MODULE 05: CHEMICAL THERMODYNAMICS — Study Notes Summary & Study Notes

🔥 Introduction

Chemical thermodynamics studies energy changes and transfers in chemical systems. It connects heat, work, and the direction of chemical processes using a set of fundamental laws and measurable state functions.

⚖️ Systems, Surroundings, and States

A system is the portion of the universe under study; everything else is the surroundings. Systems can be open, closed, or isolated. A state function depends only on the current state (e.g., internal energy, enthalpy, entropy), while path functions (e.g., heat $q$, work $w$) depend on the process.

🔁 First Law of Thermodynamics (Conservation of Energy)

The first law states that energy is conserved. For a closed system: $\Delta U = q + w$, where $\Delta U$ is change in internal energy, $q$ is heat added to the system, and $w$ is work done on the system. For pressure–volume work commonly: $w = -P_{ext}\Delta V$.

📦 Enthalpy and Constant-Pressure Processes

Enthalpy $H$ is defined as $H = U + PV$. At constant pressure, heat exchanged equals enthalpy change: $q_p = \Delta H$. Useful relations: $\Delta H = \Delta U + P\Delta V$ and for ideal gases, $\Delta H$ depends primarily on temperature.

🌡️ Calorimetry and Heat Capacity

Heat capacity $C$ relates heat and temperature change: $q = C\Delta T$. Molar heat capacity: $C_m = \frac{C}{n}$. In calorimetry experiments, use conservation of energy between system and calorimeter to determine $q$ values.

➕ Hess's Law

Hess's law: total enthalpy change for a reaction is the same regardless of pathway. This lets you combine known reaction enthalpies to find unknown $\Delta H$. Symbolically, enthalpies are additive when reactions are summed.

⚖️ Second Law of Thermodynamics and Entropy

The second law introduces entropy $S$ as a measure of disorder and dispersion of energy. For a spontaneous process in an isolated system: $\Delta S_{universe} > 0$. For a reversible process: $\Delta S = \frac{q_{rev}}{T}$. Total entropy change: $\Delta S_{universe} = \Delta S_{system} + \Delta S_{surroundings}$.

🧭 Gibbs Free Energy and Spontaneity

At constant temperature and pressure, the Gibbs free energy determines spontaneity: $\Delta G = \Delta H - T\Delta S$. If $\Delta G < 0$, the process is spontaneous; if $\Delta G > 0$, it is nonspontaneous; if $\Delta G = 0$, the system is at equilibrium.

Useful relation to equilibrium: $\Delta G = \Delta G^{\circ} + RT\ln Q$ and at equilibrium $\Delta G^{\circ} = -RT\ln K$, where $Q$ is the reaction quotient, $K$ is the equilibrium constant, $R$ is the gas constant, and $T$ is temperature in kelvins.

❄️ Third Law and Absolute Entropy

The third law states that a perfect crystalline substance has $S = 0$ at absolute zero ($0,\text{K}$). This provides a reference for calculating absolute entropies and allows tabulation of standard molar entropies $S^{\circ}$.

⚙️ Reversible vs Irreversible Processes

A reversible process proceeds infinitesimally close to equilibrium and maximizes work extraction; it also yields the minimum entropy generation. Real (irreversible) processes produce extra entropy and less useful work.

🔁 Thermodynamic Cycles and Heat Engines

Heat engines convert heat into work across cycles. Efficiency $\eta$ of a heat engine is $\eta = 1 - \frac{Q_C}{Q_H}$ for heat rejected $Q_C$ and heat absorbed $Q_H$. The Carnot efficiency (ideal reversible engine) is $\eta_{Carnot} = 1 - \frac{T_C}{T_H}$, showing temperature limits on efficiency.

⚗️ Chemical Equilibrium and Thermodynamics

Thermodynamics links energy changes to equilibrium composition through $\Delta G^{\circ} = -RT\ln K$. Changes in $T$ affect $K$ according to the van 't Hoff relationship (qualitative here): exothermic reactions shift with temperature changes based on enthalpy sign.

🧾 Standard States and Tabulated Values

Standard state quantities are indicated with a superscript circle: $\Delta H^{\circ}$, $\Delta G^{\circ}$, $S^{\circ}$. Standard conditions commonly mean $1,\text{bar}$ (or $1,\text{atm}$ historically) and specified temperature, often $298.15,\text{K}$.

🧩 Quick Reference Formulas

• First law: $\Delta U = q + w$
• PV work: $w = -P_{ext}\Delta V$
• Enthalpy: $H = U + PV$ and $q_p = \Delta H$
• Entropy (reversible): $\Delta S = \frac{q_{rev}}{T}$
• Gibbs: $\Delta G = \Delta H - T\Delta S$
• Relation to equilibrium: $\Delta G^{\circ} = -RT\ln K$

✅ Practical Tips

• Identify whether conditions are constant-$P$ or constant-$V$ to choose $\Delta H$ vs $\Delta U$.
• Use Hess's law to build complicated enthalpy changes from simpler steps.
• Check sign conventions carefully: $q$ positive for heat into system, $w$ positive for work done on system.
• For spontaneity at nonstandard conditions, compute $\Delta G = \Delta G^{\circ} + RT\ln Q$.

These notes summarize core concepts and formulas for MODULE 05: CHEMICAL THERMODYNAMICS. Review standard tables for numerical values ($\Delta H^{\circ}$, $S^{\circ}$, $\Delta G^{\circ}$) and practice applying formulas to sample problems.