Chapter 5: Thermochemistry – Study Notes

Thermochemistry

Introduction to Energy and Thermochemistry

Thermochemistry is the branch of chemistry that studies the energy changes, particularly heat, that accompany chemical reactions and physical changes. It is a subset of thermodynamics, which is the broader study of energy and its transformations.

• Energy is the capacity to do work or transfer heat.

• Thermodynamics deals with the principles governing energy transformations.

• Thermochemistry focuses on the heat involved in chemical processes.

Kinetic and Potential Energy

Energy exists in various forms, with kinetic and potential energy being the most fundamental in chemistry.

• Kinetic Energy (E_k): The energy of motion, given by the formula:

$E_k = \frac{1}{2}mv^2$

• Potential Energy: Stored energy due to position or composition. In chemistry, electrostatic potential energy between charged particles is especially important.

Electrostatic Potential Energy

Electrostatic interactions between charged particles are a major source of potential energy in chemical systems. The energy depends on the charges and their separation distance.

• Energy is released when chemical bonds form (exothermic).

• Energy is consumed when chemical bonds break (endothermic).

First Law of Thermodynamics

Law Statement and Energy Conservation

The First Law of Thermodynamics states that energy can be converted from one form to another, but it cannot be created or destroyed. This principle is fundamental to all chemical and physical processes.

• Examples: Chemical energy in fuel is converted to heat; sunlight is converted to chemical energy in plants.

System and Surroundings

In thermochemistry, we define a system (the part of the universe under study) and its surroundings (everything else).

• System: The specific part of the universe being studied (e.g., reactants and products in a reaction).

• Surroundings: Everything outside the system (e.g., container, air).

Types of Systems

• Open System: Can exchange both matter and energy with surroundings.

• Closed System: Can exchange energy but not matter with surroundings.

• Isolated System: Cannot exchange either matter or energy with surroundings.

Work and Heat

Energy transfer can occur as work or heat:

• Work (w): Energy used to move an object over a distance. $w = F \times d$

• Heat (q): Energy transferred due to temperature difference; flows from hot to cold objects.

Internal Energy (E)

The internal energy of a system is the sum of all kinetic and potential energies of its components. The change in internal energy ($\Delta E$) is a state function and depends only on the initial and final states, not the path taken.

• $\Delta E = E_{final} - E_{initial}$

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

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

Thermodynamic Quantities: Number, Unit, and Sign

• Every thermodynamic quantity has a magnitude, a unit (usually Joules), and a sign indicating direction of energy flow.

• Sign conventions:

  • q > 0: System gains heat

  • q < 0: System loses heat

  • w > 0: Work done on system

  • w < 0: Work done by system

  • $\Delta E$ > 0: Net gain of energy by system

  • $\Delta E$ < 0: Net loss of energy by system

Heat Exchange: Endothermic and Exothermic Processes

• Endothermic: System absorbs heat from surroundings (temperature of surroundings drops).

• Exothermic: System releases heat to surroundings (temperature of surroundings rises).

State Functions

A state function depends only on the current state of the system, not on how it got there. Internal energy ($E$), enthalpy ($H$), and pressure are state functions, while heat ($q$) and work ($w$) are not.

Enthalpy (H)

Definition and Calculation

Enthalpy is a thermodynamic quantity defined as the internal energy plus the product of pressure and volume:

$H = E + PV$

• At constant pressure, the change in enthalpy ($\Delta H$) equals the heat gained or lost by the system:

$\Delta H = \Delta E + P\Delta V$

• Endothermic: $\Delta H > 0$

• Exothermic: $\Delta H < 0$

Pressure–Volume Work

When a reaction involves gases, the system may do work by changing its volume against external pressure (pressure–volume work).

• Work done by the system (expansion): $w = -P\Delta V$

Enthalpy of Reaction and Calorimetry

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

The enthalpy change for a chemical reaction is the difference between the enthalpy of the products and the reactants:

$\Delta H_{rxn} = H_{products} - H_{reactants}$

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

• Reversing a reaction changes the sign of $\Delta H$.

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

Calorimetry

Calorimetry is the measurement of heat flow. The instrument used is a calorimeter.

• Heat capacity: Energy required to raise the temperature of a substance by 1 K.

• Specific heat: Energy required to raise 1 gram of a substance by 1 K.

• Molar heat capacity: Energy required to raise 1 mole of a substance by 1 K.

Substance	Specific Heat (J/g·K)
N2 (gas)	1.04
H2O (liquid)	4.18
Al (solid)	0.90
Fe (solid)	0.45
CH4 (gas)	2.20
CO2 (gas)	0.84
CaCO3 (solid)	0.82

Constant-Pressure and Constant-Volume Calorimetry

• Constant-pressure calorimetry: Used for reactions in solution; measures $q_p = \Delta H$.

• Bomb calorimetry: Used for combustion reactions; measures $q_v = \Delta E$ (constant volume).

Hess’s Law

Statement and Application

Hess’s Law states that if a reaction is carried out in a series of steps, the overall enthalpy change is the sum of the enthalpy changes for the individual steps. This is possible because enthalpy is a state function.

• Allows calculation of $\Delta H$ for reactions that are difficult to measure directly.

Enthalpies of Formation

Standard Enthalpy of Formation ($\Delta H_f^\circ$)

The standard enthalpy of formation of a compound is the enthalpy change for the formation of 1 mole of the compound from its elements in their standard states.

• By definition, $\Delta H_f^\circ$ for an element in its standard state is zero.

Substance	Formula	$\Delta H_f^\circ$ (kJ/mol)
Acetylene	C2H2 (g)	226.7
Ammonia	NH3 (g)	-46.19
Benzene	C6H6 (l)	49.0
Calcium carbonate	CaCO3 (s)	-1207.1
Carbon dioxide	CO2 (g)	-393.5
Water	H2O (l)	-285.8

Calculating Reaction Enthalpy from Formation Enthalpies

The enthalpy change for a reaction can be calculated using standard enthalpies of formation:

$\Delta H_{rxn}^\circ = \sum n \Delta H_f^\circ (products) - \sum m \Delta H_f^\circ (reactants)$

• n and m are stoichiometric coefficients.

Bond Enthalpies

Definition and Use

Bond enthalpy is the energy required to break one mole of a specific bond in a gaseous molecule. It is always positive, as energy is required to break bonds.

• Stronger bonds have higher bond enthalpies.

• Energy is released when bonds form.

Bond	Bond Enthalpy (kJ/mol)
C–H	413
C–C	348
C=C	614
O–H	463
H–H	436
O=O	495

Estimating Enthalpy of Reaction Using Bond Enthalpies

• Add bond energies for all bonds broken (energy input, positive).

• Subtract bond energies for all bonds formed (energy released, negative).

• The result is an estimate of $\Delta H_{rxn}$.

$\Delta H_{rxn} \approx \sum \text{(bond energies of bonds broken)} - \sum \text{(bond energies of bonds formed)}$

Summary Table: Key Thermochemical Quantities

Quantity	Symbol	Definition	State Function?
Internal Energy	E	Total energy (kinetic + potential) of a system	Yes
Enthalpy	H	E + PV	Yes
Work	w	Energy transfer by force over distance	No
Heat	q	Energy transfer due to temperature difference	No