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

5.6 Hess's Law

Definition and Principle

Hess's Law states that if a chemical reaction is carried out in a series of steps, the overall enthalpy change (ΔH) for the reaction is equal to the sum of the enthalpy changes for the individual steps. This law is a direct consequence of the fact that enthalpy is a state function, meaning its change depends only on the initial and final states, not on the path taken.

• State Function: Enthalpy depends only on the initial and final states of the reactants and products.

• Application: Allows calculation of enthalpy changes for reactions that are difficult to measure directly by using known enthalpy changes of related reactions.

Calculating ΔH Using Hess's Law

To calculate the enthalpy change for a reaction using Hess's Law, sum the enthalpy changes of the individual steps that lead to the overall reaction.

• Example Reaction: $\mathrm{C_3H_8 (g) + 5 O_2 (g) \rightarrow 3 CO_2 (g) + 4 H_2O (l)}$

• Break the overall reaction into steps with known enthalpy changes:

Step	Reaction	ΔH (kJ)
1	$\mathrm{C_3H_8 (g) \rightarrow 3 C (graphite) + 4 H_2 (g)}$	+103.85
2	$\mathrm{3 C (graphite) + 3 O_2 (g) \rightarrow 3 CO_2 (g)}$	-1181
3	$\mathrm{4 H_2 (g) + 2 O_2 (g) \rightarrow 4 H_2O (l)}$	-1143
Overall Reaction		-2220

• Sum of ΔH: $+103.85 + (-1181) + (-1143) = -2220$ kJ

5.7 Enthalpies of Formation

Definition and Importance

Enthalpy of formation (ΔH_f) is the enthalpy change for the reaction in which one mole of a compound is formed from its constituent elements in their standard states. It is a fundamental quantity for calculating reaction enthalpies.

• Standard State: The most stable physical form of an element at 25°C and 1 atm pressure.

• Units: kJ/mol

• Stoichiometry: The number of moles of each substance in the equation is crucial for accurate calculations.

Standard Enthalpies of Formation

• Elements in Standard State: The enthalpy of formation for elements in their standard state (e.g., Fe(s), O2(g)) is defined as 0 kJ/mol.

• Data Tables: Standard enthalpies of formation for compounds are listed in reference tables.

• Notation: $\Delta H_f^\circ$ indicates standard enthalpy of formation.

Substance	Formula	$\Delta H_f^\circ$ (kJ/mol)
Methane	CH4(g)	-74.80
Ethane	C2H6(g)	-84.68
Propane	C3H8(g)	-103.85
Oxygen	O2(g)	0
Carbon Monoxide	CO(g)	-110.5
Carbon Dioxide	CO2(g)	-393.5
Water	H2O(l)	-285.8
Water	H2O(g)	-241.8

Using Hess's Law with Enthalpies of Formation

Hess's Law can be used to calculate the enthalpy change of a reaction from the standard enthalpies of formation of reactants and products.

• Formula:

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

• n and m are the stoichiometric coefficients from the balanced chemical equation.

Example Calculation

Calculate the enthalpy for the complete combustion of propane:

• Reaction: $\mathrm{C_3H_8 (g) + 5 O_2 (g) \rightarrow 3 CO_2 (g) + 4 H_2O (l)}$

• Using the formula:

$\Delta H = [3 \times (-393.5) + 4 \times (-241.8)] - [1 \times (-103.85) + 5 \times 0]$

$\Delta H = [-1180.5 + (-967.2)] - [-103.85]$

$\Delta H = -2147.7 + 103.85 = -2043.9$ kJ

5.8 Bond Enthalpies

Bond Enthalpy and Reaction Energy

Bond enthalpy (or bond energy) is the energy required to break one mole of a particular type of bond in a gaseous molecule. Chemical reactions involve breaking bonds in reactants and forming new bonds in products.

• Energy Input: Breaking bonds requires energy (endothermic, $\Delta H > 0$).

• Energy Release: Forming bonds releases energy (exothermic, $\Delta H < 0$).

• Overall Reaction Enthalpy: $\Delta H_{\text{rxn}} = \Delta H_1 + \Delta H_2$ (sum of enthalpy changes for bond breaking and forming).

Enthalpy (H) and Entropy (S)

Whether a reaction proceeds depends on both enthalpy and entropy changes:

• Exothermic Reaction: Products are at a lower energy state than reactants; reaction is energetically favorable.

• Endothermic Reaction: Products are at a higher energy state; reaction may proceed if entropy increases sufficiently.

• Entropy (S): A measure of disorder or randomness. Reactions tend to proceed toward greater disorder.

Summary: A reaction proceeds if the change in enthalpy and/or entropy is favorable.

Additional info:

• Bond enthalpy values are typically averaged over many compounds and are most accurate for gases.

• The spontaneity of a reaction is determined by the Gibbs free energy ($\Delta G$), which combines enthalpy and entropy: $\Delta G = \Delta H - T\Delta S$.