Chapter 10: Thermodynamics – Energy Changes in Chemical Reactions

Thermodynamics: Energy Changes in Chemical Reactions

Introduction to Thermodynamics

Thermodynamics is the study of energy flow and transformation in chemical systems. In chemistry, it is essential to understand how energy is transferred as heat and work during chemical reactions, and how these changes affect the system and its surroundings.

Energy and Energy Changes

Kinetic and Potential Energy

• Kinetic Energy (Ek): The energy of motion, given by the equation: $E_k = \frac{1}{2}mu^2$ where m is mass and u is velocity.

• Thermal Energy: A form of kinetic energy associated with the random motion of atoms and molecules; measured with a thermometer.

• Potential Energy: Stored energy due to position or arrangement.

  • Electrostatic Energy: Results from interactions between charged particles.

  • Chemical Energy: Stored within the structural units (bonds) of chemical substances.

Example: The combustion of a hydrocarbon (e.g., (CH3)3CCH2CH(CH3)2 + O2 → CO2 + H2O + heat) converts potential energy in chemical bonds to kinetic energy (heat and light).

Energy Units

• Joule (J): The SI unit of energy. $1\ \text{J} = 1\ \text{kg} \cdot \text{m}^2 \text{s}^{-2}$ $1\ \text{J} = 1\ \text{N} \cdot \text{m}$ (when discussing force)

• Calorie (cal): $1\ \text{cal} = 4.184\ \text{J}$ $1000\ \text{cal} = 1\ \text{Calorie}$ (food calorie) 1 cal is the energy required to raise the temperature of 1 g of H2O by 1°C.

Energy Changes in Chemical Reactions

System and Surroundings

• System: The part of the universe being studied (often the reaction vessel).

• Surroundings: Everything else (e.g., the laboratory, the observer).

Energy can flow as heat between the system and surroundings during a chemical reaction.

Thermodynamics vs. Thermochemistry

• Thermodynamics: The study of the flow and transformation of energy.

• Thermochemistry: The study of heat (thermal energy transfer) in chemical reactions.

Exothermic and Endothermic Processes

• Exothermic Process: Heat is transferred from the system to the surroundings. The system's potential energy decreases. Example: $2\ \text{H}_2(g) + \text{O}_2(g) \rightarrow 2\ \text{H}_2\text{O}(l) + \text{energy}$

• Endothermic Process: Heat is absorbed by the system from the surroundings. The system's potential energy increases. Example: $\text{Energy} + 2\ \text{HgO}(s) \rightarrow 2\ \text{Hg}(l) + \text{O}_2(g)$

States and State Functions

Thermodynamics tracks changes in the state of a system, defined by macroscopic properties such as composition, energy, temperature, pressure, and volume.

• State Function: A property that depends only on the initial and final states, not on the path taken (e.g., energy, pressure, volume, temperature).

First Law of Thermodynamics

The first law states that energy can be converted from one form to another but cannot be created or destroyed (Law of Conservation of Energy).

• Change in internal energy: $\Delta U = U_{\text{final}} - U_{\text{initial}}$

• For chemical reactions: $\Delta U = U_{\text{products}} - U_{\text{reactants}}$

Example: For $2\ \text{Mg}(s) + \text{O}_2(g) \rightarrow 2\ \text{MgO}(s)$, $\Delta U = [\text{energy content of 2 mol MgO(s)}] - [\text{energy content of 2 mol Mg(s)} + \text{energy content of 1 mol O}_2(g)]$

If the reaction releases heat, $\Delta U < 0$ (exothermic).

Work (w) and Heat (q)

• $\Delta U_{\text{sys}} = q + w$

• q: Heat released or absorbed by the system

• w: Work done on or by the system (often due to volume change)

• $\Delta U$ is a state function; $q$ and $w$ are path functions.

Sign Conventions:

• Heat into system (endothermic): $+q$

• Heat released by system (exothermic): $-q$

• Work done by system: $-w$

• Work done on system: $+w$

Enthalpy (H)

Definition and Measurement

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

• Enthalpy is a state function and is easier to measure than internal energy.

• At constant pressure: $\Delta H = q_p$ (heat at constant pressure)

• At constant volume: $\Delta U = q_v$ (heat at constant volume)

• Relationship: $\Delta H = \Delta U + P\Delta V$

Enthalpy Change in Reactions

• For a chemical reaction: $\Delta H = H_{\text{products}} - H_{\text{reactants}}$

• $\Delta H > 0$: Endothermic reaction

• $\Delta H < 0$: Exothermic reaction

Thermochemical Equations

Thermochemical equations show the balanced chemical reaction and the associated enthalpy change ($\Delta H$), which is a molar quantity (per mole of reaction).

