Chapter 9: Thermochemistry

Chapter 9: Thermochemistry

Introduction

Thermochemistry is the study of energy changes that occur during chemical reactions and changes of state. It is a fundamental topic in general chemistry, focusing on the concepts of energy, heat, work, and the laws governing their transfer and transformation.

9.1 Fire and Ice

Spontaneous Processes and Energy Transfer

• Spontaneous processes occur without outside intervention, often involving energy transfer.

• Energy transfer is crucial for understanding chemical and physical changes, such as melting ice or burning fuel.

• Example: Ice melting absorbs energy from the surroundings, while burning fuel releases energy.

9.2 The Nature of Energy: Key Definitions

Energy and Its Forms

• Energy is the capacity to do work or produce heat.

• Kinetic energy is energy due to motion: $E_k = \frac{1}{2}mv^2$

• Potential energy is energy due to position or composition.

• Chemical energy is a form of potential energy stored in chemical bonds.

• Thermal energy relates to temperature and the random motion of particles.

• Units: The SI unit of energy is the joule (J); 1 calorie (cal) = 4.184 J.

Energy Conservation and Energy Transfer

Law of Conservation of Energy

• Energy cannot be created or destroyed, only transformed.

• Energy transfer occurs between the system (the part of the universe being studied) and the surroundings.

• System and surroundings: Energy lost by the system is gained by the surroundings, and vice versa.

9.3 The First Law of Thermodynamics: Nothing Is Free

First Law of Thermodynamics

• Statement: The total energy of the universe is constant.

• Mathematical form: $\Delta E_{universe} = 0$

• Internal energy (E): The sum of kinetic and potential energies of all particles in a system.

• Change in internal energy: $\Delta E = E_{final} - E_{initial}$

• Energy flow: $\Delta E_{system} = -\Delta E_{surroundings}$

• Example: Combustion of octane: $2C_8H_{18}(l) + 25O_2(g) \rightarrow 16CO_2(g) + 18H_2O(g)$

Summarizing Energy Flow

• If reactants have higher internal energy than products, $\Delta E$ is negative (energy released).

• If reactants have lower internal energy than products, $\Delta E$ is positive (energy absorbed).

Heat and Work

Definitions and Relationships

• Heat (q): Energy transfer due to temperature difference.

• Work (w): Energy transfer due to force acting over a distance.

• Relationship: $\Delta E = q + w$

• Example: Piston compressing gas (work), ice melting (heat).

9.4 Quantifying Heat and Work

Heat Capacity and Specific Heat

• Heat capacity (C): Amount of heat required to change temperature of a substance by 1°C.

• Specific heat capacity (c): Amount of heat required to change temperature of 1 g of substance by 1°C.

• Formula: $q = m \cdot c \cdot \Delta T$

• Example: Heating copper penny: $q = 3.10 \text{g} \times 0.385 \text{J/g}^\circ\text{C} \times 45.0^\circ\text{C}$

Temperature Changes and Heat Capacity

Calculating Heat Transfer

• When a system absorbs heat, its temperature changes by $\Delta T$.

• Heat capacity depends on mass and material.

• Formula: $q = C \cdot \Delta T$ (C = heat capacity)

• Specific heat: $q = m \cdot c \cdot \Delta T$

Thermal Energy Transfer

Mixing Substances of Different Temperatures

• Thermal energy flows from hot to cold until equilibrium is reached.

• Formula for heat transfer: $q_{lost} + q_{gained} = 0$

• Example: Mixing hot metal with water: $q_{metal} = -q_{water}$

Work: Pressure–Volume Work

Calculating Work Done by Expanding Gases

• Formula: $w = -P_{ext} \Delta V$

• Work is negative when the system does work on the surroundings.

• Units: 1 L·atm = 101.3 J

• Example: Balloon expansion: $w = -P_{ext} \Delta V$

9.5 Measuring ΔE for Chemical Reactions: Constant-Volume Calorimetry

Bomb Calorimeter

• Measures change in internal energy ($\Delta E$) at constant volume.

• Calorimeter equation: $q_{cal} = C_{cal} \cdot \Delta T$

• Heat absorbed by calorimeter equals heat released by reaction.

9.6 Enthalpy: The Heat Evolved in a Chemical Reaction at Constant Pressure

Definition and Calculation

• Enthalpy (H): $H = E + PV$

• Change in enthalpy: $\Delta H = \Delta E + P \Delta V$

• At constant pressure, $\Delta H$ equals heat exchanged ($q_p$).

Exothermic and Endothermic Processes

Definitions and Examples

• Exothermic reactions: Release heat to surroundings ($\Delta H < 0$).

• Endothermic reactions: Absorb heat from surroundings ($\Delta H > 0$).

• Example: Combustion (exothermic), melting ice (endothermic).

Stoichiometry Involving ΔH: Thermochemical Equations

Thermochemical Equations

• Show enthalpy change ($\Delta H$) for a reaction.

