Thermochemistry: Internal Energy, Enthalpy, and Calorimetry

Thermochemistry

Introduction

Thermochemistry is the study of energy changes, particularly heat, that occur during chemical reactions and changes of state. It is a fundamental topic in general chemistry, providing insight into how energy is transferred and conserved in chemical processes.

First Law of Thermodynamics

Conservation of Energy

• The total energy of the universe is constant.

• Energy can be transformed from one form to another but cannot be created or destroyed.

Types of Energy

• Kinetic Energy – Energy of motion; includes thermal energy related to temperature.

• Potential Energy – Energy due to position or composition; includes chemical energy stored in bonds and interactions of charged particles.

Internal Energy (E)

Definition and Properties

• Internal energy is the sum of the kinetic and potential energies of all particles in a system.

• It is a state function: depends only on the current state, not the path taken to reach it.

• Change in internal energy ($\Delta E$) is the difference between the final and initial states:

$\Delta E = E_{\text{final}} - E_{\text{initial}}$ $\Delta E = E_{\text{products}} - E_{\text{reactants}}$

• If $E_{\text{reactants}} > E_{\text{products}}$, $\Delta E$ is negative: energy flows out of the system (exothermic).

• If $E_{\text{reactants}} < E_{\text{products}}$, $\Delta E$ is positive: energy flows into the system (endothermic).

• Energy conservation: $\Delta E_{\text{sys}} = -\Delta E_{\text{surr}}$

Heat and Work

Exchange of Energy

• Internal energy can be changed by heat ($q$) or work ($w$).

• Change in internal energy: $\Delta E = q + w$

Heat ($q$)

• Flow of energy due to a temperature difference.

• Positive when the system absorbs heat.

Work ($w$)

• Result of a force acting through a distance.

• Positive when the surroundings do work on the system.

Units: All forms of energy (heat, work, internal energy) are measured in Joules (J).

Example Calculation

• What is the change in internal energy of a system that absorbs 22 J of heat and does 58 J of work?

$\Delta E = q + w = 22\,\text{J} + 58\,\text{J} = 80\,\text{J}$

Heat Capacity

Definitions

• Heat capacity (C): The amount of heat required to raise the temperature of a system by 1 K (or 1 °C).

• Specific heat capacity ($C_s$): Heat required to raise 1 g of a substance by 1 °C.

• Molar heat capacity ($C_p$): Heat required to raise 1 mol of a substance by 1 °C.

Formulas: $\Delta T = \frac{q}{C}$ $q = C \times \Delta T$ $q = m \times C_s \times \Delta T$ $q = n \times C_p \times \Delta T$

Example Calculations

• How much heat is required to increase the temperature of 21.5 g of aluminum from 5.00 °C to 38.2 °C? ($C_s = 0.897\,\text{J/g} \cdot \text{°C}$)

• What is the final temperature of water when 275 g of water at 21.5 °C is heated with 15.8 kJ? ($C_s = 4.184\,\text{J/g} \cdot \text{°C}$)

For the second example: $q = m C_s \Delta T$ $15,800\,\text{J} = (275\,\text{g})(4.184\,\text{J/g} \cdot \text{°C})(T_f - 21.5\,°C)$ $T_f = \frac{15,800}{(275)(4.184)} + 21.5 = 35.2\,°C$

Work

Pressure-Volume Work

• Work is a force acting through a distance: $w = F \times D$

• Pressure-volume work: $w = -P \Delta V$

• If the system expands ($\Delta V > 0$), the system does work on the surroundings ($w < 0$).

Enthalpy (H)

Definition and Properties

• Enthalpy (H) is a state function defined as $H = E + PV$

• Change in enthalpy: $\Delta H = \Delta E + P \Delta V + V \Delta P$

• At constant pressure: $\Delta H = q_p$

• At constant volume: $\Delta H = q_v + V \Delta P$

Exothermic vs. Endothermic

• Exothermic: Releases heat, $\Delta H$ is negative.

