Thermochemistry: Hess's Law, Enthalpies of Formation, and Bond Enthalpies

Chapter 5: Thermochemistry

Overview

Thermochemistry is the study of the energy and heat associated with chemical reactions and physical transformations. This section focuses on the calculation of enthalpy changes using Hess's Law, standard enthalpies of formation, and bond enthalpies.

Hess's Law

Definition and Principle

Hess's Law states that if a chemical reaction can be expressed as the sum of two or more reactions, the enthalpy change for the overall reaction is the sum of the enthalpy changes for the individual steps. This is possible because enthalpy (H) is a state function, meaning its value depends only on the initial and final states, not on the path taken.

• Key Point 1: The enthalpy change, $\Delta H$, for a reaction is the same whether the reaction occurs in one step or multiple steps.

• Key Point 2: Hess's Law allows us to calculate $\Delta H$ for reactions that are difficult to measure directly by using known enthalpy changes of related reactions.

• Equation: $\Delta H_{\text{overall}} = \sum \Delta H_{\text{steps}}$

• Example: The combustion of methane can be broken into steps, and the sum of the enthalpy changes for each step equals the enthalpy change for the overall reaction.

Enthalpies of Formation

Definition

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

• Key Point 1: The standard enthalpy of formation, $\Delta H_f^\circ$, is measured under standard conditions (298 K and 1.00 atm pressure).

• Key Point 2: By convention, the standard enthalpy of formation of any element in its most stable form is zero.

• Example: The formation of water from hydrogen and oxygen: $\ce{H2(g) + 1/2 O2(g) -> H2O(l)}$; $\Delta H_f^\circ = -285.8\ \text{kJ/mol}$.

Standard Enthalpies of Formation Table

The following table summarizes standard enthalpies of formation for selected substances at 298 K:

Substance	Formula	$\Delta H_f^\circ$ (kJ/mol)
Carbon dioxide	CO2(g)	-393.5
Water (liquid)	H2O(l)	-285.8
Methane	CH4(g)	-74.8
Propane	C3H8(g)	-103.85
Oxygen	O2(g)	0
Hydrogen	H2(g)	0
Additional info: Table values are selected for illustration; consult a full table for more substances.

Calculation of $\Delta H$ Using Enthalpies of Formation

General Method

The enthalpy change for a reaction can be calculated using the standard enthalpies of formation of the reactants and products:

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

• Where $n_p$ and $n_r$ are the stoichiometric coefficients of products and reactants, respectively.

• Example: For the combustion of propane:

  • $\ce{C3H8(g) + 5 O2(g) -> 3 CO2(g) + 4 H2O(l)}$

  • $\Delta H = [3 \times (-393.5) + 4 \times (-285.8)] - [1 \times (-103.85) + 5 \times 0]$

  • $\Delta H = (-1180.5 + -1143.2) - (-103.85)$

  • $\Delta H = -2323.7 + 103.85 = -2219.9\ \text{kJ}$

Bond Enthalpies

Definition and Application

Bond enthalpy (or bond dissociation energy) is the enthalpy change required to break one mole of a specific type of bond in a gaseous molecule. Bond enthalpies are always positive because energy is required to break bonds, and energy is released when bonds form.

• Key Point 1: The greater the bond enthalpy, the stronger the bond.

• Key Point 2: Average bond enthalpies can be used to estimate the enthalpy change of reactions involving gases.

• Formula: $\Delta H_{\text{reaction}} \approx \sum \text{Bond enthalpies of bonds broken} - \sum \text{Bond enthalpies of bonds formed}$

• Example: To estimate the enthalpy change for the reaction $\ce{H_2(g) + Cl_2(g) -> 2 HCl(g)}$, use the bond enthalpies for H–H, Cl–Cl, and H–Cl.

Average Bond Enthalpies Table

The following table provides average bond enthalpies for selected bonds (values in kJ/mol):

Bond	Bond Enthalpy (kJ/mol)
H–H	436
Cl–Cl	243
H–Cl	431
C–H	413
C–C	348
C=O	799
O–H	463
Additional info: Values are averages and may vary depending on molecular environment.

Summary

• Hess's Law enables calculation of enthalpy changes for complex reactions using known enthalpy changes of simpler reactions.

• Standard enthalpies of formation provide a reference for calculating reaction enthalpies under standard conditions.

• Bond enthalpies allow estimation of reaction enthalpies, especially for reactions involving gases.