• Enthalpy change depends on the amount of substance.

• Example: $2H_2(g) + O_2(g) \rightarrow 2H_2O(l); \Delta H = -571.6 \text{kJ}$

9.7 Measuring ΔH for Chemical Reactions: Constant-Pressure Calorimetry

Coffee-Cup Calorimeter

• Measures enthalpy change ($\Delta H$) at constant pressure.

• Heat absorbed or lost by solution: $q_{solution} = m \cdot c \cdot \Delta T$

Summarizing Calorimetry

• Bomb calorimeter: Measures $\Delta E$ at constant volume.

• Coffee-cup calorimeter: Measures $\Delta H$ at constant pressure.

9.8 Relationships Involving ΔHrxn

Manipulating Thermochemical Equations

• Reverse reaction: Change sign of $\Delta H$.

• Multiply reaction: Multiply $\Delta H$ by factor.

• Add reactions: Add $\Delta H$ values.

• Example: Hess's Law: $\Delta H_{overall} = \sum \Delta H_{steps}$

9.9 Determining Enthalpies of Reaction from Bond Energies

Bond Energies and Enthalpy Change

• Bond energy: Energy required to break a bond in one mole of gaseous molecules.

• Calculating $\Delta H_{rxn}$: $\Delta H_{rxn} = \sum \text{Bond energies broken} - \sum \text{Bond energies formed}$

• Example: For $CH_4 + Cl_2 \rightarrow CH_3Cl + HCl$, sum bond energies for all bonds broken and formed.

9.10 Determining Enthalpies of Reaction from Standard Enthalpies of Formation

Standard Enthalpy of Formation ($\Delta H_f^\circ$)

• Enthalpy change when 1 mole of compound forms from its elements in standard states.

• Formula: $\Delta H_{rxn}^\circ = \sum \Delta H_f^\circ \text{(products)} - \sum \Delta H_f^\circ \text{(reactants)}$

• Units: kJ/mol

• Example: $MgCO_3(s) + 2HCl(aq) \rightarrow MgCl_2(aq) + CO_2(g) + H_2O(l)$

9.11 Lattice Energies for Ionic Compounds

Definition and Calculation

• Lattice energy: Energy required to separate one mole of an ionic solid into gaseous ions.

• Born–Haber cycle: Series of steps to calculate lattice energy.

• Trends: Lattice energy increases with higher ion charge and smaller ion size.

Trends in Lattice Energies

Ion Size and Charge

• Lattice energy decreases as ion size increases.

• Lattice energy increases as ion charge increases.

• Example: $KBr < KCl < NaCl < CaO$ (increasing lattice energy)

Key Terms and Concepts

• Thermochemistry: Study of energy changes in chemical reactions.

• Heat capacity (C): Amount of heat needed to change temperature by 1°C.

• Specific heat (c): Amount of heat needed to change temperature of 1 g by 1°C.

• Enthalpy ($\Delta H$): Heat evolved at constant pressure.

• Standard enthalpy of formation ($\Delta H_f^\circ$): Enthalpy change for formation from elements in standard states.

• Bond energy: Energy required to break a chemical bond.

• Lattice energy: Energy required to separate ionic solid into ions.

Equations and Relationships

• Change in Internal Energy: $\Delta E = E_{products} - E_{reactants}$

• Energy Flow: $\Delta E_{system} = -\Delta E_{surroundings}$

• Heat, Temperature, and Heat Capacity: $q = m \cdot c \cdot \Delta T$

• Work (Pressure–Volume): $w = -P_{ext} \Delta V$

• Enthalpy Change: $\Delta H = \Delta E + P \Delta V$

• Standard Enthalpy of Reaction: $\Delta H_{rxn}^\circ = \sum \Delta H_f^\circ \text{(products)} - \sum \Delta H_f^\circ \text{(reactants)}$

• Bond Energies: $\Delta H_{rxn} = \sum \text{Bond energies broken} - \sum \text{Bond energies formed}$

Summary Table: Types of Energy

Type of Energy	Description	Example
Kinetic Energy	Energy of motion	Moving car
Potential Energy	Energy due to position/composition	Stretched spring
Chemical Energy	Energy stored in chemical bonds	Glucose molecule
Thermal Energy	Energy due to temperature	Hot coffee

Summary Table: Calorimetry Methods

Calorimeter Type	Measured Quantity	Conditions
Bomb Calorimeter	ΔE (internal energy)	Constant volume
Coffee-Cup Calorimeter	ΔH (enthalpy)	Constant pressure

Summary Table: Lattice Energy Trends

Compound	Lattice Energy (kJ/mol)
KBr	-671
KCl	-701
NaCl	-786
CaO	-3414

Additional info: These notes expand on the original content by providing full definitions, formulas, and examples for each concept, ensuring a comprehensive and self-contained study guide for thermochemistry in general chemistry.