Thermochemistry: Energy, Heat, and Enthalpy in Chemical Systems

Nature of Energy, Work, and Heat

Definitions and Concepts

Energy is the capacity to do work or produce heat. In chemistry, energy can be exchanged between objects through contact, such as collisions. Work is defined as a force acting over a distance, and heat is the flow of energy caused by a temperature difference between objects. Both heat and work are the two main ways that energy can be transferred between a system and its surroundings.

• Energy: The ability to do work or transfer heat.

• Work (w): Force applied over a distance. $w = \text{force} \times \text{distance}$

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

Classification of Energy

Types of Energy

Energy can be classified as potential, kinetic, or thermal energy. Potential energy is stored due to position, kinetic energy is due to motion, and thermal energy is associated with temperature.

• Potential Energy: Stored energy due to position (e.g., a compressed spring).

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

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

Units of Energy and Conversions

Common Energy Units

The SI unit of energy is the joule (J). Other units include the calorie (cal), kilocalorie (kcal), and kilowatt-hour (kWh). The calorie is commonly used in chemistry and nutrition.

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)

Conservation of Energy: The First Law of Thermodynamics

Law of Conservation of Energy

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed or transferred. The total energy of the universe remains constant during any process.

• First Law of Thermodynamics: $\Delta E_{universe} = 0$

• Energy lost by the system is gained by the surroundings, and vice versa.

System and Surroundings

Definitions

In thermochemistry, the system is the part of the universe we are studying (e.g., a chemical reaction), and the surroundings are everything else. Energy can flow between the system and surroundings as heat or work.

• System: The material or process under study.

• Surroundings: Everything outside the system.

Exothermic and Endothermic Processes

Energy Flow Directions

Energy can flow out of the system (exothermic) or into the system (endothermic). In exothermic processes, the system loses energy and the surroundings gain it. In endothermic processes, the system gains energy and the surroundings lose it.

• Exothermic: $\Delta E_{sys} < 0$ (energy released)

• Endothermic: $\Delta E_{sys} > 0$ (energy absorbed)

Internal Energy and State Functions

Internal Energy (E)

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

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

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

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

Energy Diagrams

Exothermic and Endothermic Energy Diagrams

Energy diagrams visually represent the energy changes during a chemical process. In exothermic reactions, products have lower energy than reactants ($\Delta E < 0$). In endothermic reactions, products have higher energy than reactants ($\Delta E > 0$).

• Exothermic: $\Delta E < 0$

• Endothermic: $\Delta E > 0$

Energy Exchange: Heat and Work

Heat (q) and Work (w)

Energy is exchanged between the system and surroundings as heat (q) or work (w). The total change in internal energy is the sum of heat and work:

• $\Delta E = q + w$

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

Heat Capacity and Specific Heat

Definitions and Equations

Heat capacity (C) is the amount of heat required to raise the temperature of an object by 1°C. Specific heat capacity ($C_s$) is the amount of heat required to raise the temperature of 1 gram of a substance by 1°C. Molar heat capacity is the heat required to raise the temperature of 1 mole of a substance by 1°C.

• Heat Capacity: $q = C \times \Delta T$

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

• Molar Heat Capacity: Units: J/(mol·°C)

Substance	Specific Heat Capacity, $C_s$ (J/g·°C)
Lead	0.128
Gold	0.128
Silver	0.235
Copper	0.385
Iron	0.449
Aluminum	0.903
Ethanol	2.42
Water	4.18
Glass (Pyrex)	0.75
Granite	0.79
Sand	0.84

Thermal Energy Transfer and Calorimetry

Heat Transfer Between Substances

When two objects at different temperatures are placed in contact, heat flows from the hotter object to the colder one until thermal equilibrium is reached. The heat lost by the hot object equals the heat gained by the cold object:

• $q_{metal} = -q_{water}$

• $q = m \times C_s \times \Delta T$

Enthalpy: Heat at Constant Pressure

Definition and Equations

Enthalpy (H) is the sum of the internal energy and the product of pressure and volume. The change in enthalpy ($\Delta H$) at constant pressure equals the heat exchanged ($q_p$):

• $H = E + PV$

• $\Delta H = \Delta E + P\Delta V$

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

Exothermic reactions have $\Delta H < 0$ (heat released), while endothermic reactions have $\Delta H > 0$ (heat absorbed).

Enthalpy Stoichiometry

Using Enthalpy in Calculations

The enthalpy change for a reaction is proportional to the amount of reactants used. It is often used as a conversion factor in stoichiometric calculations.

• Example: $\text{C}_3\text{H}_8(g) + 5\text{O}_2(g) \rightarrow 3\text{CO}_2(g) + 4\text{H}_2\text{O}(g)$, $\Delta H_{rxn} = -2044$ kJ

• Interpretation: 1 mol $\text{C}_3\text{H}_8$ releases 2044 kJ of energy.

Calorimetry at Constant Pressure

Coffee-Cup Calorimeter

Calorimetry is used to measure the heat exchanged in a chemical reaction. At constant pressure, the heat measured equals the enthalpy change. The coffee-cup calorimeter is a common device for these measurements.

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

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

Hess's Law

Summing Enthalpy Changes

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 each step. This allows calculation of $\Delta H$ for reactions that are difficult to measure directly.

• If a reaction is reversed, the sign of $\Delta H$ is reversed.

• If a reaction is multiplied by a factor, $\Delta H$ is multiplied by the same factor.

• $\Delta H_{overall} = \sum \Delta H_{steps}$

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

Definitions and Calculations

The standard enthalpy of formation is the enthalpy change for the formation of 1 mole of a compound from its elements in their standard states. The standard enthalpy change for a reaction can be calculated using the enthalpies of formation:

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

• The $\Delta H_f^\circ$ for any element in its standard state is zero.

Bond Energies and Reaction Enthalpy

Estimating $\Delta H_{rxn}$ from Bond Energies

The enthalpy change for a reaction can be estimated using average bond energies. Breaking bonds requires energy (endothermic), while forming bonds releases energy (exothermic):

• $\Delta H_{rxn} = \sum \text{Bond Energies (bonds broken)} - \sum \text{Bond Energies (bonds formed)}$

• Bond breaking: $\Delta H > 0$

• Bond making: $\Delta H < 0$

Bond	Bond Energy (kJ/mol)
H–H	436
O=O	498
C–H	414
C=O	799
N≡N	946