CHEM 205 Physical Chemistry Study Notes

Course Content

Part I: Thermodynamics
Part II: Spectroscopy
Part III: Kinetics

Part I: Thermodynamics

Purpose of Thermodynamics: - Establishes appropriate state functions to determine chemical systems' tendencies to change. - Central to chemistry and biological processes; explains why reactions occur and what conditions are needed for a reaction to proceed.

1. Introduction: Properties of Gases

Gases are critical in many applications like heat engines and refrigerators.
The gas phase is the simplest state to analyze theoretically, providing useful generalizations.
Understanding thermodynamic concepts will initially focus on gases due to their simplicity and generality.

2. State Functions and Equations of State

State of a System: Defined by a set of properties, referred to as state functions including: - Pressure (p) - Volume (V) - Temperature (T) - Number of moles (n)
Related by an equation of state: - For ideal gases, $pV = nRT$ (Ideal Gas Equation). - Alternative form: $pV_m = RT$ where $V_m = V/n$ (molar volume).

3. Ideal Gas Law

Ideal gas equation is crucial for understanding the behavior of gases under various conditions: - $p:$ pressure - $V:$ volume - $n:$ number of moles - $R:$ ideal gas constant - $8.314 ext{ J K}^{-1} ext{ mol}^{-1}$ - other units: $0.082 ext{ L atm K}^{-1} ext{ mol}^{-1}$ , $62.36 ext{ L Torr K}^{-1} ext{ mol}^{-1}$ . - $T:$ temperature, where $K = °C + 273.15$

4. Pressure Units

Pressure Units: - SI: Pascal (Pa) - 1 bar = 10^5 Pa = 100 kPa - 1 atm = 101.325 kPa - 1 atm = 760 Torr. - Weather maps use isobars indicating constant atmospheric pressure.

5. Gas Response to Change

Example Calculation: Balloon Volume Change - Given input: balloon radius = 2.5 m, pressure = 1.01325 bar, temperature = 25°C. - Use the ideal gas law for calculations: - $n = rac{pV}{RT}$ - Results: - Amount of helium needed: $n = 2675.35 ext{ mol}$ - Volume when temperature increases: $V_{new} = 66.55 ext{ m}^3$ .

6. Kinetic Model of Gases, Internal Energy and Temperature

The kinetic model interprets the ideal gas law: - Assumptions of a perfect gas: 1. Molecules are in random motion. 2. Molecules are infinitely small points. 3.Travel in straight lines until collisions (elastic collisions). 4. No interactions between molecules, except upon collision.
Pressure from a single molecule in a box with mass $m$ moving at velocity $v$ is derived: - $P_i = rac{mv_{x,i}^2}{V}$
Total pressure: $P = rac{Nm\bar{v}^2}{3V}$ (where $\bar{v}$ is the mean square velocity).
Internal energy $U$ is a function of temperature only: - For ideal gas, $U = (3/2)nRT$

7. Equipartition Principle

Each degree of freedom contributes $rac{1}{2}RT$ per mole to the internal energy. - Translational: contributes $rac{3}{2}RT$ (3 degrees of freedom). - Rotational: contributes $rac{2}{2}RT$ for diatomics (2 degrees).
At high temperature, vibrational contributions become significant, but usually, diatomic gases (like $N_2$ ) are treated with: - $U = rac{5}{2}RT$ at room temperature.

8. Real Gases and Van der Waals Equation

The Van der Waals equation accounts for: - Repulsive interactions based on the size of molecules (varies with $b$ ) - Attractive forces between molecules (affects the pressure calculation).
Equation: $\bigg(p + rac{a n^2}{V^2}\bigg)(V - nb) = nRT$

9. Compressibility Factor

$z = rac{pV}{nRT}$ - For an ideal gas, $z = 1$ . At moderate pressures, $z$ often has a linear relationship.
Virial Equation: - $p = rac{nRT}{V_{m}} + B_2(T) rac{n^2}{V_{m}^{2}} + B_3(T) rac{n^3}{V_{m}^{3}} + …$

10. Thermodynamic Laws Overview

Zeroth Law: Defines temperature
First Law: Conservation of energy; internal energy $U$ is a state function.
Second Law: Direction of spontaneous processes; entropy increases.
Third Law: Absolute entropy at 0 K.

11. System Properties

System: Interested part; Surroundings: Rest of universe; Boundary: Interface.

12. Types of Systems

Open: Exchange both energy and matter
Closed: Exchange energy only
Isolated: No exchange.

13. Thermodynamics Laws Applied

First Law Applied: Closed System: $ΔU = q + w$ .
State functions include internal energy $U$ , while $q$ and $w$ are path dependent.

14. Heat Exchange in Systems

Heat (q): > 0 means heat absorbed; < 0 expelled.
Work (w): Positive when done on system, negative when done by the system.

15. Reversible vs Irreversible Processes

Reversible: Infinitely small changes; both system & surroundings return to initial states.
Irreversible: Cannot return to initial states without changes in surroundings.

16. Specific Process Types

Isothermal: constant temperature.
Isobaric: constant pressure.
Isochoric: constant volume.
Adiabatic: no heat exchange.
Exothermic: heat released; Endothermic: heat absorbed.

17. Work Assignments and Results

Work calculations during expansions or compressions in equipment.
When calculating work done during stressed variations (system under external pressure) conversions are addressed.
Equations derived:
$dw = -pex dV$ and $w = rac{- ext{Pex}(Vfinal - Vinitial)}{dim(V)}$

18. Enthalpy (H)

$H = U + PV$ defined as a state function as well.
Calculation of changes at constant volume and pressure.

19. Measurements of Heat (Calorimetry)

Principles of calorimetry relate to heat capacity.
Heat capacity is material dependent; $C = dq/dT$

20. Specific Heat Capacities

Comparison of materials using their specific heat capacities, e.g., copper, water, etc., in J/K.

21. Colligative Properties

Modifications to boiling/freezing points caused by the introduction of solutes.
Calculations include equations for boiling point elevation and freezing point depression.

22. Osmotic Pressure

Concept and definition of osmotic pressure as driven by concentration differences across membranes.
Key formulas and implications.

23. Donnan Equilibrium and its Implications

Definition relates to ion distribution across semi-permeable membranes under equilibrium conditions.

Summary

Physical chemistry draws connections between thermodynamics, kinetics, and overall chemistry behaviors, providing critical insights into material properties and reactions.