Chapter 7: Thermochemistry – Study Notes

Chapter 7: Thermochemistry

Learning Outcomes

• Analyze types of energy and convert between energy units

• Analyze changes in internal energy in terms of heat and work

• Determine heat from temperature changes

• Calculate quantities in thermal energy transfer

• Analyze processes involving pressure-volume work

• Analyze energy changes for combustion reactions inside a bomb calorimeter

• Predict endothermic and exothermic processes

• Perform stoichiometric calculations involving the enthalpy of reaction

• Analyze enthalpy changes for reactions in a coffee-cup calorimeter

• Analyze how changes in chemical reactions affect the enthalpy of reaction

• Determine the standard enthalpy change for a reaction using standard enthalpies of formation

• Analyze the effects of energy use on the environment

7.1 Chemical Hand Warmers

Introduction to Thermochemistry

Thermochemistry is the study of the relationship between chemistry and energy. Everyday items such as chemical hand warmers utilize thermochemical principles, typically involving exothermic reactions that release heat.

• Thermochemistry: Study of energy changes during chemical reactions.

• Example Reaction: Iron pouch in hand warmers: $4Fe(s) + 3O_2(g) \rightarrow 2Fe_2O_3(s) + \text{heat}$

• Energy is exchanged as heat during the reaction.

7.2 The Nature of Energy: Key Definitions

Forms and Definitions of Energy

Energy is the capacity to do work. In chemistry, energy is exchanged as heat and work, and can exist in several forms:

• Energy: Capacity to do work.

• Work: Result of a force acting through a distance.

• Heat: Flow of energy caused by a temperature difference.

• Work and heat are the primary ways objects exchange energy.

Types of Energy

• Kinetic Energy: Energy associated with motion. $KE = \frac{1}{2}mv^2$

• Thermal Energy: Energy associated with temperature.

• Potential Energy: Energy due to position or composition.

• Chemical Energy: Energy due to the relative positions of electrons and nuclei in atoms and molecules.

Law of Conservation of Energy

• Law of Conservation of Energy: Energy cannot be created nor destroyed; it can only be transformed from one form to another.

• Potential energy can become kinetic energy; chemical energy can become thermal energy.

System and Surroundings

• System: The part of the universe under study (e.g., chemicals in a reaction).

• Surroundings: Everything else (e.g., water, beaker, air, your hand).

• If a system loses energy, the surroundings gain the exact same amount, and vice versa.

Units of Energy

• Joule (J): $1 \text{J} = 1 \text{kg} \cdot \text{m}^2/\text{s}^2$

• Calorie (cal): $1 \text{cal} = 4.184 \text{J}$ (exact)

• 1 Calorie (nutritional) = 1 kcal = 1000 cal

• Kilowatt-hour (kWh): $1 \text{kWh} = 3.60 \times 10^6 \text{J}$

Unit	Conversion Factor
1 calorie (cal)	4.184 joules (J)
1 Calorie (kcal)	4184 joules (J)
1 kilowatt-hour (kWh)	3.60 × 106 joules (J)

7.3 The First Law of Thermodynamics

Energy Conservation and Internal Energy

The first law of thermodynamics states that the total energy of the universe is constant. Energy can be transferred or transformed, but not created or destroyed.

• Thermodynamics: Study of energy and its interconversions.

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

• State Function: Property dependent only on the state of the system, not the path taken.

• Change in Internal Energy: $\Delta E = E_{final} - E_{initial}$

• Energy change can be visualized with energy diagrams.

• If $\Delta E$ is negative, the system loses energy; if positive, the system gains energy.

• Energy lost by the system is gained by the surroundings: $\Delta E_{sys} = -\Delta E_{surr}$

• First Law Equation: $\Delta E = q + w$ where $q$ is heat and $w$ is work.

Quantity	Sign Convention
q (heat)	+ system gains thermal energy; - system loses thermal energy
w (work)	+ work done on the system; - work done by the system
$\Delta E$ (internal energy)	+ energy flows into the system; - energy flows out of the system

7.4 Quantifying Heat and Work

Heat, Temperature, and Thermal Equilibrium

Heat is the transfer of thermal energy, while temperature measures the average thermal energy. When two objects reach the same temperature, thermal equilibrium is achieved and no net heat transfer occurs.

• Heat Capacity (C): Measure of a system's ability to absorb thermal energy without a large temperature change. $C = \frac{q}{\Delta T}$

• Specific Heat Capacity ($C_s$): Amount of heat required to raise the temperature of 1 gram of a substance by 1°C (J/g·°C).

• Molar Heat Capacity ($C_m$): Amount of heat required to raise the temperature of 1 mole of a substance by 1°C (J/mol·°C).

• Specific Heat Equation: $q = m \times C_s \times \Delta T$

• Temperature change ($\Delta T$) can be in °C or K, but not in °F.

