Thermochemistry: Energy, Heat, and Work in Chemical Systems

Introduction to Thermochemistry

Thermochemistry is the study of energy changes, particularly heat, that occur during chemical reactions and physical changes of state. Understanding how energy interacts with matter is fundamental to predicting and controlling chemical processes.

• Energy interacts with matter

• Matter can contain energy

Key Definitions

• Exothermic & Endothermic Processes:

  • Exothermic: Processes where the system loses heat energy to the surroundings.

  • Endothermic: Processes where the system gains heat energy from the surroundings.

• System & Surroundings:

  • System: The part of the universe under study (e.g., the reactants in a reaction).

  • Surroundings: Everything else outside the system.

• Specific Heat Capacity (c): The amount of heat required to raise the temperature of one gram of a substance by one degree Celsius.

• Calorimeter: An instrument used to measure heat changes in chemical reactions.

• P-V Work (w): Work done by or on the system due to changes in pressure and volume.

• Enthalpy (ΔH): The heat content of a system at constant pressure.

• Formation Reactions: Chemical reactions that form one mole of a compound from its elements in their standard states.

Energy Basics

Nature and Measurement of Energy

Energy is a property of matter that enables it to do work. It cannot be created or destroyed, only transformed from one form to another. Thermodynamics is the study of these energy transformations.

• Unit of Energy: Joule (J)

• Joule Definition: $J = N \times m = \frac{kg \times m^2}{s^2}$

• Calorie: $1 \text{ cal} = 4.184 \text{ J}$

Forms of Energy

• Potential Energy (PE): Energy due to position. In chemistry, electrostatic potential energy is important for understanding bond energies. Electrostatic Energy Equation: $E_{el} = \frac{k Q_1 Q_2}{d}$ Where: $Q$ is charge, $d$ is distance, $k = 8.99 \times 10^9 \text{ J m}/\text{C}^2$

• Kinetic Energy (KE): Energy of motion. For molecules and atoms: $E_k = \frac{1}{2} m v^2$ Where: $m$ is mass (kg), $v$ is velocity (m/s)

Energy Transfer: Heat and Work

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

• Work (w): Energy transferred when a force moves an object over a distance. $w = F \times d$ In chemistry, work is often pressure-volume work: $w = -P \Delta V$

Heat Transfer and Measurement

Heat Transfer Between System and Surroundings

Heat can be transferred from the system to the surroundings or vice versa. The direction of heat flow determines whether a process is exothermic or endothermic.

• Loss of heat (-q): System's temperature falls; surroundings gain heat (+q).

• Gain of heat (+q): System's temperature rises; surroundings lose heat (-q).

Specific Heat Capacity

Each substance has a unique capacity to absorb heat, called specific heat capacity ($c$). It is defined as:

• $c = \frac{q}{m \Delta T}$

• Where: $q$ is heat (J), $m$ is mass (g), $\Delta T$ is temperature change ($T_f - T_i$)

This equation expresses "the amount of energy absorbed per gram, per change in temperature."

Example 1: Calculating Specific Heat

• Problem: An unknown metal (23.4 g) is heated to 100.0°C, transferred to 69.4 g of water, and the final temperature is 25.7°C. The metal releases -669.4 J of heat. Find the specific heat ($c$) of the metal.

• Steps:

  1. Identify system and surroundings.

  2. Match given values to the equation.

  3. Solve for $c$ using correct units and significant figures.

Example 2: Calculations Using Specific Heat

• Problem: 0.563 g NaCl absorbs 22.18 J of heat. Initial temperature is 20.5°C, $c = 5.05 \frac{J}{g \cdot °C}$. Find the final temperature.

• Steps:

  1. Rearrange $c = \frac{q}{m \Delta T}$ to solve for $\Delta T$.

  2. Plug in values and solve.

Calorimetry

Calorimetry is the measurement of heat flow. A calorimeter is used to measure heat changes indirectly, often at constant pressure.

• Key equation: $q_{surroundings} = -q_{system}$

• Standard calorimetry is usually done at constant pressure (P).

Common Set-Up for Calorimetry Problems

1. Calculate $q_{surroundings}$ (usually water): $q_{surroundings} = c \times m \times \Delta T$

2. Change sign to get $q_{system}$: $q_{system} = -q_{surroundings}$

Example 3: Calorimetry Calculations

• Problem: 0.563 g NaCl is dissolved in 100.0 mL water at 23.0°C; final temperature is 18.7°C. $c = 4.184 \frac{J}{g \cdot °C}$, $\rho = 1.00 \frac{g}{mL}$.

• Steps:

  1. Add masses to find total mass of solution.

  2. Calculate $q_{surroundings}$.

  3. Flip sign for $q_{system}$.

Bomb Calorimetry

A bomb calorimeter measures heat of combustion reactions at constant volume, minimizing heat loss to surroundings.

• Heat capacity (C): $q_{sample} = q_{bomb} = C \times \Delta T$

• Units for $C$: kJ/°C or J/K

Work, Internal Energy, and Enthalpy

Internal Energy (ΔE)

The internal energy of a system ($\Delta E$) is the sum of heat and work exchanged with the surroundings.

• $\Delta E = q + w$

Flow of Energy: Work

• Work (w): $w = F \times d$

• In chemistry, $w = -P \Delta V$

• Work has the opposite sign to $\Delta V$

Summary Table: Work, Heat, and Internal Energy

Type of Energy	Sign	Represents
q	+	Heat is added (heat comes in)
q	-	Heat is lost (heat goes out)
w	+	Receives work (work done upon)
w	-	Does work (work done by)
ΔE	+	Net gain (due to q and/or w gain)
ΔE	-	Net loss (due to q and/or w loss)

Enthalpy (ΔH)

Enthalpy is a measure of the total heat content of a system at constant pressure. It is especially useful for chemical reactions.

• Definition: $\Delta H = \frac{q_{system}}{\text{mol}_{system}}$

• Relationship to Internal Energy:

  • $\Delta H = \Delta E + P \Delta V$

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

Calculating Enthalpy

• Use $q_{system}$ from calorimetry and divide by moles of system.

• For reactions at constant pressure, $\Delta H$ is equivalent to $q_p$.

Example: Calorimetry to Enthalpy

• Problem: 0.563 g NaCl dissolved in 100.0 g water; $q_{system}$ calculated from calorimetry. Find enthalpy ($\Delta H$) per mole of NaCl.

• Steps:

  1. Calculate $q_{system}$.

  2. Convert mass of NaCl to moles.

  3. Divide $q_{system}$ by moles to get $\Delta H$.

Summary of Key Concepts

• Relationship between heat, work, and internal energy

• Connection between mass, specific heat, and temperature change

• How calorimetry is used to measure heat changes

• Difference between exothermic and endothermic processes

• Equations for energy calculations:

  • $q = m c \Delta T$

  • $\Delta E = q + w$

  • $w = -P \Delta V$

  • $\Delta H = \Delta E + P \Delta V$