Enthalpies Of Different Types Of Reactions

Enthalpies For Different Types Of Reactions

This section covers various specific enthalpy changes associated with different types of chemical processes, building upon the fundamental concept of reaction enthalpy.

Standard Enthalpy Of Combustion ($\Delta H^\circ_c$)

Definition: The standard enthalpy of combustion is the enthalpy change when one mole of a substance undergoes complete combustion in excess oxygen, with both reactants and products in their standard states.

Process: Combustion typically involves reacting with oxygen ($O_2$) to produce oxides of the elements present in the substance. For organic compounds containing C, H, and O, the products are usually carbon dioxide ($CO_2$) and water ($H_2O$). If nitrogen is present, $N_2(g)$ is often formed. If sulfur is present, $SO_2(g)$ or $SO_3(g)$ can be formed.

Measurement: Usually measured using bomb calorimetry (constant volume), and then converted to constant pressure using $\Delta H = \Delta U + (\Delta n_g)RT$ if necessary.

Example: The standard enthalpy of combustion of ethanol ($C_2H_5OH$):

$$C_2H_5OH(l) + 3O_2(g) \rightarrow 2CO_2(g) + 3H_2O(l)$$ $$\Delta H^\circ_c = -1367 \text{ kJ/mol}$$

Applications: Crucial for calculating the energy content of fuels.

Enthalpy Of Atomization ($\Delta H_{atom}$)

Definition: The standard enthalpy of atomization is the enthalpy change required to convert one mole of a substance into its gaseous atoms.

For Elements:

For a solid element: $M(s) \rightarrow M(g)$
For a gaseous element that exists as diatomic molecules (like $O_2, N_2, H_2$): $\frac{1}{2}X_2(g) \rightarrow X(g)$ (Note the factor of 1/2 for diatomic elements)

Example:

For Sodium: $Na(s) \rightarrow Na(g)$ $\Delta H_{atom} = +108.4 \text{ kJ/mol}$
For Chlorine: $\frac{1}{2}Cl_2(g) \rightarrow Cl(g)$ $\Delta H_{atom} = +243.1 \text{ kJ/mol}$

Significance: Enthalpy of atomization is a measure of the strength of bonding in the element's elemental form. It is a key component in Born-Haber cycles for calculating lattice enthalpies.

Bond Enthalpy (or Bond Dissociation Enthalpy, BDE)

Definition: Bond enthalpy is the average enthalpy change required to break one mole of a specific type of bond in the gaseous state, to form gaseous atoms or radicals. It is always an endothermic process ($\Delta H > 0$).

Average vs. Specific: For polyatomic molecules, bond enthalpies are often given as averages because the enthalpy required to break a particular type of bond can vary slightly depending on the molecular environment.

Example:

$H-H$ bond in $H_2$: $\Delta H = +436 \text{ kJ/mol}$
$C-H$ bond in $CH_4$: $\Delta H = +413 \text{ kJ/mol}$ (average)
$O=O$ bond in $O_2$: $\Delta H = +498 \text{ kJ/mol}$
$C=O$ bond in $CO_2$: $\Delta H = +805 \text{ kJ/mol}$ (average for the two bonds)

Calculating Enthalpy of Reaction from Bond Enthalpies: The enthalpy change of a reaction can be estimated by summing the bond enthalpies of bonds broken (reactants) and subtracting the sum of bond enthalpies of bonds formed (products).

$$\Delta H_{rxn} \approx \sum (\text{Bond enthalpies of bonds broken}) - \sum (\text{Bond enthalpies of bonds formed})$$

Note: This method provides an approximation because it uses average bond enthalpies and assumes reactants and products are in the gaseous state, ignoring changes in phase and crystal lattice energy.

Example: Estimate the enthalpy of combustion of methane ($CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g)$) using average bond enthalpies. (Assume $O=O$ is $498$ kJ/mol, $C-H$ is $413$ kJ/mol, $C=O$ is $805$ kJ/mol, $O-H$ is $463$ kJ/mol).

Example 1. Estimate the enthalpy of combustion of methane ($CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g)$) using average bond enthalpies.