Substance	Specific Heat Capacity (J/g·°C)
Water	4.184
Aluminum	0.897
Iron	0.449
Gold	0.129
Glass	0.840
Lead	0.128

Thermal Equilibrium in Practice

• When two substances are thermally isolated, heat lost by one is gained by the other: $q_{sys} = -q_{surr}$

• Exact temperature change depends on mass and specific heat capacities: $m_{metal} \times C_{s,metal} \times \Delta T_{metal} = -m_{water} \times C_{s,water} \times \Delta T_{water}$

Pressure-Volume Work

• Work is done when a force acts through a distance: $w = F \times D$

• For gases, work is associated with volume change against external pressure: $w = -P_{ext} \Delta V$

• 1 L·atm = 101.3 J

7.5 Measuring ΔE for Chemical Reactions: Constant-Volume Calorimetry

Calorimetry and Bomb Calorimeter

Calorimetry measures the thermal energy exchanged between a reaction and its surroundings by observing temperature changes. A bomb calorimeter is used for reactions at constant volume.

• Bomb Calorimeter: Sealed container ensuring constant volume.

• Measures $\Delta E$ for the reaction and heat capacity of surroundings.

• Calorimeter Equation: $q_{cal} = C_{cal} \times \Delta T$

• At constant volume: $\Delta E_{rxn} = q_v$

• Heat lost by reaction equals heat gained by calorimeter: $q_{cal} = -q_{rxn}$

7.6 Enthalpy: The Heat Evolved in a Chemical Reaction at Constant Pressure

Definition and Calculation of Enthalpy

Enthalpy (H) is the sum of a system's internal energy and the product of its pressure and volume. It is a state function and is especially useful for reactions at constant pressure.

• Enthalpy Equation: $H = E + PV$

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

• At constant pressure, $\Delta H$ equals the heat exchanged ($q_p$).

• For reactions with little or no volume change, $\Delta H$ and $\Delta E$ are nearly identical.

Endothermic vs. Exothermic Reactions

• Exothermic Reaction: Releases heat to surroundings ($\Delta H < 0$).

• Endothermic Reaction: Absorbs heat from surroundings ($\Delta H > 0$).

• Examples:

  • Sweat evaporating from skin: Endothermic ($\Delta H > 0$)

  • Water freezing in a freezer: Exothermic ($\Delta H < 0$)

  • Wood burning in a fire: Exothermic ($\Delta H < 0$)

Bond Energy and Enthalpy

• Breaking bonds always absorbs energy (endothermic).

• Forming stronger bonds releases energy (exothermic).

Enthalpy of Reaction

• Enthalpy of Reaction ($\Delta H_{rxn}$): Amount of heat generated or absorbed when a chemical reaction occurs.

• Magnitude reflects stoichiometric amounts of reactants and products.

• Use ratios as conversion factors between reactants/products and heat emitted.

• Example: $C_3H_8(g) + 5O_2(g) \rightarrow 3CO_2(g) + 4H_2O(g) \quad \Delta H_{rxn} = -2044 \text{ kJ}$

7.7 Constant-Pressure Calorimetry: Measuring ΔHrxn

Coffee-Cup Calorimeter

Coffee-cup calorimetry is used to measure enthalpy changes at constant pressure, typically for reactions in solution.

• Consists of two nested Styrofoam cups for insulation.

• Measures $\Delta H_{rxn}$ using: $q_{soln} = m_{soln} \times C_s \times \Delta T$

• Heat lost by reaction equals heat gained by solution: $q_{rxn} = -q_{soln}$

Comparison with Bomb Calorimeter

• Bomb calorimeter: measures $\Delta E$ at constant volume.

• Coffee-cup calorimeter: measures $\Delta H$ at constant pressure.

7.8 Relationships Involving ΔHrxn

Quantitative Relationships and Hess's Law

Enthalpy changes are associated with specific chemical reactions. There are three key relationships:

• If a chemical equation is multiplied by a factor, $\Delta H_{rxn}$ is multiplied by the same factor.

• If a chemical equation is reversed, $\Delta H_{rxn}$ changes sign.

• If a chemical equation is the sum of a series of steps, $\Delta H_{rxn}$ for the overall reaction is the sum of the enthalpy changes for each step (Hess's Law).

Relationship	Effect on ΔHrxn
Multiply equation by n	Multiply ΔHrxn by n
Reverse equation	Change sign of ΔHrxn
Add equations	Add ΔHrxn values

7.9 Determining Enthalpies of Reaction from Standard Enthalpies of Formation

Standard Enthalpy of Formation

Standard enthalpy of formation ($\Delta H_f^\circ$) is the enthalpy change when 1 mole of a compound forms from its elements in their standard states.

• Standard State:

  • Gas: pure gas at 1 atm

  • Liquid/Solid: pure substance in most stable form at 1 atm and 25°C

  • Solution: 1 M concentration

• Standard Enthalpy Change ($\Delta H^\circ$): Change in enthalpy for a process when all reactants and products are in their standard states.

• Standard Enthalpy of Formation ($\Delta H_f^\circ$): For pure elements in their standard state, $\Delta H_f^\circ = 0$.

Calculating Reaction Enthalpy from Formation Enthalpies

• Use formation and decomposition steps to calculate overall reaction enthalpy.

• Apply Hess's Law to sum enthalpies of individual steps.

7.10 Energy Use and the Environment

Environmental Impact of Energy Use

Chemical reactions and energy use have significant effects on the environment, including resource consumption and pollution. Understanding thermochemistry helps in evaluating and minimizing these impacts.