Thermochemistry: Chemical Energetics and Calorimetry

Chapter 3: Chemical Energetics (Thermochemistry)

3.1 Concept of Enthalpy

Thermochemistry is the study of heat changes that accompany chemical reactions and physical changes. Understanding enthalpy and related concepts is essential for analyzing energy flow in chemical systems.

• Heat: Energy transferred between two bodies of different temperatures.

• System: The specific part of the universe under study (e.g., the reaction vessel).

• Surroundings: Everything outside the system.

• Energy: The ability to do work. SI unit: Joule (J); 1 calorie (cal) = 4.184 J.

• Types of Systems:

  • Open system: Exchanges mass and energy with surroundings.

  • Closed system: Exchanges energy but not mass.

  • Isolated system: Exchanges neither mass nor energy.

Types of Chemical Reactions

• Exothermic reactions: Release energy to surroundings; enthalpy of products < enthalpy of reactants; $\Delta H$ is negative. Example: Combustion, neutralization.

• Endothermic reactions: Absorb energy from surroundings; enthalpy of products > enthalpy of reactants; $\Delta H$ is positive. Example: Melting of ice, melting of salts.

Energy Profile Diagrams

• Exothermic: Products are at a lower energy level than reactants; $\Delta H$ is negative.

• Endothermic: Products are at a higher energy level than reactants; $\Delta H$ is positive.

Enthalpy ($\Delta H$)

• The heat content or total energy of a system at constant pressure.

• Only changes in enthalpy ($\Delta H$) can be measured, not absolute values.

Standard Enthalpy of Reaction ($\Delta H^\circ$)

• The enthalpy change for a reaction at standard conditions (298 K, 1 atm).

Thermochemical Equations

• Show both the chemical change and the associated enthalpy change.

• Example: $\mathrm{H_2O(s) \rightarrow H_2O(l)} \quad \Delta H = +6.01\ \mathrm{kJ}$

Types of Enthalpy Changes

• Enthalpy of formation ($\Delta H_f^\circ$): Heat change when 1 mole of a compound forms from its elements in their standard states. $\mathrm{H_2(g) + \frac{1}{2}O_2(g) \rightarrow H_2O(l)} \quad \Delta H_f^\circ = -286\ \mathrm{kJ\ mol^{-1}}$ Note: $\Delta H_f^\circ$ for elements in their standard state is zero.

• Enthalpy of combustion ($\Delta H_c^\circ$): Heat released when 1 mole of a substance is burned in excess oxygen. $\mathrm{C(s) + O_2(g) \rightarrow CO_2(g)} \quad \Delta H_c^\circ = -393\ \mathrm{kJ\ mol^{-1}}$

• Enthalpy of atomization ($\Delta H_a^\circ$): Heat required to form 1 mole of gaseous atoms from the element in its standard state. $\mathrm{Na(s) \rightarrow Na(g)} \quad \Delta H_a^\circ = +109\ \mathrm{kJ\ mol^{-1}}$

• Enthalpy of neutralization ($\Delta H_n^\circ$): Heat change when 1 mole of water forms from acid-base neutralization. $\mathrm{HCl(aq) + NaOH(aq) \rightarrow NaCl(aq) + H_2O(aq)} \quad \Delta H_n^\circ = -58\ \mathrm{kJ\ mol^{-1}}$

• Enthalpy of hydration ($\Delta H_{hyd}^\circ$): Heat change when 1 mole of gaseous ions is hydrated in water. $\mathrm{Na^+(g) \rightarrow Na^+(aq)} \quad \Delta H_{hyd}^\circ = -406\ \mathrm{kJ\ mol^{-1}}$

• Enthalpy of dissolution ($\Delta H_{diss}^\circ$): Heat change when 1 mole of a substance dissolves in water. $\mathrm{KCl(s) \rightarrow K^+(aq) + Cl^-(aq)} \quad \Delta H_{diss}^\circ = +690\ \mathrm{kJ\ mol^{-1}}$

• Enthalpy of sublimation ($\Delta H_{sub}^\circ$): Heat change when 1 mole of a substance sublimes (solid to gas). $\mathrm{I_2(s) \rightarrow I_2(g)} \quad \Delta H_{sub}^\circ = +106\ \mathrm{kJ\ mol^{-1}}$

General Formula for Enthalpy Change of Reaction

• $\Delta H^\circ = \sum \Delta H_f^\circ \text{(products)} - \sum \Delta H_f^\circ \text{(reactants)}$

3.2 Calorimetry

Calorimetry is the experimental technique used to measure heat changes in chemical reactions. It involves the use of calorimeters to determine the amount of heat absorbed or released.

Key Terms

• Specific heat capacity (c): Amount of heat required to raise the temperature of 1 gram of a substance by 1°C or 1 K (units: J g-1 °C-1 or J g-1 K-1).

• Heat capacity (C): Amount of heat required to raise the temperature of a given quantity of substance by 1°C (units: J °C-1).

