Chapter 9: Thermochemistry – Energy, Heat, and Work in Chemical Reactions

Thermochemistry: The Study of Energy in Chemical Reactions

Nature of Energy, Work, and Heat

Thermochemistry explores how energy is transferred during chemical reactions and physical changes. Energy is the capacity to do work, and it can be exchanged between objects through contact, such as collisions.

• Energy: Anything with the capacity to do work.

• Work: Force acting over a distance. $\text{Work} = \text{Force} \times \text{Distance}$

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

• Energy can be transferred as heat or work, either into or out of a system.

Classification of Energy

Energy is classified as kinetic or potential, with several forms relevant to chemistry.

• Kinetic Energy: Energy of motion or energy being transferred.

• Thermal Energy: Energy associated with temperature; a form of kinetic energy.

• Potential Energy: Energy stored in an object or associated with its composition and position.

• Chemical Energy: Potential energy due to the structure and arrangement of atoms in molecules.

• Electrical, Light, Nuclear: Other forms relevant in specific contexts.

Manifestations and Transformations of Energy

Energy can be transformed from one type to another, such as potential energy converting to kinetic energy.

• Example: Dropping a ball converts gravitational potential energy to kinetic energy.

Units of Energy and Conversion

Energy is measured in several units, with the joule (J) as the SI unit. Other units include calories (cal), kilocalories (kcal), and kilowatt-hours (kWh).

• Kinetic Energy Formula: $KE = \frac{1}{2}mv^2$

• 1 J = 1 kg·m2/s2 = 1 N·m

• 1 cal = 4.184 J

• 1 kcal = 1000 cal = 1 food Calorie (Cal)

• 1 kWh = $3.60 \times 10^6$ J

The First Law of Thermodynamics: Conservation of Energy

Law of Conservation of Energy

The first law states that energy cannot be created or destroyed, only transferred or converted. The total energy in the universe remains constant.

• Energy gained or lost by a system equals the energy lost or gained by the surroundings.

System and Surroundings

In thermochemistry, the system is the part of the universe being studied, and the surroundings are everything else.

• Energy can flow from system to surroundings (exothermic) or from surroundings to system (endothermic).

Energy Flow and Conservation

Conservation of energy requires that the sum of energy changes in the system and surroundings is zero.

• $\Delta E_{universe} = 0 = \Delta E_{system} + \Delta E_{surroundings}$

• $\Delta$ denotes change: final amount minus initial amount.

Internal Energy and State Functions

The internal energy of a system is the sum of kinetic and potential energies of all particles. The change in internal energy depends only on initial and final states, not the path taken.

• State Function: Depends only on initial and final conditions.

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

• $\Delta E_{reaction} = E_{products} - E_{reactants}$

Energy Diagrams: Exothermic and Endothermic Processes

Exothermic Process

In exothermic reactions, energy flows out of the system into the surroundings. The internal energy of the system decreases.

• $\Delta E_{sys} < 0$ (negative)

Endothermic Process

In endothermic reactions, energy flows into the system from the surroundings. The internal energy of the system increases.

• $\Delta E_{sys} > 0$ (positive)

Summary of Energy Flow

• Energy flowing out of the system is negative (withdrawal).

• Energy flowing into the system is positive (deposit).

Energy Exchange: Heat and Work

Heat and Work as Energy Exchange

Energy is exchanged between system and surroundings through heat (q) and work (w).

• $\Delta E = q + w$

• q and w are not state functions; they depend on the process.

Heat Exchange and Thermal Equilibrium

Heat is the exchange of thermal energy between system and surroundings, occurring when there is a temperature difference. Heat flows from high to low temperature until thermal equilibrium is reached.

Heat Capacity and Specific Heat

Heat capacity (C) is the quantity of heat absorbed to raise the temperature of an object by 1°C or 1 K.

• Units: J/°C or J/K

• $q = C \times \Delta T$

• Specific heat capacity ($C_s$): Amount of heat required to raise 1 g of a substance by 1°C.

• Units: J/(g·°C)

• Molar heat capacity: Amount of heat required to raise 1 mol of a substance by 1°C.

Quantifying Heat Energy

• $q = m \times C_s \times \Delta T$

• Where m = mass, $C_s$ = specific heat, $\Delta T$ = temperature change

Heat Transfer and Final Temperature

When two objects at different temperatures are in contact, heat flows until both reach the same final temperature. The heat lost by the hot material equals the heat gained by the cold material.