Answer:

Bonds broken (Reactants):

4 $C-H$ bonds in $CH_4$: 4 $\times$ 413 kJ/mol = 1652 kJ/mol
2 $O=O$ bonds in $2O_2$: 2 $\times$ 498 kJ/mol = 996 kJ/mol
Total energy input (bonds broken) = 1652 + 996 = 2648 kJ/mol

Bonds formed (Products):

2 $C=O$ bonds in $CO_2$: 2 $\times$ 805 kJ/mol = 1610 kJ/mol
4 $O-H$ bonds in $2H_2O$: 4 $\times$ 463 kJ/mol = 1852 kJ/mol
Total energy released (bonds formed) = 1610 + 1852 = 3462 kJ/mol

Calculate $\Delta H_{rxn}$

$\Delta H_{rxn} \approx (\text{Energy input}) - (\text{Energy released})$

$\Delta H_{rxn} \approx 2648 \text{ kJ/mol} - 3462 \text{ kJ/mol} = -814 \text{ kJ/mol}$

The estimated enthalpy of combustion is -814 kJ/mol.

Lattice Enthalpy ($\Delta H_{lattice}$)

Definition: As discussed previously, lattice enthalpy is the enthalpy change associated with the formation or breaking of the crystal lattice of an ionic compound from its constituent gaseous ions. It is a measure of the strength of ionic bonding.

Two Definitions:

Energy required to break 1 mole of ionic solid into gaseous ions (endothermic, $\Delta H_{lattice} > 0$).
Energy released when 1 mole of gaseous ions form an ionic solid (exothermic, $\Delta H_{lattice} < 0$). The latter is commonly used in Born-Haber cycles.

Factors: Ionic charge and ionic size.

Measurement: Determined indirectly using the Born-Haber cycle, which involves measurable enthalpy changes like enthalpy of formation, atomization, ionization energy, and electron affinity.

Significance: High lattice enthalpy contributes to high melting points and low solubility of ionic compounds.

Enthalpy Of Solution ($\Delta H_{sol}$)

Definition: The enthalpy of solution is the enthalpy change when one mole of solute dissolves in a specific amount of solvent to form a solution, typically at constant pressure. The process can be described as:

$$Solute(s/l/g) + Solvent \rightarrow Solution$$

Components of Enthalpy of Solution: Dissolution involves breaking solute-solute interactions (lattice energy for ionic solids, intermolecular forces for molecular solids) and solvent-solvent interactions, and forming solute-solvent interactions.

$$ \Delta H_{sol} = \Delta H_{lattice} + \Delta H_{hydration} $$

Where:

$\Delta H_{lattice}$ is the energy required to break the ionic lattice (endothermic, positive if defined as breaking).
$\Delta H_{hydration}$ is the enthalpy change when gaseous ions are hydrated by solvent molecules (exothermic, negative).

Types of Enthalpy of Solution:

Endothermic: If the energy required to break the lattice is greater than the energy released during hydration ($\Delta H_{sol} > 0$). Example: Potassium nitrate ($KNO_3$).
Exothermic: If the energy released during hydration is greater than the energy required to break the lattice ($\Delta H_{sol} < 0$). Example: Sodium hydroxide ($NaOH$).
Near Zero: If the energy changes roughly cancel out.

Measurement: Measured using calorimetry, usually constant pressure calorimetry.

Enthalpy Of Dilution

Definition: The enthalpy of dilution is the enthalpy change that occurs when a solution is diluted by adding more solvent, typically at constant pressure.

Process: When a concentrated solution is diluted, the solute-solvent interactions and solvent-solvent interactions change. The enthalpy of dilution reflects these changes.

Types:

Exothermic Dilution: Occurs when the process of increasing the separation between solute particles and increasing solvent-solvent interactions releases more energy than is absorbed for breaking solute-solvent interactions. Example: Concentrated sulfuric acid ($H_2SO_4$) in water.
Endothermic Dilution: Occurs when breaking solute-solvent interactions requires more energy than is released by other changes. Example: Ammonium nitrate ($NH_4NO_3$) in water (used in cold packs).

Measurement: Measured using calorimetry.