Thermochemistry and Enthalpy: Study Notes for General Chemistry

Thermochemistry

Introduction to Thermochemistry

Thermochemistry is the study of heat released or absorbed during chemical reactions. It is a fundamental topic in general chemistry, focusing on energy changes associated with chemical processes.

• Heat is energy transferred due to temperature difference.

• Work is force applied over a distance.

• Example chemical reaction: $4Fe(s) + 3O_2(g) \rightarrow 2Fe_2O_3(s)$

Types of Energy

• Potential Energy (PE): Energy due to position or composition. Example: Chemical energy stored in bonds.

• Kinetic Energy (KE): Energy due to movement. Example: Thermal energy (motion of particles).

Internal Energy and Work

Internal energy ($E$) is the total energy contained within a system. Changes in internal energy are related to heat and work:

• $\Delta E = q + w$ where $q$ is heat and $w$ is work.

• Work done by the system: $w = -P_{ext} \Delta V$

• Energy flows from system to surroundings or vice versa.

State Functions

State functions depend only on the initial and final states, not the path taken. Examples include internal energy ($E$), enthalpy ($H$), and entropy ($S$).

• Pathway-independent: The change in a state function is the same regardless of the process.

• Energy is a state function: $\Delta E$ does not depend on the steps taken.

First Law of Thermodynamics

The first law states that energy cannot be created or destroyed, only transferred or transformed.

• $\Delta E_{universe} = 0$

• $\Delta E_{system} = -\Delta E_{surroundings}$

• Applies to both heat and work.

Enthalpy ($H$)

Definition and Calculation

Enthalpy is the heat content of a system at constant pressure. The change in enthalpy ($\Delta H$) for a reaction is:

• $\Delta H_{rxn} = H_{final} - H_{initial}$

• For reactions: $\Delta H_{rxn} = \sum H_{products} - \sum H_{reactants}$

Enthalpy of Reaction

Enthalpy changes can be calculated using standard enthalpies of formation:

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

• Example calculation for combustion of methane:

$\Delta H_{rxn} = [2 \times \Delta H_f^{\circ}(CO_2) + 2 \times \Delta H_f^{\circ}(H_2O)] - [\Delta H_f^{\circ}(CH_4) + 2 \times \Delta H_f^{\circ}(O_2)]$

Exothermic and Endothermic Reactions

• Exothermic: $\Delta H < 0$; energy is released, temperature of surroundings increases.

• Endothermic: $\Delta H > 0$; energy is absorbed, temperature of surroundings decreases.

Energy Diagrams

Energy diagrams illustrate the energy changes during a reaction:

• Reactants start at a certain energy level.

• Products end at a higher (endothermic) or lower (exothermic) energy level.

Specific Heat and Heat Capacity

Definitions

• Specific Heat ($C_s$): Amount of heat required to raise the temperature of 1 gram of a substance by 1°C.

• Heat Capacity: Amount of heat required to raise the temperature of an object by 1°C.

Calculating Heat Transfer

• $q = m C_s \Delta T$ where $m$ is mass, $C_s$ is specific heat, and $\Delta T$ is temperature change.

• Example: For Al, $C_s = 0.908 \frac{J}{g \cdot ^\circ C}$

• Problem: Calculate heat required to raise 35.0 g of Al from 55.0°C to 75.0°C:

$q = (35.0 \text{ g})(0.908 \frac{J}{g \cdot ^\circ C})(75.0^\circ C - 55.0^\circ C) = +636 \text{ J}$

Law of Summation (Hess's Law)

Hess's Law

The enthalpy change for a reaction is the same whether it occurs in one step or several steps. This allows calculation of $\Delta H$ for complex reactions by adding the $\Delta H$ values of individual steps.

• Example: $\Delta H_{rxn}$ for formation of $CO_2$ from graphite and $O_2$ can be calculated by summing enthalpy changes for intermediate steps.

Reversing and Manipulating Equations

• Reversing a reaction changes the sign of $\Delta H$.

• Multiplying a reaction by a coefficient multiplies $\Delta H$ by the same factor.

HTML Table: Summary of Key Equations and Concepts

Concept	Equation	Description
Internal Energy Change	$\Delta E = q + w$	Sum of heat and work
Work (at constant pressure)	$w = -P_{ext} \Delta V$	Work done by system
Enthalpy Change	$\Delta H_{rxn} = \sum H_{products} - \sum H_{reactants}$	Heat change at constant pressure
Specific Heat	$q = m C_s \Delta T$	Heat required for temperature change
Hess's Law	$\Delta H_{rxn} = \sum \Delta H_{steps}$	Sum of enthalpy changes for steps

Additional info:

• Calorie (cal) is a unit of energy; 1 cal = amount of thermal energy required to raise 1 g H2O by 1°C.

• State functions are independent of the path taken; only initial and final states matter.

• Energy conservation applies to all chemical and physical processes.