• Endothermic: Absorbs heat, $\Delta H$ is positive.

Reaction Enthalpy ($\Delta H_{rxn}$)

Definition

• Enthalpy of reaction or heat of reaction.

• Extensive property: depends on the amount of material undergoing reaction.

• Usually specified with a balanced chemical equation; magnitude relates to stoichiometric amounts.

Endothermic or Exothermic?

Reaction	$\Delta H_{rxn}$ (kJ)	Type
2 Al(s) + 3 Cl2(g) → 2 AlCl3(s)	-1408.4	Exothermic
2 NaOH(aq) + H2(g) → 2 Na(s) + 2 H2O(l)	+368.4	Endothermic
CaO(s) + 3 Cl2(g) → CaCl2(s) + CO(g)	+464.6	Endothermic
Fe2O3(s) + 3 CO(g) → 2 Fe(s) + 3 CO2(g)	-24.8	Exothermic

Stoichiometry and Enthalpy

• Heat released or absorbed is proportional to the amount of reactant.

• Example: For 5.00 mol Al reacting with excess Cl2:

$5.00\,\text{mol Al} \times \frac{-1408.4\,\text{kJ}}{2\,\text{mol Al}} = -3520\,\text{kJ}$

Calorimetry

Introduction

Calorimetry is the experimental technique used to measure the heat evolved or absorbed during a chemical reaction. It relies on observing temperature changes in the surroundings.

Types of Calorimetry

Type	System	Surroundings	Measured Quantity
Constant Volume (Bomb Calorimeter)	Sample + O2	Water, apparatus	$\Delta E_{rxn}$
Constant Pressure (Coffee-Cup Calorimeter)	Reactants in solution	Solution, apparatus	$\Delta H_{rxn}$

Key Equations

• Bomb calorimeter: $q_{cal} = C_{cal} \Delta T$; $q_{rxn} = -q_{cal}$

• Coffee-cup calorimeter: $q_{soln} = m_{soln} C_{s,soln} \Delta T$; $q_{rxn} = -q_{soln}$

• At constant volume: $\Delta E = q_v$

• At constant pressure: $\Delta H = q_p$

Example Calculations

• Bomb Calorimeter: 1.010 g sucrose combusted, $C_{cal} = 4.90\,\text{kJ}/°C$, $\Delta T = 3.41°C$ $-C_{cal} \Delta T = \Delta E_{rxn}$ $-4.90 \times (28.33 - 24.92) = -16.71\,\text{kJ}$ $\Delta E_{rxn}$ per mol: $\frac{-16.71\,\text{kJ}}{1.010\,\text{g}} \times 342.34\,\text{g/mol} = -5660\,\text{kJ/mol}$

• Coffee-Cup Calorimeter: 0.158 g Mg reacts, $m_{soln} = 100.0\,\text{g}$, $C_{s,soln} = 4.18\,\text{J/g} \cdot °C$, $\Delta T = 7.2°C$ $q_{soln} = m_{soln} C_{s,soln} \Delta T$ $q_{soln} = 100.0 \times 4.18 \times (32.8 - 25.6) = 3010\,\text{J}$ $\Delta H_{rxn} = \frac{-3010\,\text{J}}{0.158\,\text{g}} \times 24.31\,\text{g/mol} = -460\,\text{kJ/mol}$

Summary Table: Key Equations

Equation	Description
$\Delta E = q + w$	Change in internal energy
$q = C \Delta T$	Heat transfer (general)
$q = m C_s \Delta T$	Heat transfer (specific heat)
$q = n C_p \Delta T$	Heat transfer (molar heat)
$w = -P \Delta V$	Pressure-volume work
$\Delta H = q_p$	Enthalpy change at constant pressure
$\Delta E = q_v$	Internal energy change at constant volume

Additional Info

• All calculations assume ideal conditions and complete reactions.

• Units must be consistent (Joules for energy, grams or moles for mass).

• Calorimetry is a practical method for determining enthalpy changes in the laboratory.