Types of Calorimeters

• Simple calorimeter (constant-pressure): Used for reactions in solution; typically uses a Styrofoam cup to minimize heat loss.

• Bomb calorimeter (constant-volume): Used for combustion reactions; consists of a sealed container (the bomb) surrounded by water.

Calorimetry Principle and Formula

• Heat released by the system = Heat absorbed by the surroundings (calorimeter and water).

• General equation: $q = mc\Delta T$ where:

  • $q$ = heat (J)

  • $m$ = mass (g)

  • $c$ = specific heat capacity (J g-1 °C-1)

  • $\Delta T$ = temperature change ($T_{final} - T_{initial}$)

• For calorimeter with known heat capacity: $q = C\Delta T$

Example Calculations

• Combustion of Ethanol in Bomb Calorimeter: 3.36 g ethanol burned; calorimeter heat capacity = 2.3 kJ °C-1; $\Delta T = 43.4$°C. $q = C\Delta T = 2.3 \times 43.4 = 99.82$ kJ Moles ethanol = $3.36/46.068 = 0.0729$ mol Energy per mole = $-99.82/0.0729 = -1370$ kJ/mol

• Heat Exchange Between Copper and Water: 0.45 g Cu at 87.0°C placed in water at 23.0°C; final temp 24.8°C. For Cu: $q = 0.45 \times 0.385 \times (24.8 - 87.0) = -10.776$ J For water: $q = m \times 4.184 \times (24.8 - 23.0)$; solve for $m$.

• Finding Specific Heat of Titanium: 20.8 g Ti heated to 99.5°C, placed in 75.0 g water at 21.7°C; final temp 24.3°C. For water: $q = 75.0 \times 4.184 \times (24.3 - 21.7) = 815.88$ J For Ti: $-815.88 = 20.8 \times c \times (24.3 - 99.5)$; solve for $c$.

3.3 Hess's Law

Hess's Law states that the total enthalpy change for a reaction is the same, no matter how many steps the reaction is carried out in. This allows calculation of enthalpy changes for reactions that are difficult to measure directly.

• Mathematical Statement: $\Delta H_{overall} = \Delta H_1 + \Delta H_2 + \ldots$

• When reversing a reaction, change the sign of $\Delta H$.

• When multiplying a reaction, multiply $\Delta H$ by the same factor.

• Arrange equations so that reactants and products match the target equation.

Example: Combustion of Propane

• Given reactions and their $\Delta H$ values, rearrange and sum to match the target reaction.

• Sum the $\Delta H$ values to find the enthalpy change for the overall reaction.

3.4 Born-Haber Cycle

The Born-Haber cycle is a thermochemical cycle used to analyze the formation of ionic compounds, especially to calculate lattice enthalpy, which cannot be measured directly.

• Lattice enthalpy (U): The enthalpy change when 1 mole of solid ionic compound forms from its gaseous ions.

• The cycle combines several steps: atomization, ionization, electron affinity, and formation of the ionic solid.

• General Born-Haber Cycle Equation: $\Delta H_f = \Delta H_{sub} + \sum IE + \sum EA + \Delta H_{atom} + U$

Example: Formation of NaCl

Step	Process	Enthalpy Change
1	Na(s) → Na(g)	Atomization of Na
2	Na(g) → Na+(g) + e-	Ionization energy
3	1/2 Cl2(g) → Cl(g)	Atomization of Cl
4	Cl(g) + e- → Cl-(g)	Electron affinity
5	Na+(g) + Cl-(g) → NaCl(s)	Lattice enthalpy (U)

Application: By knowing all steps except lattice enthalpy, it can be calculated by difference.

Summary Table: Types of Enthalpy Changes

Type	Definition	Example Equation
Formation ($\Delta H_f^\circ$)	1 mol compound from elements	$\mathrm{H_2(g) + \frac{1}{2}O_2(g) \rightarrow H_2O(l)}$
Combustion ($\Delta H_c^\circ$)	1 mol substance burned in O2	$\mathrm{C(s) + O_2(g) \rightarrow CO_2(g)}$
Atomization ($\Delta H_a^\circ$)	1 mol gaseous atoms from element	$\mathrm{Na(s) \rightarrow Na(g)}$
Neutralization ($\Delta H_n^\circ$)	1 mol water from acid/base	$\mathrm{HCl(aq) + NaOH(aq) \rightarrow NaCl(aq) + H_2O(aq)}$
Hydration ($\Delta H_{hyd}^\circ$)	1 mol gaseous ions hydrated	$\mathrm{Na^+(g) \rightarrow Na^+(aq)}$
Dissolution ($\Delta H_{diss}^\circ$)	1 mol substance dissolves	$\mathrm{KCl(s) \rightarrow K^+(aq) + Cl^-(aq)}$
Sublimation ($\Delta H_{sub}^\circ$)	1 mol solid to gas	$\mathrm{I_2(s) \rightarrow I_2(g)}$