Chapter 6: Thermochemistry – Study Notes

Ch6: Thermochemistry

Introduction

Thermochemistry is the study of energy changes, particularly heat, that accompany chemical reactions and physical processes. This chapter explores the concepts of heat (q), work (w), enthalpy (H), and internal energy (U), and how these quantities are measured and related in chemical systems.

6.1 Chemical Hand Warmers

Thermochemistry in Everyday Applications

• Thermochemistry quantifies how energy is transformed from one state to another through either work (w) and/or heat (q).

• Many chemical reactions release or absorb heat, with practical applications such as hand warmers.

• Example: Iron oxidation in hand warmers:

  • $2Fe(s) + \frac{3}{2}O_2(g) \rightarrow Fe_2O_3(s)$

• Work (w): Energy associated with ordered motion, e.g., moving a piston or pulling an object.

• Heat (q): Energy transfer due to temperature differences, resulting in random molecular motion.

6.2 The Nature of Energy: Key Definitions

Forms and Units of Energy

• Kinetic Energy (KE): Energy of motion.

  • $KE = \frac{1}{2}mv^2 = \frac{1}{2}(kg)\left(\frac{m}{s}\right)^2 = J$

• Potential Energy: Energy stored due to position or composition.

• Thermal Energy: Energy due to random motion of particles.

• Chemical Energy: Energy stored in chemical bonds.

• Units of Energy:

  • Joule (J): SI unit of energy.

  • Calorie (cal): $1\,cal = 4.184\,J$

  • Nutritional Calorie (Cal): $1\,Cal = 1000\,cal = 1\,kcal$

6.3 The First Law of Thermodynamics

Energy Conservation and Internal Energy

• First Law of Thermodynamics: Energy is neither created nor destroyed.

• Energy is transferred between the system and surroundings as heat or work.

• Internal Energy (U): Sum of kinetic and potential energies of all particles in a system.

• Mathematical Expression:

  • $\Delta U = q + w$

  • $\Delta U = U_f - U_i$

• Sign Conventions:

  • $q$ is negative when the system loses heat, positive when it gains heat.

  • $w$ is negative when the system does work on surroundings, positive when surroundings do work on the system.

6.4 Quantifying Heat and Work

Heat Transfer and Heat Capacity

• Heat (q): Energy flow due to temperature difference.

• Heat flows from high to low temperature until thermal equilibrium is reached.

• Heat Capacity (C): Amount of heat required to change temperature of a system by 1 K or 1°C.

  • $q = C \times \Delta T$

  • $C = \frac{q}{\Delta T}$

• Specific Heat Capacity ($C_s$): Heat capacity per gram.

  • $C_s = \frac{C}{m}$ (units: J/g·K or J/g·°C)

• Molar Heat Capacity ($C_m$): Heat capacity per mole.

  • $C_m = \frac{C}{n}$ (units: J/mol·K or J/mol·°C)

• Common Expressions for Heat:

  • $q = C \times \Delta T$

  • $q = m \times C_s \times \Delta T$

  • $q = n \times C_m \times \Delta T$

Table: Specific Heat Capacities

Substance	Specific Heat Capacity (J/g·°C)
Lead	0.128
Gold	0.128
Silver	0.235
Copper	0.385
Aluminum	0.903
Water	4.184
Granite	0.79
Glass (Pyrex)	0.75

Pressure-Volume Work

• Pressure-Volume Work: Work done by a system during expansion or compression against external pressure.

• Mathematical Expression:

  • $w = -P_{ext} \Delta V$

• For reactions involving gases, use the ideal gas law:

  • $V = \frac{nRT}{P}$

  • $w = -\Delta nRT$

• Change in moles of gas ($\Delta n$): Calculated from stoichiometry of reaction.

• Example calculation:

  • $w = -8.314\,mol^{-1}\,K^{-1} \times 298\,K \times (-3) = 7432\,J/mol$

6.5 Measuring $\Delta U$ for Reactions

Constant-Volume Calorimetry

• In a constant-volume container, $\Delta V = 0$, so:

  • $\Delta U = q_v$

• Bomb Calorimeter: Device used to measure heat released at constant volume.

• Heat change in calorimeter:

  • $q_{v,cal} = C_{v,cal} \Delta T$

• $C_{v,cal}$ is determined by calibration with a known substance.

