Thermochemistry - Enthalpy, Hess's Law, and Standard Enthalpies of Reaction

Thermochemistry

Introduction

Thermochemistry is the study of the energy and heat associated with chemical reactions. A key concept in thermochemistry is enthalpy (H), which measures the heat content of a system at constant pressure. This chapter focuses on the relationships involving enthalpy changes in chemical reactions, methods for determining enthalpy changes, and the use of standard enthalpies of formation.

Relationships Involving ΔHrxn

Properties and Manipulation of Enthalpy Changes

The enthalpy change associated with a particular reaction, ΔHrxn, can be manipulated in predictable ways based on the chemical equation:

• Multiplying the Chemical Equation by a Factor: If the chemical equation is multiplied by a factor, ΔHrxn is also multiplied by the same factor.

• Reversing the Chemical Equation: If the chemical equation is reversed, the sign of ΔHrxn is also reversed.

• Adding Chemical Equations: If a chemical equation can be expressed as the sum of a series of steps, then ΔHrxn for the overall equation is the sum of the heats of reaction for each step.

Extensive Property

Enthalpy is an extensive property, meaning it depends on the quantity of reactants undergoing the reaction.

• Example:

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

  • $2\mathrm{C}(s) + 2\mathrm{O}_2(g) \rightarrow 2\mathrm{CO}_2(g)$    $\Delta H = 2(-393.5\ \mathrm{kJ}) = -787.0\ \mathrm{kJ}$

State Function

Enthalpy is a state function, meaning it depends only on the initial and final states of the system, not on the path taken.

• Reversing the reaction reverses the sign of ΔH:

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

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

Hess's Law

Hess's Law states that the change in enthalpy for a stepwise process is the sum of the enthalpy changes of the individual steps. This allows calculation of ΔH for complex reactions by combining known enthalpy changes.

• Mathematical expression:

  • If $A + 2B \rightarrow C$ has $\Delta H_1$ and $C \rightarrow D$ has $\Delta H_2$, then $A + 2B \rightarrow D$ has $\Delta H_3 = \Delta H_1 + \Delta H_2$.

• Example:

  • Given $2A + B \rightarrow C$ with $\Delta H_{rxn} = 122\ J$, what is ΔH for $2C \rightarrow 4A + 2B$? Since the reaction is reversed and multiplied by 2, $\Delta H = 2(-122\ J) = -244\ J$.

Determining Enthalpies of Reaction from Standard Enthalpies of Formation

Methods to Determine ΔHrxn

There are several ways to determine the enthalpy change for a reaction:

• Experimentally through calorimetry

• Indirectly through Hess's law

• Using standard enthalpies of formation

The change in enthalpy for a chemical reaction is the difference in enthalpy between the products and reactants, similar to measuring the altitude of a mountain relative to sea level.

Standard Conditions

The standard state is the state of a material at a defined set of conditions:

• Gas: exactly 1 atm pressure

• Solid or liquid: most stable form at exactly 1 atm pressure and temperature of interest (often 25 °C)

• Substance in solution: concentration 1 M

Standard enthalpy change ($\Delta H^\circ$): The enthalpy change when all reactants and products are in their standard states.

Standard enthalpy of formation ($\Delta H_f^\circ$): The enthalpy change for the reaction forming 1 mol of a compound from its elements in their standard states. For any element in its standard state, $\Delta H_f^\circ = 0$.

Using Standard Enthalpies of Formation to Calculate ΔHrxn

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

• Formula:

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

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

Example Calculation

Given the reaction:

• $\mathrm{NH}_3(g) + 5\mathrm{O}_2(g) \rightarrow 4\mathrm{NO}(g) + 6\mathrm{H}_2O(g)$

Suppose the standard enthalpies of formation are:

Substance	$\Delta H_f^\circ$ (kJ/mol)
$\mathrm{NH}_3(g)$	-45.9
$\mathrm{O}_2(g)$	0
$\mathrm{NO}(g)$	91.3
$\mathrm{H}_2O(g)$	-241.8

Calculation:

• $\Delta H_{rxn}^\circ = [4 \times 91.3 + 6 \times (-241.8)] - [1 \times (-45.9) + 5 \times 0]$

• Calculate each term and sum for the final answer.

Additional Example: Combustion of Methane

For the reaction:

• $\mathrm{CH}_4(g) + 2\mathrm{O}_2(g) \rightarrow \mathrm{CO}_2(g) + 2\mathrm{H}_2O(l)$

Suppose the standard enthalpies of formation are:

Substance	$\Delta H_f^\circ$ (kJ/mol)
$\mathrm{CH}_4(g)$	-74.87
$\mathrm{O}_2(g)$	0
$\mathrm{CO}_2(g)$	-393.5
$\mathrm{H}_2O(l)$	-285.8

Calculation:

• $\Delta H_{rxn}^\circ = [-393.5 + 2 \times (-285.8)] - [-74.87 + 2 \times 0]$

• Calculate each term and sum for the final answer.

Summary Table: Key Terms and Definitions

Term	Definition
Enthalpy (H)	Heat content of a system at constant pressure
ΔHrxn	Enthalpy change for a chemical reaction
State Function	Property depending only on initial and final states
Extensive Property	Property depending on the amount of substance
Standard State	Reference state for a substance at 1 atm, 25°C, or 1 M
ΔHf°	Standard enthalpy of formation
Hess's Law	ΔH for a reaction is the sum of ΔH for each step

Additional info: Some values and example calculations were inferred for completeness and clarity. The notes are structured to provide a comprehensive overview suitable for exam preparation in General Chemistry.