Chapter 7: Thermochemistry – Energy Changes in Chemical Reactions

Thermochemistry

Introduction to Thermochemistry

Thermochemistry is a branch of chemical thermodynamics that focuses on the study of energy changes, particularly heat, during chemical processes. Understanding how energy is transferred and transformed in chemical reactions is essential for predicting reaction behavior and designing experiments.

• Chemical Thermodynamics deals with heat and power in chemical systems.

• Energy is defined as the capacity to do work or transfer heat.

• Energy is an abstract concept but is fundamental to all chemical changes.

Types of Energy

Kinetic and Potential Energy

Energy in chemical systems can exist in various forms, each with distinct characteristics and roles in reactions.

• Kinetic Energy (KE): The energy of motion. For a moving object, kinetic energy is given by:

$KE = \frac{1}{2}mv^2$

• Where m is mass (g) and v is velocity (m/s).

• Potential Energy (PE): Stored energy due to position or composition. Types include:

  • Gravitational

  • Electrical

  • Chemical

• Thermal Energy: Energy associated with temperature (heat).

• Radiant Energy: Electromagnetic energy, such as light.

• SI Unit for Energy: The Joule (J), where $1\,\text{J} = 1\,\text{kg}\,\text{m}^2/\text{s}^2$.

Energy Transformations in Biological Systems

Energy transformations are common in biological and chemical systems. For example, during exercise:

• Stored chemical energy in carbohydrates or fats is released by breaking chemical bonds.

• This energy is converted into kinetic energy and heat.

• Heat is dissipated by sweating, which cools the body through evaporation.

The First Law of Thermodynamics

Conservation of Energy

The first law of thermodynamics states that energy can be transformed from one form to another, but it cannot be created or destroyed. The total energy of the universe remains constant.

• Energy lost by a system is gained by its surroundings.

• Mathematically: $\Delta E_{\text{system}} = -\Delta E_{\text{surroundings}}$

Internal Energy

Definition and Calculation

The internal energy (E) of a system is the sum of all kinetic and potential energies of its components. In chemical reactions, the change in internal energy is important.

• Initial internal energy ($E_{\text{init}}$): Total energy of reactants.

• Final internal energy ($E_{\text{final}}$): Total energy of products.

• Change in internal energy:

$\Delta E = E_{\text{final}} - E_{\text{init}} = q + w$

• Where q is heat and w is work.

System and Surroundings

Definitions

In thermochemistry, it is crucial to distinguish between the system and its surroundings:

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

• Surroundings: Everything else (e.g., beaker, bench, air).

Energy Transfer

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

Signs for q and w of the System

The sign conventions for heat (q), work (w), and change in internal energy ($\Delta E$) are important:

Quantity	Positive (+)	Negative (-)
q (heat)	System gains heat	System loses heat
w (work)	Work done on system	Work done by system
$\Delta E$	Net gain of energy by system	Net loss of energy by system

Enthalpy

Definition and Measurement

Enthalpy (H) is the internal energy of a system at constant pressure. It is a useful quantity for reactions occurring at atmospheric pressure.

• Symbol: H

• Cannot measure H directly; only changes ($\Delta H$) can be measured.

• $\Delta H = H_{\text{final}} - H_{\text{init}}$

• $\Delta H$ indicates whether a reaction is endothermic or exothermic.

Endothermic and Exothermic Reactions

Definitions and Examples

Reactions can absorb or release energy:

• Endothermic Reaction: Absorbs energy from surroundings ($\Delta H > 0$). Surroundings become colder.

• Exothermic Reaction: Releases energy to surroundings ($\Delta H < 0$). Surroundings become warmer.

Example: Cold packs (endothermic) absorb heat; hot packs (exothermic) release heat.

Enthalpies of Reaction

Calculating Enthalpy Changes

The enthalpy change for a reaction is calculated as:

$\Delta H_{\text{rxn}} = H_{\text{products}} - H_{\text{reactants}}$

• Enthalpy change is an extensive property (depends on amount).

• Reverse reaction has equal magnitude but opposite sign.

• Depends on the physical state of reactants and products.

Heat Capacity and Specific Heat

Definitions

Heat capacity and specific heat are measures of how substances respond to energy input.

• Heat Capacity: The temperature change experienced by an object when it absorbs a certain amount of energy.

• Specific Heat (Capacity): The energy absorbed per gram of substance that causes a 1°C (or 1 K) temperature rise.

$\text{Specific Heat} = \frac{\text{quantity of heat transferred (J)}}{\text{grams of substance (g)} \times \text{temperature change (K)}}$

Calorimetry

Constant Pressure Calorimetry

Used to measure heat changes in reactions at constant pressure, typically in aqueous solution.

• Energy gained by water equals energy lost by reaction.

• Equation:

$q_{\text{soln}} = s \times m \times \Delta T$

• Where s is specific heat, m is mass, and $\Delta T$ is temperature change.

• $q_{\text{rxn}} + q_{\text{soln}} = 0$

Constant Volume Calorimetry (Bomb Calorimetry)

Used for combustion reactions at constant volume.

• Measures energy released by reaction via temperature change in surrounding water.

• Equation:

$q_{\text{rxn}} + q_{\text{bomb}} + q_{\text{water}} = 0$

$q_{\text{rxn}} = - (q_{\text{bomb}} + q_{\text{water}})$

$q_{\text{rxn}} = - (C_{\text{bomb}} \Delta T_{\text{bomb}} + C_{\text{water}} \Delta T_{\text{water}})$

• Calibration is required to determine the heat capacity of the bomb calorimeter.

Enthalpies of Formation

Standard Enthalpy of Formation

The standard enthalpy of formation ($\Delta H_f^\circ$) is the enthalpy change when one mole of a compound is formed from its elements in their standard states.

• $\Delta H_f^\circ$ of an element in its standard state is defined as zero.

• Allows prediction of enthalpy changes in reactions.

• Basis for Hess's Law.

Example: $2C(s) + H_2(g) \rightarrow C_2H_2(g)$    $\Delta H_f^\circ(C_2H_2) = 226.8\,\text{kJ}$

Standard Enthalpies of Formation Table

Substance	Formula	$\Delta H_f^\circ$ (kJ/mol)
Acetylene	C2H2(g)	226.8
Ammonia	NH3(g)	-45.9
Carbon dioxide	CO2(g)	-393.5
Water (liquid)	H2O(l)	-285.8
Water (gas)	H2O(g)	-241.8
Hydrogen	H2(g)	0
Oxygen	O2(g)	0
Methane	CH4(g)	-74.8
Sodium chloride	NaCl(s)	-411.2
Additional info: Table includes more compounds and their standard enthalpies of formation.

Note: The physical state (phase) of a compound affects its enthalpy of formation. For example, for water:

$\Delta H_f^\circ(\text{H}_2\text{O}(g)) - \Delta H_f^\circ(\text{H}_2\text{O}(l)) = -241.8 - (-285.8) = 44.0\,\text{kJ/mol} = \Delta H_{\text{vap}}$

Hess's Law

Calculating Enthalpy Changes for Multi-Step Reactions

Hess's Law states that if a reaction is carried out in a series of steps, the overall enthalpy change is the sum of the enthalpy changes for each step.

$\Delta H_{\text{rxn}}^\circ = \sum n \Delta H_f^\circ(\text{products}) - \sum m \Delta H_f^\circ(\text{reactants})$

• Where n and m are stoichiometric coefficients.

• Allows calculation of enthalpy changes for reactions not easily measured directly.

Example: The enthalpy change for the formation of CO2 and H2O from graphite and oxygen can be calculated by summing the enthalpy changes of intermediate steps.