• Heat of reaction:

  • $q_{v,r} = -q_{v,cal} = \Delta U$

6.6 Enthalpy $\Delta H$

Constant-Pressure Calorimetry and Enthalpy

• At constant pressure, the heat measured is the change in enthalpy ($\Delta H$).

• Enthalpy ($H$): Defined as $H = U + PV$

• Change in Enthalpy:

  • $\Delta H = \Delta U + P \Delta V + V \Delta P$

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

6.7 Constant-Pressure Calorimetry: Measuring $\Delta H$

Coffee-Cup Calorimeter

• Simple device for measuring enthalpy changes at constant pressure.

• Heat change:

  • $\Delta H_{r,p} = q_{p,r} = -C_{p,cal} \Delta T$

• Direct measure of $\Delta H$; indirect measure from bomb calorimeter using $\Delta H = \Delta U + RT \Delta n$ for reactions involving gases.

6.8 Relationships Involving $\Delta H$

Endothermic and Exothermic Reactions

• Endothermic: Absorbs heat; $\Delta H > 0$ (e.g., cold packs).

• Exothermic: Releases heat; $\Delta H < 0$ (e.g., hand warmers).

• Enthalpy values are tabulated under standard conditions.

State Functions

• State Function: Depends only on initial and final states, not the path taken.

• Example: Height difference between two points is a state function; work done climbing is a path function.

• Mathematical property:

  • $\int_{i}^{f} dX = X_f - X_i = \Delta X$

Calculating Reaction Enthalpy

• For a general reaction $aA + bB \rightarrow cC + dD$:

  • $\Delta_r H^\circ = \sum v_p \Delta H^\circ_{products} - \sum v_r \Delta H^\circ_{reactants}$

• Stoichiometric coefficients ($v$) are used for products and reactants.

• Enthalpy change is independent of the reaction path.

Manipulating Chemical Equations and Hess's Law

• If a chemical equation is multiplied by a factor, enthalpy is multiplied by the same factor.

• If a chemical equation is reversed, the sign of enthalpy is reversed.

• If a reaction is the sum of other reactions, its enthalpy is the sum of the enthalpies (Hess's Law).

6.9 Reaction Enthalpies at Standard State

Standard States and Standard Enthalpy of Formation

• Standard State:

  • Gas: Pure gas at 1 bar pressure.

  • Liquid/Solid: Pure substance in most stable form at 1 bar and 25°C.

  • Solution: 1 mol/L concentration.

• Standard Enthalpy of Formation ($\Delta H_f^\circ$): Enthalpy change when 1 mole of a compound forms from its elements in their standard states.

• Enthalpy of pure elements in standard state is defined as zero.

• Example: Formation of methane:

  • $C_{(graphite)} + 2H_2(g) \rightarrow CH_4(g)$

  • $\Delta H_f^\circ = -74.6\,kJ/mol$

• Calculating reaction enthalpy using enthalpies of formation:

  • $\Delta_r H^\circ = \sum v_p \Delta H_f^\circ (products) - \sum v_r \Delta H_f^\circ (reactants)$

Summary Table: Key Equations in Thermochemistry

Concept	Equation (LaTeX)	Description
Kinetic Energy	$KE = \frac{1}{2}mv^2$	Energy of motion
First Law of Thermodynamics	$\Delta U = q + w$	Change in internal energy
Heat Capacity	$q = C \Delta T$	Heat transfer at constant volume
Specific Heat	$q = m C_s \Delta T$	Heat transfer per gram
Molar Heat	$q = n C_m \Delta T$	Heat transfer per mole
Pressure-Volume Work	$w = -P_{ext} \Delta V$	Work done by system
Enthalpy Change	$\Delta H = \Delta U + P \Delta V$	Change in enthalpy
Standard Reaction Enthalpy	$\Delta_r H^\circ = \sum v_p \Delta H_f^\circ (products) - \sum v_r \Delta H_f^\circ (reactants)$	Reaction enthalpy from formation enthalpies

Additional info: These notes expand on the provided slides and handwritten notes, filling in academic context and definitions for clarity and completeness. All equations are presented in LaTeX format for clarity. Tables are reconstructed from the original content and standard chemistry references.