Thermochemistry: Enthalpy Relationships and Hess's Law (General Chemistry, Chapter 7)

Thermochemistry

Introduction to Thermochemistry

Thermochemistry is the study of the energy and heat associated with chemical reactions and physical transformations. The central concept is enthalpy (ΔH), which measures the heat change at constant pressure.

• Enthalpy (ΔH): The heat content of a system at constant pressure.

• State Function: Enthalpy is a state function, meaning its value depends only on the initial and final states, not the path taken.

Relationships Involving ΔH

1. Multiplying Chemical Equations

If a chemical equation is multiplied by a factor, the enthalpy change (ΔH) is also multiplied by the same factor.

• Example:

• A + 2B → C     ΔH₁

• 2A + 4B → 2C     ΔH₂ = 2 × ΔH₁

Application: Formation of 1 mole of CaO(s):

• $\frac{1}{2} \text{O}_2(g) + \text{Ca}(s) \rightarrow \text{CaO}(s)$      $\Delta H = -635.1\ \text{kJ}$

• For 2 moles: $\text{O}_2(g) + 2\text{Ca}(s) \rightarrow 2\text{CaO}(s)$      $\Delta H = 2 \times (-635.1\ \text{kJ}) = -1270.2\ \text{kJ}$

2. Reversing Chemical Equations

If a chemical equation is reversed, the sign of ΔH is also reversed.

• Recall: $\Delta H = H_{\text{final}} - H_{\text{initial}}$

• A + 2B → C     ΔH₁

• C → A + 2B     ΔH₂ = -ΔH₁

Example:

• $\text{C}(s) + \text{O}_2(g) \rightarrow \text{CO}_2(g)$      $\Delta H < 0$ (exothermic)

• Reverse: $\text{CO}_2(g) \rightarrow \text{C}(s) + \text{O}_2(g)$      $\Delta H > 0$ (endothermic)

3. Adding Chemical Equations (Hess's Law)

If a chemical equation can be expressed as the sum of a series of steps, the overall ΔH is the sum of the ΔH values for each step. This is known as Hess's Law.

• A + 2B → C     ΔH₁

• C → 2D     ΔH₂

• A + 2B → 2D     ΔH₃ = ΔH₁ + ΔH₂

Example Calculation:

• If $\Delta H_1 = 50\ \text{kJ}$ and $\Delta H_2 = -125\ \text{kJ}$, then $\Delta H_3 = 50\ \text{kJ} + (-125\ \text{kJ}) = -75\ \text{kJ}$

Applying Hess's Law: Sample Problem

Manipulating Equations to Find ΔHrxn

To find the enthalpy change for a target reaction, combine given reactions (and their ΔH values) so that their sum yields the desired equation. Reverse or multiply reactions as needed, adjusting ΔH accordingly.

• Target Reaction: $\text{C}(s) + \text{H}_2\text{O}(g) \rightarrow \text{CO}(g) + \text{H}_2(g)$

• Given:

• $\text{C}(s) + \text{O}_2(g) \rightarrow \text{CO}_2(g)$      $\Delta H = -393.5\ \text{kJ}$

• $2\text{CO}(g) + \text{O}_2(g) \rightarrow 2\text{CO}_2(g)$      $\Delta H = -566.0\ \text{kJ}$

• $2\text{H}_2(g) + \text{O}_2(g) \rightarrow 2\text{H}_2\text{O}(g)$      $\Delta H = -483.6\ \text{kJ}$

Reverse and scale reactions as needed:

• Reverse reaction 2 and 3, divide by 2:

• $\text{CO}_2(g) \rightarrow \text{CO}(g) + \frac{1}{2}\text{O}_2(g)$      $\Delta H = +283.0\ \text{kJ}$

• $\text{H}_2\text{O}(g) \rightarrow \text{H}_2(g) + \frac{1}{2}\text{O}_2(g)$      $\Delta H = +241.8\ \text{kJ}$

Sum:

• $\Delta H_{\text{rxn}} = -393.5\ \text{kJ} + 283.0\ \text{kJ} + 241.8\ \text{kJ} = 131.3\ \text{kJ}$

Summary Table: Relationships Involving ΔH

Operation	Effect on ΔH	Example
Multiply equation by n	Multiply ΔH by n	$A \rightarrow B,\ \Delta H$ $2A \rightarrow 2B,\ 2\Delta H$
Reverse equation	Change sign of ΔH	$A \rightarrow B,\ \Delta H$ $B \rightarrow A,\ -\Delta H$
Add equations	Add ΔH values	$A \rightarrow B,\ \Delta H_1$ $B \rightarrow C,\ \Delta H_2$ $A \rightarrow C,\ \Delta H_1 + \Delta H_2$

Key Terms and Concepts

• Enthalpy (ΔH): Heat change at constant pressure.

• Exothermic Reaction: Releases heat ($\Delta H < 0$).

• Endothermic Reaction: Absorbs heat ($\Delta H > 0$).

• Hess's Law: The enthalpy change for a reaction is the sum of the enthalpy changes for each step.

Example Applications

• Formation of CaO: $\frac{1}{2}\text{O}_2(g) + \text{Ca}(s) \rightarrow \text{CaO}(s)$, $\Delta H = -635.1\ \text{kJ}$

• Combining reactions to find ΔH: Use Hess's Law to manipulate and sum reactions to obtain the desired overall reaction and enthalpy change.

Summary

Understanding how enthalpy changes are affected by manipulating chemical equations is essential in thermochemistry. The three main relationships—scaling, reversing, and adding equations—allow chemists to calculate enthalpy changes for complex reactions using known values and Hess's Law.