calorimeter (constant volume) measures the heat of combustion: $$q_{reaction} = -q_{calorimeter} = -C_{cal}\Delta T$$ Where $C_{cal}$ is the heat capacity of the calorimeter.

For coffee cup calorimeter (constant pressure): $$q_{reaction} = -\Delta H_{reaction} = -m \cdot c \cdot \Delta T$$

Kirchhoff’s Law (Temperature Dependence of $\Delta H$): $$\frac{d(\Delta H)}{dT} = \Delta C_p$$ Where $\Delta C_p = \sum C_p(\text{products}) - \sum C_p(\text{reactants})$ This allows calculation of $\Delta H$ at any temperature if heat capacities are known.

Enthalpy of Combustion ($\Delta H_c^\circ$): Energy released when 1 mole of a substance burns completely in oxygen. $$CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(l) \quad \Delta H_c^\circ = -890 \text{ kJ/mol}$$

Enthalpy of Neutralisation: For strong acid-strong base: $\Delta H \approx -57.3$ kJ/mol (per mole of water formed) For weak acids/bases: $\Delta H$ is less exothermic because some energy is used to dissociate the weak electrolyte.

Bond Dissociation Energy vs Bond Enthalpy: For a molecule like H$_2$O with two O–H bonds:

• Bond dissociation: H$_2O(g) \rightarrow H(g) + OH(g)$ — energy for first bond
• Average bond enthalpy: mean value from successive bond dissociations
• $\Delta H_{reaction} = \sum D(\text{bonds broken}) - \sum D(\text{bonds formed})$

Spontaneity and Gibbs Free Energy: $$\Delta G = \Delta H - T\Delta S$$

• $\Delta G < 0$: Spontaneous process
• $\Delta G > 0$: Non-spontaneous process
• $\Delta G = 0$: System at equilibrium

At equilibrium: $\Delta G = 0$, so $T_{eq} = \frac{\Delta H}{\Delta S}$

Entropy (S): A measure of disorder or randomness. Second law: $\Delta S_{universe} = \Delta S_{system} + \Delta S_{surroundings} > 0$ for spontaneous processes.

Factors increasing entropy:

• Gas > Liquid > Solid
• More moles of gas → higher entropy
• Temperature increase → higher entropy
• Dissolution of crystalline solids → usually increases entropy

Standard Gibbs Energy: $$\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$$ Also: $\Delta G^\circ = -RT\ln K_{eq}$ and $\Delta G^\circ = -nFE^\circ_{cell}$

MDCAT Question Patterns: MDCAT Pakistan thermochemistry questions frequently test: (1) calculating $\Delta H$ using Hess’s law, (2) calorimetry problems with $q = mc\Delta T$, (3) bond enthalpy calculations for $\Delta H_{reaction}$, (4) Born-Haber cycles for lattice energy, (5) entropy and Gibbs free energy for spontaneity. 2–3 questions per paper. High-scoring students focus on Hess’s law problems and calorimetry calculations.

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