Ch. 5 – Thermochemistry: Enthalpies of Formation

Introduction to Enthalpy Estimation

In thermochemistry, it is often necessary to estimate the enthalpy change of a reaction without direct experimentation. This can be achieved using tabulated thermodynamic data, specifically the standard enthalpies of formation. These values allow chemists to calculate the enthalpy changes for a wide variety of chemical reactions under standard conditions.

Thermodynamic Standard Conditions

Thermodynamic standard conditions are defined as:

• Pressure: 1 bar (approximately 1 atm)

• Temperature: 298 K (25°C), unless otherwise specified

All standard enthalpy values are referenced to these conditions, ensuring consistency and comparability across different reactions and substances.

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

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

• By definition, the standard enthalpy of formation for any element in its most stable form is zero (e.g., \( \Delta H_f^\circ (O_2(g)) = 0 \)).

• Tabulated values for \( \Delta H_f^\circ \) can be found in reference tables (e.g., Appendix C in textbooks).

Example: The formation of water from hydrogen and oxygen:

\[ H_2(g) + \frac{1}{2}O_2(g) \rightarrow H_2O(l) \qquad \Delta H_f^\circ = -285.8\ \text{kJ/mol} \]

Using Standard Enthalpies of Formation to Calculate Reaction Enthalpy

The standard enthalpy change of a reaction (\( \Delta H_{rxn}^\circ \)) can be calculated using the standard enthalpies of formation of the reactants and products:

\[ \Delta H_{rxn}^\circ = \sum n_p \Delta H_f^\circ (\text{products}) - \sum n_r \Delta H_f^\circ (\text{reactants}) \]

• \( n_p \) and \( n_r \) are the stoichiometric coefficients of the products and reactants, respectively.

• This equation is a direct application of Hess's Law, which states that the total enthalpy change for a reaction is independent of the pathway taken.

Hess's Law and Enthalpies of Formation

Hess's Law allows us to combine known enthalpy changes to determine unknown values. The equation for calculating reaction enthalpy from formation enthalpies is derived from this law, ensuring that the sum of enthalpy changes for a series of steps equals the overall enthalpy change for the reaction.

Tabulated Standard Enthalpies of Formation

Standard enthalpies of formation for common substances are provided in tables for reference. These values are essential for calculating reaction enthalpies and for understanding the relative stability of compounds.

Example Calculation

To calculate the standard enthalpy change for the combustion of methane:

\[ CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(l) \]

Using tabulated values:

• \( \Delta H_f^\circ (CH_4(g)) = -74.8\ \text{kJ/mol} \)

• \( \Delta H_f^\circ (CO_2(g)) = -393.5\ \text{kJ/mol} \)

• \( \Delta H_f^\circ (H_2O(l)) = -285.8\ \text{kJ/mol} \)

• \( \Delta H_f^\circ (O_2(g)) = 0 \) (element in standard state)

\[ \Delta H_{rxn}^\circ = [(-393.5) + 2(-285.8)] - [(-74.8) + 0] = -890.3\ \text{kJ/mol} \]

Thermodynamic Data Tables

Thermodynamic tables often include not only \( \Delta H_f^\circ \) but also standard Gibbs free energy (\( \Delta G_f^\circ \)) and standard entropy (\( S^\circ \)) values. These are useful for predicting reaction spontaneity and entropy changes.

Summary

• Standard enthalpies of formation are essential for calculating reaction enthalpies using Hess's Law.

• Thermodynamic tables provide the necessary data for a wide range of substances.

• Understanding and applying these concepts is fundamental for predicting the energy changes in chemical reactions.