• Example (Endothermic): $\text{H}_2\text{O}(s) \rightarrow \text{H}_2\text{O}(l)\quad \Delta H = +6.01\ \text{kJ mol}^{-1}$ Requires 6.01 kJ to melt 1 mole of ice.

• Example (Exothermic): $\text{CH}_4(g) + 2\ \text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\ \text{H}_2\text{O}(l)\quad \Delta H = -890.4\ \text{kJ mol}^{-1}$ 890.4 kJ released when 1 mole of CH4 reacts.

Manipulating Thermochemical Equations

1. Always specify the physical states of reactants and products.

2. When multiplying an equation by a factor n, multiply $\Delta H$ by the same factor. Example: $3\ \text{C}(s) + 3\ \text{O}_2(g) \rightarrow 3\ \text{CO}_2(g)\quad \Delta H = -1181\ \text{kJ mol}^{-1}$

3. Reversing an equation changes the sign of $\Delta H$ but not its magnitude. Example: $\text{CO}_2(g) \rightarrow \text{C}(s) + \text{O}_2(g)\quad \Delta H = +393.5\ \text{kJ mol}^{-1}$

Calorimetry

Measuring Heat Changes

• Calorimetry: The experimental measurement of heat changes in a process.

• Specific Heat (s): Heat required to raise the temperature of 1 g of a substance by 1°C. Units: J g-1 °C-1

• Heat Capacity (C): Heat required to raise the temperature of an object by 1°C. Units: J °C-1

• If something gains heat, another object loses that heat: $q_{\text{object 1}} = -q_{\text{object 2}}$

Formulas for Calorimetry

• If specific heat (s), mass (m), and temperature change ($\Delta T$) are known: $q = sm\Delta T$

• If heat capacity (C) and $\Delta T$ are known: $q = C\Delta T$

• Relationship: $sm = C$ (specific heat × mass = heat capacity)

Table: Specific Heats of Substances

Substance	Specific heat (J g-1 K-1)
Water	4.184
Gold	0.129
Aluminum	0.900
Iron	0.444

Example Calculation

Calculate the energy required to heat 95.0 g of water from 22.5°C to 95.5°C:

• $q = sm\Delta T$

• $q = (4.184\ \text{J g}^{-1}\ ^\circ\text{C}^{-1})(95.0\ \text{g})(73.0\ ^\circ\text{C})$

• $q = 2.90 \times 10^4\ \text{J}$ or $29.0\ \text{kJ}$

Types of Calorimetry

• Constant Pressure Calorimetry ("coffee-cup calorimeter"): - Used for reactions in solution (e.g., neutralization, dissolution). - System: reactants and products; Surroundings: water in calorimeter. - $q_{\text{system}} = -q_{\text{surroundings}}$

• Constant Volume Calorimetry ("bomb calorimeter"): - Used for combustion reactions. - Isolated system; sample is ignited in a steel container. - $q_{\text{rxn}} = -C_{\text{cal}} \Delta T$

Example: Bomb Calorimeter Calculation

A snack chip (2.35 g) is burned in a bomb calorimeter with heat capacity 38.57 kJ °C-1. The temperature rises by 2.70°C. Calculate the energy in kJ g-1 for the chip:

• $q = C \Delta T = (38.57\ \text{kJ} \ ^\circ\text{C}^{-1})(2.70\ ^\circ\text{C}) = 104.139\ \text{kJ}$

• Per gram: $104.139\ \text{kJ} / 2.35\ \text{g} = 44.3\ \text{kJ g}^{-1}$

System vs. Surroundings in Calorimetry

• System: The reaction, piece of metal, or whatever causes heat flow/change.

• Surroundings: Water and calorimeter.

• Heat lost by system = heat gained by surroundings, and vice versa.

Choosing the Right Calorimetry Equation

• Bomb calorimeter (constant volume): Use when heat capacity of calorimeter is given or needs to be found; used for combustion.

• Coffee cup calorimeter (constant pressure): Use for reactions in solution or when both mass of water and reactants are given.

Additional info:

• Some slides and handwritten notes included worked examples and diagrams for calorimetry problems, reinforcing the application of $q = sm\Delta T$ and $q = C\Delta T$ in practical scenarios.

• Further sections (not shown in these slides) would likely cover Hess's Law, standard enthalpies of formation, and bond enthalpies, which are also key topics in thermochemistry.