Enthalpy, Internal Energy, and Calorimetry: Study Notes for General Chemistry

Enthalpy and Thermochemistry

Introduction to Enthalpy

Enthalpy (H) is a central concept in thermochemistry, describing the heat content of a system at constant pressure. Understanding enthalpy allows chemists to quantify energy changes during chemical reactions and physical processes.

Internal Energy and Thermodynamic Quantities

Systems and Surroundings

• System: The part of the universe under study (e.g., the contents of a beaker).

• Surroundings: Everything outside the system.

• Systems can be open (exchange matter and energy), closed (exchange energy, not matter), or isolated (no exchange).

Internal Energy (E)

• Internal energy is the total energy contained within a system, including kinetic and potential energies of particles.

• Changes in internal energy ($\Delta E$) occur when energy is transferred as heat or work.

Thermodynamic Quantities: Number, Unit, and Sign

• Every thermodynamic value must include:

  1. A number (magnitude)

  2. A unit (e.g., Joules, J)

  3. A sign (+ or –) indicating direction of energy flow

• Positive $\Delta E$: System gains energy from surroundings.

• Negative $\Delta E$: System loses energy to surroundings.

Energy in Bonds: Attraction Between Ions

• Electrostatic attraction between oppositely charged ions forms ionic bonds.

• Energy is released when bonds form ($E_{bond} < 0$); energy is consumed when bonds break ($E_{bond} > 0$).

• This energy change is a component of the system's internal energy.

Heat (q) and Work (w)

• Heat (q): Random molecular motion; energy transfer due to temperature difference.

• Work (w): Organized molecular motion; energy transfer due to force acting over a distance (e.g., gas expansion).

• Relationship: $\Delta E = q + w$

Signs of q, w, and $\Delta E$

Quantity	Positive (+)	Negative (–)
q (heat)	System gains heat	System loses heat
w (work)	Work done on system	Work done by system
$\Delta E$	Net gain of energy by system	Net loss of energy by system

Endothermic and Exothermic Processes

• Endothermic: System absorbs heat from surroundings ($q > 0$); temperature of surroundings drops.

• Exothermic: System releases heat to surroundings ($q < 0$); temperature of surroundings rises.

State Functions and Energy Diagrams

State Functions

• A state function depends only on the current state of the system, not the path taken to reach it.

• Internal energy ($E$) and enthalpy ($H$) are state functions; heat ($q$) and work ($w$) are not.

Energy Diagrams / Reaction Coordinate Diagrams

• Plot energy (y-axis) vs. reaction progress (x-axis).

• Show energy difference between reactants and products ($\Delta E$ or $\Delta H$).

• Products lower than reactants: exothermic; higher: endothermic.

Manipulating Internal Energy and Enthalpy

Mathematical Relationships

• At constant pressure, work done by expansion/compression of a gas: $w = -P\Delta V$

• Thus, $\Delta E = q + w = q - P\Delta V$

• At constant volume ($\Delta V = 0$): $\Delta E = q_v$

• At constant pressure: $q_p = \Delta E + P\Delta V$

Defining Enthalpy (H)

• Enthalpy is defined as $H = E + PV$

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

• At constant pressure, $\Delta H = q_p$ (heat at constant pressure)

Enthalpy Change and Heat

• Positive $\Delta H$ (endothermic): heat absorbed by system.

• Negative $\Delta H$ (exothermic): heat released by system.

Pressure-Volume (PV) Work

• PV work is mechanical work associated with volume changes in gases.

• Equation: $w = -P\Delta V$

• Expansion ($\Delta V > 0$): work done by system (w negative).

• Compression ($\Delta V < 0$): work done on system (w positive).

Enthalpies of Reaction

Definition

• Change in enthalpy for a reaction: $\Delta H_{rxn} = H_{products} - H_{reactants}$

• Direction matters: reversing a reaction changes the sign of $\Delta H$.

Heat of Reaction

• $\Delta H_{rxn}$ is also called the Enthalpy of Reaction or Heat of Reaction.

Key Points about Enthalpy

• Enthalpy is an extensive property (depends on amount of substance).

