Lecture 19

Enthalpy and State Functions

Hess's Law

Hess's Law is a fundamental principle in thermochemistry that states the total enthalpy change for a chemical reaction is the same, regardless of the pathway taken from reactants to products. This allows chemists to calculate enthalpy changes for complex reactions by summing the enthalpy changes of individual steps.

• Key Point: The enthalpy change ($\Delta H$) for a reaction is independent of the number of steps or the specific pathway taken.

• Example: If a reaction occurs in one step or through multiple intermediate steps, the overall $\Delta H$ remains constant.

State Functions

A state function is a property of a system that depends only on its current state, not on the path taken to reach that state. Enthalpy ($H$), internal energy ($U$), and entropy ($S$) are examples of state functions.

• Key Point: State functions are determined by the initial and final states of a system.

• Example: The change in enthalpy ($\Delta H$) for a reaction depends only on the enthalpy of the reactants and products, not on how the reaction proceeds.

Bond Enthalpies and Bond Dissociation Energies

Bond Enthalpy

Bond enthalpy (or bond energy) is the energy required to break one mole of a specific type of bond in a gaseous molecule. It is an average value, as actual bond energies can vary depending on the molecular environment.

• Key Point: Bond enthalpy values are used to estimate the enthalpy change of reactions by considering the bonds broken and formed.

• Formula: The enthalpy change for a reaction can be estimated using bond enthalpies:

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

• Example: For the reaction $\text{NO}(g) + \text{O}(g) \rightarrow \text{NO}_2(g)$, you would use bond enthalpy values to calculate $\Delta H^\circ_{\text{rxn}}$.

Bond Dissociation Energy (BDE)

Bond Dissociation Energy (BDE) is the energy required to break a particular bond in a molecule in the gas phase, resulting in neutral fragments. BDEs are typically reported in kJ/mol.

• Key Point: BDEs are used to understand reaction energetics and stability of molecules.

• Example: The BDE for the H–H bond in $\text{H}_2$ is 436 kJ/mol.

Average Bond Energies Table

The following table summarizes average bond energies (kJ/mol) for common single, double, and triple bonds. These values are used to estimate reaction enthalpies.

Bond	Energy (kJ/mol)	Bond	Energy (kJ/mol)	Bond	Energy (kJ/mol)
H–H	436	O–H	463	C–H	414
C–C	348	C–O	358	C–N	305
O=O	498	C=O	799	C=N	615
N≡N	941	C≡C	839	C≡N	891
Cl–Cl	243	Br–Br	193	I–I	151
F–F	154	H–F	565	H–Cl	431
H–Br	366	H–I	299

Additional info: Table values inferred and summarized from provided images; actual tables may contain more entries.

Example Calculation Using Bond Energies

To estimate the enthalpy change for the reaction:

$\text{CH}_4(g) + 3\text{Cl}_2(g) \rightarrow \text{CHCl}_3(g) + 2\text{HCl}(g)$

• List all bonds broken and formed.

• Use the bond energies from the table above.

• Apply the formula:

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

Additional info: For a full calculation, identify the bonds in each reactant and product, sum their energies, and substitute into the formula.

Reversible Processes in Ideal Gases

Overview

Reversible processes in ideal gases involve changes that occur infinitely slowly, allowing the system to remain in equilibrium at all times. These processes are important in thermodynamics for calculating maximum work and understanding entropy changes.

• Key Point: Reversible processes are theoretical constructs used to define limits in thermodynamic calculations.

• Note: This topic is not covered in detail in this semester but is relevant for advanced or honors chemistry courses.

Additional info: For further study, review section 12.7 in your textbook for mathematical treatment of reversible expansion and compression of ideal gases.