• $q_{metal} = -q_{water}$

• $m_{metal} \times C_{s,metal} \times \Delta T_{metal} = -m_{water} \times C_{s,water} \times \Delta T_{water}$

Work: Pressure–Volume Work

Pressure–Volume (PV) Work

Work is done when a gas expands or contracts against an external pressure.

• $w = -P \Delta V$

• Work is negative when the system does work on the surroundings (expansion).

• 1 atm·L = 101.3 J

Energy Exchange Summary

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

• Work: $w = -P \Delta V$

Calorimetry: Measuring Energy Changes

Calorimetry at Constant Volume (Bomb Calorimeter)

Calorimetry measures energy changes by observing temperature changes in the surroundings. At constant volume, $w = 0$, so $\Delta E_{system} = q_{system}$.

• Bomb calorimeter: Sealed, insulated container filled with water.

• $q_{system} = -q_{surroundings}$

Calorimetry at Constant Pressure (Coffee-Cup Calorimeter)

Reactions in solution are often measured at constant pressure using nested foam cups. The heat change for the system is measured by the heat change for the water.

• $q_{reaction} = -q_{solution} = -(m_{solution} \times C_{s,solution} \times \Delta T)$

• $\Delta H_{reaction} = q_{constant\ pressure} = q_{reaction}$

Enthalpy: Heat at Constant Pressure

Definition and Calculation of Enthalpy

Enthalpy (H) is the internal energy plus the product of pressure and volume. At constant pressure, the change in enthalpy ($\Delta H$) equals the heat gained or lost.

• $H = E + PV$

• $\Delta H = \Delta E + P \Delta V$

• $\Delta H = q$ (at constant pressure)

Endothermicity and Exothermicity

• Endothermic: $\Delta H > 0$ (heat absorbed)

• Exothermic: $\Delta H < 0$ (heat released)

Enthalpy of Reaction

• $\Delta H = H_{products} - H_{reactants}$

• Enthalpy is an extensive property; it depends on the amount of substance.

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

Hess’s Law: Calculating Enthalpy Changes

Hess’s Law

If a reaction can be expressed as a series of steps, the overall enthalpy change is the sum of the enthalpy changes for each step.

• Manipulate reactions with known $\Delta H$ values to obtain the desired reaction.

• Multiply or reverse reactions as needed, adjusting $\Delta H$ accordingly.

Bond Energies and Enthalpy Calculations

Bond Energies

Bond energy is the energy required to break one mole of a bond in a compound. Average bond energies are used to estimate $\Delta H_{rxn}$.

• Bond breaking is endothermic (positive $\Delta H$).

• Bond making is exothermic (negative $\Delta H$).

• $\Delta H_{rxn} = \sum (\Delta H_{bonds\ broken}) + \sum (\Delta H_{bonds\ formed})$

Standard Enthalpy of Formation

Definition and Calculation

The standard enthalpy of formation ($\Delta H_f^\circ$) is the enthalpy change for forming one mole of a compound from its elements in their standard states.

• Standard state: Pure substance at 1 atm and 25°C.

• $\Delta H_f^\circ$ for pure elements in their standard state = 0 kJ/mol.

• $\Delta H^\circ_{reaction} = \sum n \Delta H_f^\circ (products) - \sum n \Delta H_f^\circ (reactants)$

Lattice Energy and the Born–Haber Cycle

Lattice Energy

Lattice energy is the energy released when an ionic solid forms from its ions in the gas phase. It is always exothermic and depends on ion size and charge.

• Larger ions = smaller lattice energy

• Larger charge = larger lattice energy

Born–Haber Cycle

The Born–Haber cycle uses Hess’s law to calculate lattice energy by summing enthalpy changes for each step in the formation of an ionic compound.

Energy in Foods and Fuels

Energy Sources

Most energy in food comes from carbohydrates and fats. The majority of energy consumed in society comes from fossil fuels, which are not renewable.

Summary Table: Energy Units and Conversions

Energy Units	Conversion
1 calorie (cal)	4.184 joules (J)
1 kilocalorie (kcal)	1000 calories (cal)
1 food Calorie (Cal)	1 kcal or 1000 calories
1 kilowatt-hour (kWh)	3.60 × 106 joules (J)

Summary Table: Specific Heat Capacities

Substance	Specific Heat Capacity, Cs (J/g·°C)
Lead	0.128
Gold	0.128
Silver	0.235
Copper	0.385
Aluminum	0.903
Ethanol	2.42
Water	4.18
Glass (Pyrex)	0.75
Granite	0.79
Sand	0.84

Additional info: Academic context and examples were added to clarify concepts and formulas, and to ensure completeness for exam preparation.