• Enthalpy change for a reaction depends on the physical states of reactants and products.

• Enthalpy change for a reaction is equal in magnitude and opposite in sign for the reverse reaction.

Measuring Enthalpy with Calorimetry

Calorimetry

• Calorimetry is the measurement of heat flow using a calorimeter.

• Basic parts: thermometer, insulation, accessories for PV work, stirring mechanism.

Heat Capacity, Specific Heat, and Molar Heat Capacity

• Heat Capacity (C): Energy required to raise temperature of a substance by 1 K (or 1°C).

• Specific Heat (c): Energy required to raise temperature of 1 gram by 1 K (or 1°C).

• Molar Heat Capacity: Energy required to raise temperature of 1 mole by 1 K (or 1°C).

Substance	Formula	Specific Heat (J/g·K)
Water (liquid)	H2O (l)	4.18
Aluminum	Al (s)	0.90
Iron	Fe (s)	0.45
Copper	Cu (s)	0.39
Gold	Au (s)	0.13
Glass	SiO2 (s)	0.84
Ice	H2O (s)	2.09

Constant-Pressure Calorimetry

• Often called "coffee cup" calorimetry.

• Used for reactions in solution at constant pressure.

• Equation: $q_{soln} = C_s m_{soln} \Delta T = q_p$

• At constant pressure, $q_p = \Delta H_{rxn}$

Constant-Volume Calorimetry

• Often called "bomb" calorimetry.

• Used for reactions in a sealed vessel at constant volume.

• Equation: $q_{rxn} = -C_{cal} \Delta T$

• Measures change in internal energy ($\Delta E$), not enthalpy ($\Delta H$).

• For most reactions, $\Delta E$ and $\Delta H$ are very similar.

Hess's Law and Enthalpy Calculations

Hess's Law

• States that the enthalpy change for a reaction is the same, no matter how many steps the reaction is carried out in.

• Allows calculation of $\Delta H$ for reactions using known enthalpy values for related reactions.

• Mathematically: $\Delta H_{rxn} = \sum n \Delta H_f^\circ (\text{products}) - \sum n \Delta H_f^\circ (\text{reactants})$

Enthalpy of Formation ($\Delta H_f$)

• Enthalpy change for the formation of 1 mole of a compound from its elements in their standard states.

• Standard enthalpy of formation: $\Delta H_f^\circ$ (measured at 25°C and 1 atm).

• For an element in its standard state, $\Delta H_f^\circ = 0$.

Examples of Standard Enthalpies of Formation

Substance	Formula	$\Delta H_f^\circ$ (kJ/mol)
Water (liquid)	H2O (l)	-285.8
Carbon dioxide	CO2 (g)	-393.5
Ammonia	NH3 (g)	-46.19
Methane	CH4 (g)	-74.80
Glucose	C6H12O6 (s)	-1273

Applying Hess's Law: Example

• For the reaction: $C_3H_8(g) + 5 O_2(g) \rightarrow 3 CO_2(g) + 4 H_2O(l)$

• Break down into formation reactions:

  • Decompose propane to elements

  • Form CO2 and H2O from elements

• Combine enthalpies: $\Delta H_{rxn}^\circ = 4\Delta H_f^\circ (H_2O) + 3\Delta H_f^\circ (CO_2) - \Delta H_f^\circ (C_3H_8)$

Summary Table: Key Equations

Concept	Equation (LaTeX)
First Law of Thermodynamics	$\Delta E = q + w$
Work (PV work)	$w = -P\Delta V$
Enthalpy	$H = E + PV$
Change in Enthalpy	$\Delta H = \Delta E + P\Delta V$
Heat at Constant Pressure	$q_p = \Delta H$
Heat at Constant Volume	$q_v = \Delta E$
Hess's Law	$\Delta H_{rxn} = \sum n \Delta H_f^\circ (\text{products}) - \sum n \Delta H_f^\circ (\text{reactants})$

Additional info: These notes are based on lecture slides and cover the core concepts of thermochemistry, including enthalpy, internal energy, calorimetry, and Hess's Law, as relevant to a General Chemistry course.