Chapter 6.4: Thermochemistry – Enthalpy, Calorimetry, and Stoichiometry

Thermochemistry Overview

Introduction to Thermochemistry

Thermochemistry is the study of energy changes, particularly heat, that occur during chemical reactions. The central concept is enthalpy (ΔH), which quantifies the heat exchanged under constant pressure conditions.

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

• Internal Energy (ΔU): The total energy contained within a system, including kinetic and potential energies.

Extensive vs. Intensive Properties

Definitions and Examples

Properties of thermodynamic systems are classified as either extensive or intensive:

• Extensive Properties: Depend on the size or amount of the system (e.g., mass, volume, ΔH, ΔU).

• Intensive Properties: Independent of the system size (e.g., temperature, pressure, molar enthalpy).

For example, ΔH and ΔU are extensive because they scale with the amount of substance present.

Equations Relating ΔH and ΔU

• For reactions involving gases: $\Delta H = \Delta U + \Delta nRT$ where $\Delta n$ is the change in moles of gas, $R$ is the gas constant, and $T$ is temperature.

Additional info: Δn is the stoichiometric equivalent, representing the change in the number of moles of gaseous products minus reactants.

Measuring Enthalpy Change (ΔH)

Calorimetry

Calorimetry is the experimental technique used to measure heat changes in chemical reactions. Two common types are bomb calorimeters (constant volume) and coffee-cup calorimeters (constant pressure).

• Coffee-cup calorimeter: Used for reactions in solution at constant pressure.

• Bomb calorimeter: Used for combustion reactions at constant volume.

Key Equations

• Heat absorbed or released by solution: $q_r = -q_{cal}$ $q_r = -m_{H_2O} \times C_{H_2O} \times \Delta T_{H_2O}$ where $m_{H_2O}$ is the mass of water, $C_{H_2O}$ is the specific heat capacity, and $\Delta T_{H_2O}$ is the temperature change.

• Enthalpy per mole: $\Delta_r H_{\text{(per mole)}} = \frac{\Delta H_{\text{(per amount)}}}{n}$

Measuring Heat of Reaction

Bomb vs. Coffee-Cup Calorimeter

Comparing measurements from bomb and coffee-cup calorimeters:

• Bomb calorimeter: Measures $q_v = \Delta U$ (internal energy change).

• Coffee-cup calorimeter: Measures $q_p = \Delta H$ (enthalpy change).

• Relationship: $\Delta U = \Delta H - \Delta nRT$

If $\Delta n > 0$, then $-\Delta nRT < 0$, so $\Delta U < \Delta H$.

Constant Pressure Calorimetry

Limiting Reagent and Enthalpy Calculation

In solution reactions, the limiting reagent determines the amount of heat evolved or absorbed.

• Example reaction: $\text{HCl(aq)} + \text{NH}_4\text{OH(aq)} \rightarrow \text{NH}_4\text{Cl(aq)} + \text{H}_2\text{O(l)}$

• Calculate moles of each reactant to identify the limiting reagent.

• Calculate $q_{cal}$: $q_{cal} = -m_{H_2O} \times C_{H_2O} \times \Delta T_{H_2O}$

• Calculate $\Delta H$ per mole of limiting reagent: $\Delta H = \frac{q_{cal}}{n_{\text{limiting}}}$

Example Calculation

• Given: $m_{H_2O} = 250.0$ g, $C_{H_2O} = 4.184$ J·g⁻¹·°C⁻¹, $\Delta T_{H_2O} = 2.15$°C, $n_{HCl} = 0.0400$ mol

• Calculate $q_{cal}$: $q_{cal} = -250.0 \times 4.184 \times 2.15 = -2587.5$ J

• Calculate $\Delta H$: $\Delta H = \frac{-2587.5}{0.0400} = -64688$ J·mol⁻¹ = $-64.7$ kJ·mol⁻¹

Types of Enthalpy

Standard Enthalpy Changes

Different types of enthalpy changes are defined for specific processes:

• Enthalpy of Combustion ($\Delta_{comb}H$): Heat released when one mole of a substance burns in oxygen. Example: $C_4H_{10}(l) + \frac{13}{2} O_2(g) \rightarrow 4 CO_2(g) + 5 H_2O(g)$

• Enthalpy of Formation ($\Delta_f H$): Heat change when one mole of a compound forms from its elements. Example: $K(s) + \frac{1}{2} Br_2(l) \rightarrow KBr(s)$

• Enthalpy of Fusion ($\Delta_{fus}H$): Heat absorbed when one mole of a solid melts. Example: $NaCl(s) \rightarrow NaCl(l)$

• Enthalpy of Vaporization ($\Delta_{vap}H$): Heat absorbed when one mole of a liquid vaporizes. Example: $C_6H_6(l) \rightarrow C_6H_6(g)$

Enthalpy of a Reaction

Bond Energies and Heat of Reaction

The enthalpy change of a reaction can be estimated using average bond energies:

• Example: $H_2(g) + F_2(g) \rightarrow 2HF(g)$, $\Delta H = -546$ kJ·mol⁻¹

• Heat stored in reactants: $2F(g)$, $\Delta H = 159$ kJ·mol⁻¹

• Heat stored in products: $2HF(g)$, $\Delta H = -1130$ kJ·mol⁻¹

• Overall enthalpy change: $\Delta H = \text{(sum of products)} - \text{(sum of reactants)}$

Additional info: The change in enthalpy is sometimes called the heat of reaction.

Stoichiometry and Thermochemistry

Thermochemical Equations

A thermochemical equation is a balanced chemical equation that includes the enthalpy change for the reaction.

• Example: $2H_2(g) + O_2(g) \rightarrow 2H_2O(l)$, $\Delta_r H = -572$ kJ·mol⁻¹ (exothermic)

• If the equation is reversed, the sign of $\Delta H$ changes (endothermic).

• $\Delta H$ is proportional to the amount of substance reacting.

• Example: $H_2(g) + \frac{1}{2} O_2(g) \rightarrow H_2O(l)$, $\Delta_r H = -286$ kJ·mol⁻¹

Stoichiometry and ΔH Calculations

Application to Phase Changes

Enthalpy changes can be calculated for phase changes using stoichiometry.

• Example: The molar enthalpy of vaporization of ethanol is $38.56$ kJ·mol⁻¹. For condensation of 2 moles: $\Delta H = 2 \times (-38.56)$ kJ·mol⁻¹ = $-77.12$ kJ

Summary Table: Types of Enthalpy Changes

Process	Equation Example	Symbol
Combustion	$C_4H_{10}(l) + \frac{13}{2} O_2(g) \rightarrow 4 CO_2(g) + 5 H_2O(g)$	$\Delta_{comb}H$
Formation	$K(s) + \frac{1}{2} Br_2(l) \rightarrow KBr(s)$	$\Delta_f H$
Fusion	$NaCl(s) \rightarrow NaCl(l)$	$\Delta_{fus}H$
Vaporization	$C_6H_6(l) \rightarrow C_6H_6(g)$	$\Delta_{vap}H$

Key Concepts

• Enthalpy changes are central to understanding energy flow in chemical reactions.

• Calorimetry allows experimental determination of ΔH.

• Thermochemical equations must be balanced and specify states of matter.

• Stoichiometry is essential for relating enthalpy changes to amounts of reactants and products.