Thermochemistry and Calorimetry: Study Notes for General Chemistry

Thermochemistry: The Study of Energy in Chemical Reactions

Introduction to Thermodynamics

Thermodynamics is the branch of chemistry that studies the energy changes accompanying chemical and physical processes. It helps us understand how energy is transferred as heat and work, and how these transfers affect matter.

• Thermal energy: Energy due to temperature differences (e.g., hot/cold packs, compressed air).

• Optical energy: Light emission (e.g., glow sticks, incandescent bulbs).

• Electrical energy: Batteries, solar panels, electric cars.

Energy (measured in joules, J) is transferred by two main means: work and heat.

• Work: Energy transfer due to force acting over a distance (mechanical or electrical work).

• Heat: Energy transfer due to temperature difference between system and surroundings.

Main Categories of Energy

• Kinetic Energy (KE): Energy of motion. $KE = \frac{1}{2}mv^2$

• Potential Energy (PE): Stored energy due to position or composition.

The Laws of Thermodynamics

First Law of Thermodynamics

The First Law states that energy cannot be created or destroyed, only transferred or transformed. In chemical reactions, the total energy of the system and surroundings remains constant.

• System: The part of the universe we are studying (e.g., the contents of a beaker).

• Surroundings: Everything outside the system.

Energy changes are measured as changes in internal energy ($\Delta E$):

• $\Delta E = q + w$

• Where $q$ is heat and $w$ is work.

State Functions

State functions depend only on the initial and final states of a system, not on the path taken. Examples include internal energy ($E$), enthalpy ($H$), pressure ($P$), volume ($V$), and temperature ($T$).

• Non-state functions depend on the process (e.g., work, heat).

Measuring Energy Changes: Calorimetry

Defining Work ($w$)

• Work is often done by gases expanding or contracting against external pressure.

• Equation: $w = -P_{ext} \Delta V$

• Units: $1 \text{ L·atm} = 101.3 \text{ J}$

Example: Calculating work done when a gas expands from 1.00 L to 2.00 L against 1.00 atm pressure:

• $w = -P_{ext} \Delta V = -(1.00 \text{ atm})(2.00 - 1.00) \text{ L} = -1.00 \text{ L·atm} = -101.3 \text{ J}$

Defining Heat ($q$)

• Heat is energy transferred due to temperature difference.

• Temperature is a measure of the average kinetic energy of particles.

• Equation: $q = mc\Delta T$

• Specific heat ($c$): The amount of heat required to raise the temperature of 1 g of a substance by 1°C.

Example: Water has a high specific heat ($c = 4.184 \text{ J/g·°C}$), making it effective at absorbing heat.

Calorimetry: Measuring Heat Transfer

Calorimetry is the experimental technique used to measure heat changes in physical and chemical processes.

• qobject: Heat absorbed or released by a material or object.

• qreaction: Heat absorbed or released by a chemical reaction.

All calorimetry problems begin with the principle of conservation of energy: $q_{system} + q_{surroundings} = 0$

Types of Calorimeters

• Bomb Calorimeter: Measures energy at constant volume (used for combustion reactions).

• Coffee Cup Calorimeter: Measures energy at constant pressure (used for reactions in solution).

Enthalpy: A New Unit of Energy

Definition and Measurement

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

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

• Measured using calorimetry under constant pressure conditions.

Example: Determining the enthalpy of dissolution for ammonium nitrate using a coffee cup calorimeter.

Determining Reaction Enthalpies

Direct and Indirect Methods

• Direct Method: Measuring $\Delta H$ directly using calorimetry.

• Indirect Method (Hess's Law): Calculating $\Delta H$ using known enthalpies of formation or reaction steps.

Standard Enthalpy of Formation ($\Delta H_f^\circ$): The enthalpy change when one mole of a compound is formed from its elements in their standard states.

Hess's Law

Hess's Law states that the total enthalpy change for a reaction is the same, no matter how many steps the reaction is carried out in. This allows us to add or subtract known enthalpy changes to find unknown values.

• When reversing a reaction, change the sign of $\Delta H$.

• When multiplying a reaction, multiply $\Delta H$ by the same factor.

Equation:

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

Lattice Energy and Bond Enthalpy

Lattice Energy Using Hess's Law

Lattice energy is the energy required to separate one mole of an ionic solid into its gaseous ions. It can be determined using Hess's Law by breaking the process into steps (Born-Haber cycle).

• Overall: $U = \sum \text{(steps)}$

Example: Calculating lattice energy for LiF, MgCl2, and theoretical NaCl2 using energy diagrams.

Bond Enthalpy

Bond enthalpy (or bond dissociation energy) is the energy required to break one mole of a specific type of bond in a molecule in the gas phase.

Bond	Avg Bond Energy (kJ/mol)	Bond	Avg Bond Energy (kJ/mol)
H–H	436	C–H	413
O=O	498	C=O	799
N≡N	945	C≡C	839
Cl–Cl	243	C–Cl	328
O–H	463	C–O	358
F–F	155	C–F	485
Br–Br	193	C–Br	276
I–I	151	C–I	238

Equation for reaction enthalpy using bond enthalpies:

• $\Delta H_{reaction} = \sum \text{(Bond energies of bonds broken)} - \sum \text{(Bond energies of bonds formed)}$

Example: Calculating $\Delta H$ for the reaction $CH_4 + 2 O_2 \rightarrow CO_2 + 2 H_2O$ using bond enthalpies.

Summary: Methods for Calculating $\Delta H$

1. Calorimetry (bomb and coffee cup calorimeters)

2. Using $\Delta H_f^\circ$ (standard enthalpies of formation)

3. Hess's Law (combining reactions to find unknown enthalpy changes)

Practice Problems and Applications

• Apply calorimetry equations to determine heat changes in reactions and phase changes.

• Use Hess's Law to calculate enthalpy changes for complex reactions.

• Analyze energy diagrams to understand lattice energy and bond enthalpy concepts.

Additional info: These notes are based on a comprehensive set of lecture slides and worksheets covering the core concepts of thermochemistry, calorimetry, enthalpy, Hess's Law, lattice energy, and bond enthalpy, as typically presented in a General Chemistry course.