Thermochemistry 6.2: Internal Energy, State Functions, Heat, and Work

Chapter 6 - Thermochemistry

Introduction

Thermochemistry is the study of energy changes, particularly heat and work, that occur during chemical reactions and physical changes. This chapter focuses on the concepts of internal energy, state functions, heat capacity, and the quantification of heat and work in chemical systems.

Internal Energy and State Functions

Definition of Internal Energy

• Internal energy (U) is the total energy contained within a system, including kinetic and potential energies of particles.

• It is a state function, meaning its value depends only on the current state of the system, not on the path taken to reach that state.

State Functions vs. Path Functions

• State functions (e.g., internal energy, altitude) depend only on the initial and final states.

• Path functions (e.g., work, heat) depend on the specific process or path taken between states.

• Example: Traveling from one location to another, the change in altitude is a state function, while the calories burned (work) depends on the route and method.

Mathematical Representation

• The change in internal energy is given by: $\Delta U = U_{\text{final}} - U_{\text{initial}}$

• For a multi-step process: $\Delta U_{\text{total}} = \Delta U_1 + \Delta U_2$

System and Surroundings

Definitions

• System: The part of the universe under study (e.g., ice cubes).

• Surroundings: Everything outside the system (e.g., the glass of water).

Energy Exchange Example

• When ice cubes are added to water and melt, they absorb energy from the water.

• The temperature of the water decreases, indicating energy loss from the surroundings and gain by the system.

• Sign convention: If the system gains energy, $\Delta U_{\text{sys}} > 0$.

• Equation: $\Delta U = U_f - U_i$

Sign of $\Delta U$, $q$, and $w$

Definitions and Conventions

• q: Heat absorbed by the system (positive if absorbed, negative if released).

• w: Work done by the system (positive if done on the system, negative if done by the system).

• Internal energy change: $\Delta U = q + w$

• Example: If a balloon absorbs 150 J of heat and does 35 J of work by expanding, $\Delta U = 150 + (-35) = 115$ J.

Quantifying Heat and Work

Heat Capacity

• Heat capacity (C): The amount of energy required to raise the temperature of a substance by 1 K.

• Equation: $q = C \times \Delta T$

• Units: Joules per Kelvin (J·K-1).

Specific and Molar Heat Capacity

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

• Molar heat capacity ($C_n$): Amount of heat required to raise 1 mol of a substance by 1 K (or 1°C).

• Equations: $C_s = \frac{C}{m}$ $q = m \times C_s \times \Delta T$ $C_n = \frac{C}{n}$ $q = n \times C_n \times \Delta T$

Temperature Change Calculations

• Temperature change is calculated as: $\Delta T = T_f - T_i$

• Example: If a substance is heated from 10°C to 100°C, $\Delta T = 100 - 10 = 90$°C.

Table: Specific Heat Capacities of Common Substances

Substance	Specific Heat Capacity, $C_s$ (J·g-1·°C-1)
Water	4.184
Ethanol	2.440
Glass (Pyrex)	0.75
Sand	0.84
Copper	0.385
Aluminum	0.903
Granite	0.79
Blank (reference)	0.128

Applications and Examples

Thermal Energy Transfer and Equilibrium

• When two substances at different temperatures are mixed, heat flows from the hotter to the cooler substance until thermal equilibrium is reached.

• Equation for heat exchange: $q_{\text{system}} = -q_{\text{surroundings}}$

• Example: Mixing hot aluminum with water, calculate final temperature using heat capacities and masses.

Work in Chemical Systems

• Work is often associated with volume changes in gases.

• Equation for work at constant pressure: $w = -P \Delta V$

• Negative sign indicates work done by the system on the surroundings.

• Units: Pressure in Pascals (Pa), Volume in cubic meters (m3), Work in Joules (J).

Work in Chemical Reactions

• For reactions involving gases, the change in moles affects the volume and thus the work done.

• Equation: $w = -\Delta n_{\text{gas}} RT$

• Where $\Delta n_{\text{gas}}$ is the change in moles of gas, $R$ is the gas constant, and $T$ is temperature in Kelvin.

• Example: Combustion of methane at 298 K, calculate work done using change in moles of gas.

Summary of Key Concepts

• Internal energy is a state function; heat and work are path functions.

• Heat capacity quantifies the energy needed for temperature change.

• Specific heat capacity and molar heat capacity are important for calculations involving heat exchange.

• Work is significant in processes involving gases and volume changes.

• Understanding these concepts is essential for analyzing energy changes in chemical reactions.

Additional info: Some equations and examples have been expanded for clarity and completeness. Table entries are inferred from standard values in general chemistry textbooks.