Chapter 7: Thermochemistry and Energy in Chemical Systems

Thermochemistry and Energy

Introduction to Energy

Energy is a fundamental concept in chemistry, describing the capacity to do work or produce heat. In chemical systems, energy can be transferred and transformed, playing a crucial role in physical and chemical changes.

• Energy: The capacity to do work.

• Work: The result of a force acting through a distance (e.g., pushing a box on the floor).

• Heat: The flow of energy caused by a temperature difference between objects.

• Objects exchange energy through heat and work.

Types of Energy

Energy exists in various forms, each relevant to chemical and physical processes.

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

• Thermal Energy: Energy associated with the temperature of an object.

• Potential Energy: Energy due to the position or composition of an object.

• Chemical Energy: Energy stored in the relative positions of electrons and nuclei in atoms and molecules; a form of potential energy.

Conservation of Energy

Law of Conservation of Energy

The law of conservation of energy states that energy can neither be created nor destroyed, only transferred or transformed.

• Energy can be transferred from one object to another.

• The universe is considered an isolated system; its total energy is constant.

System and Surroundings

In thermochemistry, the system is the part of the universe under study, while the surroundings are everything else.

Units of Energy

Common Energy Units

Energy is measured in several units, depending on context.

• Joule (J): The SI unit of energy. $1\,\text{J} = 1\,\text{kg} \cdot \text{m}^2/\text{s}^2$

• Kilojoule (kJ): $1\,\text{kJ} = 1000\,\text{J}$

• Calorie (cal): The amount of energy required to raise the temperature of 1 g of water by 1°C. $1\,\text{cal} = 4.184\,\text{J}$

• Calorie (Cal): Also known as a kilocalorie, used in nutrition. $1\,\text{Cal} = 1000\,\text{cal}$

First Law of Thermodynamics

Definition and Implications

The first law of thermodynamics states that the total energy of the universe is constant. Energy can be transferred between the system and surroundings, but the total remains unchanged.

• Internal Energy (E): The sum of kinetic and potential energies of all particles in the system.

• State Function: A property whose value depends only on the state of the system, not on the path taken to reach that state.

Change in Internal Energy

The change in a state function is the difference between its final and initial values.

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

• For a chemical system: $\Delta E = E_{\text{products}} - E_{\text{reactants}}$

• Example: $\text{C} + \text{O}_2 \rightarrow \text{CO}_2$

If the reaction is reversed, the sign of $\Delta E$ changes.

• $\Delta E_{\text{system}} < 0$, $\Delta E_{\text{surrounding}} > 0$ (energy flows out of the system)

• $\Delta E_{\text{system}} > 0$, $\Delta E_{\text{surrounding}} < 0$ (energy flows into the system)

The relationship between heat, work, and internal energy:

• $\Delta E = q + w$

• Where $q$ is heat and $w$ is work.

Quantifying Heat

Temperature and Heat Transfer

Temperature measures the thermal energy within a sample. Heat is the transfer of thermal energy from a hotter object to a cooler one.

• Thermal energy always flows from higher to lower temperature.

• Thermal Equilibrium: When two objects reach the same temperature, no net heat transfer occurs.

Heat Capacity

Heat capacity quantifies a system's ability to absorb thermal energy without a large temperature change.

• Heat Capacity (C): The quantity of heat required to change the temperature of a system by 1°C.

• Equation: $q = C \times \Delta T$

• Higher heat capacity means smaller temperature change for a given amount of absorbed heat.

• Heat capacity is an extensive property (depends on amount of material).

Specific and Molar Heat Capacity

• Specific Heat Capacity (C_s): Amount of heat required to raise the temperature of 1 g of a substance by 1°C. Intensive property (does not depend on amount).

• Molar Heat Capacity: Amount of heat required to raise the temperature of 1 mole of a substance by 1°C.

Equation for heat transfer using specific heat:

• $q = m \times C_s \times \Delta T$

Example Calculation

• How much heat is absorbed by a penny as it warms from -8.0°C to 37.0°C? Assume mass = 3.10 g, $C_s$ (Cu) = 0.385 J/g°C.

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

Thermal Energy Transfer

Heat Exchange Between Substances

When two substances at different temperatures are mixed, heat is transferred until thermal equilibrium is reached.

• Heat lost by one substance equals heat gained by the other: $q_{\text{lost}} = -q_{\text{gained}}$

Example Calculation

• 32.5 g of Al at 45.8°C is submerged in 105.3 g of water at 15.4°C. Find the final temperature at equilibrium. $C_s$ (Al) = 0.903 J/g°C, $C_s$ (water) = 4.18 J/g°C.

• Set up: $q_{\text{Al}} + q_{\text{water}} = 0$

*Additional info: These notes cover the foundational concepts of thermochemistry, including energy types, conservation laws, heat capacity, and heat transfer calculations, which are essential for understanding energy changes in chemical reactions.*