chapter 5 lec 1

Thermochemistry: Energy, Work, and Heat in Chemical Systems

5.1 Energy Basics

Thermochemistry is the study of energy changes, particularly heat, that accompany chemical reactions and physical changes. Understanding the different forms of energy and how they are transferred is essential in chemistry.

• Energy: The capacity to do work. In chemistry, work is a directed energy change resulting from a chemical process.

• Work: Defined as force multiplied by distance. In chemistry, it often refers to energy transfer due to volume changes in gases.

Types of Energy

• Kinetic Energy (KE): Energy of motion. For a moving object, it is given by $KE = \frac{1}{2}mv^2$ where m is mass and v is velocity.

• Potential Energy (PE): Energy due to position or composition. For example, water behind a dam or a rock at the top of a hill.

• Radiant Energy: Energy from electromagnetic radiation, such as sunlight. Drives processes like photosynthesis and influences climate.

• Thermal Energy: Associated with the random motion of atoms and molecules. Related to temperature; higher temperature means greater molecular motion and higher thermal energy.

• Chemical Energy: Stored within the structural units of chemical substances. Determined by the type and arrangement of atoms in molecules. Released or absorbed during chemical reactions.

Energy Conversion: All forms of energy can be converted from one form to another. For example, radiant energy from the sun is converted to thermal energy on the skin, and chemical energy in food is converted to kinetic energy during exercise.

Law of Conservation of Energy (First Law of Thermodynamics)

• Energy cannot be created or destroyed, only converted from one form to another.

• The total energy of the universe is constant.

Work and Heat in Chemical Systems

In chemical processes, energy can be transferred as heat (q) or work (w).

• If a system gives up heat to the surroundings (exothermic, $q = -$), or does work on the surroundings ($w = -$), its internal energy decreases.

• If heat is added to the system (endothermic, $q = +$), or work is done on the system ($w = +$), its internal energy increases.

Work Done by Expanding or Compressing Gases

• Work is often associated with volume changes in gases, such as in pistons or biological systems (lungs).

• For a gas expanding or compressing against a constant external pressure:

$w = -P\Delta V$

• $\Delta V = V_{f} - V_{i}$ (change in volume)

• Units: 1 L·atm = 101.3 J

• If $\Delta V > 0$ (expansion), $w$ is negative (work done by the system).

• If $\Delta V < 0$ (compression), $w$ is positive (work done on the system).

Example: Calculating Work Done by a Gas

• Inflating a balloon from 0.100 L to 1.85 L against 1.00 atm:

$w = -P\Delta V = -(1.00\ \text{atm})(1.85\ \text{L} - 0.100\ \text{L}) = -1.75\ \text{L·atm}$ $w = -1.75\ \text{L·atm} \times \frac{101.3\ \text{J}}{1\ \text{L·atm}} = -177\ \text{J}$

Example: Internal Energy Change ($\Delta E$)

• When fuel is burned in a cylinder, volume expands from 0.255 L to 1.45 L against 1.02 atm, and 875 J is emitted as heat:

$\Delta E = q + w$ $w = -P\Delta V = -(1.02\ \text{atm})(1.45\ \text{L} - 0.255\ \text{L}) \times 101.3\ \text{J/L·atm} = -123.5\ \text{J}$ $\Delta E = -875\ \text{J} + (-123.5\ \text{J}) = -998.5\ \text{J} \approx -999\ \text{J}$

This process is exothermic (energy released).

State Functions

• State Function: A property whose value depends only on the current state, not the path taken (e.g., internal energy, volume, pressure).

• Work and heat are not state functions; they depend on the process path.

Example: Energy Change with Compression

• Gas is compressed (work done on the system = 891 J), and 335 J of heat is transferred from the gas to the surroundings:

$\Delta E = q + w = -335\ \text{J} + 891\ \text{J} = +556\ \text{J}$

This process is endothermic (energy absorbed).

Specific Heat and Heat Capacity

Understanding how substances absorb or release heat is crucial in thermochemistry.

• Specific Heat (c): The amount of heat required to raise the temperature of 1 gram of a substance by 1°C.

• Heat Capacity (C): The amount of heat required to raise the temperature of a given quantity of a substance by 1°C.

• Relationship: $C = m c$ where m is mass in grams.

Calculating Heat Transfer

The amount of heat (q) absorbed or released by a substance can be calculated as:

$q = c \times m \times (T_{\text{final}} - T_{\text{initial}})$

• c: specific heat (J/g·°C)

• m: mass (g)

• Tfinal and Tinitial: final and initial temperatures (°C)

Example: Cooling of Iron

• 21.2 g iron cools from 91.6°C to 25.1°C; $c = 0.449$ J/g·°C:

$q = 0.449\ \text{J/g·°C} \times 21.2\ \text{g} \times (25.1 - 91.6)\ ^\circ\text{C} = -633\ \text{J}$

Negative sign indicates an exothermic process (heat released).

Example: Heating Iron

• 1.2 g iron, $q = 11.1$ J, $T_{\text{initial}} = 20.0^\circ$C. Find $T_{\text{final}}$:

$q = c m (T_{\text{final}} - T_{\text{initial}})$ $11.1 = 0.449 \times 1.2 \times (T_{\text{final}} - 20.0)$ $T_{\text{final}} = 40.6^\circ \text{C}$

Since $q$ is positive, the process is endothermic (heat absorbed).

Example: Calculating Specific Heat

• 14.2 g 18K gold ring, $q = 22.1$ J, $T_{\text{initial}} = 16.7^\circ$C, $T_{\text{final}} = 28.8^\circ$C:

$c = \frac{q}{m (T_{\text{final}} - T_{\text{initial}})} = \frac{22.1}{14.2 \times (28.8 - 16.7)} = 0.129\ \text{J/g·°C}$

Table: Specific Heats of Selected Substances

Substance	Specific Heat (J/g·°C)
Aluminum (Al)	0.897
Copper (Cu)	0.385
Water (H2O)	4.184
Gold (Au)	0.129
Iron (Fe)	0.449

Additional info: The specific heat of water is much higher than most metals, which is why water is effective for thermal regulation in biological and environmental systems.