Chemistry 1770 Final Study Guide: Gases and Intermolecular Forces

Chapter 10 - Gases

Deep Time and Atmospheric Temperature

The concept of deep time refers to understanding Earth's history over hundreds of thousands of years. Scientists estimate past atmospheric temperatures using ice cores.

• Ice Core Analysis: Glaciers form from layers of snow that compress into ice over time. The top layers are younger, while deeper layers are older.

• Age Determination: The age of ice is determined by its depth in the glacier; deeper ice is older.

• Gas Trapping: Air bubbles trapped in ice contain ancient atmospheric gases, allowing temperature estimation.

Role of Gas Velocity Distribution (Boltzmann Distribution)

• Boltzmann Distribution: Describes the spread of molecular speeds in a gas.

• Temperature: Higher temperatures increase average molecular speed.

• Isotopes: Heavier isotopes move slower; their distribution helps infer past temperatures.

Kinetic Molecular Theory

The kinetic molecular theory explains the behavior of gases based on molecular motion.

• Postulates:

  1. Gas particles are in constant, random motion.

  2. Collisions are elastic; no energy is lost.

  3. Volume of gas particles is negligible compared to container volume.

  4. No intermolecular forces act between particles.

  5. Average kinetic energy is proportional to temperature.

• Distribution of Speeds: Lighter molecules move faster; higher temperatures broaden the speed distribution.

• Comparison: At the same temperature, lighter gases have higher average speeds than heavier gases.

Pressure

• Definition: Pressure is the force exerted per unit area.

• Formula: $P = \frac{F}{A}$

• Units: Common units include atm, Pa, mmHg, and torr.

• Conversions: 1 atm = 101,325 Pa = 760 mmHg = 760 torr

Combined Gas Law

The combined gas law relates pressure, volume, and temperature for a fixed amount of gas.

• Formula: $\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$

• Historical Gas Laws: If one variable is constant, the equation simplifies to Boyle's, Charles's, or Gay-Lussac's law.

Ideal Gas Law

• Formula: $PV = nRT$

• Variables: P = pressure, V = volume, n = moles, R = gas constant, T = temperature (K)

• Gas Constant: $R = 0.0821$ L·atm·mol–1·K–1 or $R = 8.314$ J·mol–1·K–1

• Calculations: Solve for any variable if the other three are known.

• Stoichiometry: Use the ideal gas law to relate moles of gas to volume in chemical reactions.

• Density and Molar Mass: $\text{Density} = \frac{PM}{RT}$, where M is molar mass.

• Application: Density of water vapor affects storm strength, such as hurricanes.

Partial Pressure and Dalton's Law

• Partial Pressure: The pressure exerted by a single gas in a mixture.

• Dalton's Law: $P_{\text{total}} = P_1 + P_2 + \ldots + P_n$

• Mole Fraction: $X_i = \frac{n_i}{n_{\text{total}}}$

• Partial Pressure Formula: $P_i = X_i \times P_{\text{total}}$

Chapter 11 - Intermolecular Forces

Types of Intermolecular Forces

Intermolecular forces are attractions between molecules, affecting physical properties like boiling and melting points.

• Dispersion Forces (London Forces):

  • Present in all molecules.

  • Strength increases with molecular size and mass.

• Dipole-Dipole Interactions:

  • Occur in molecules with permanent dipoles (polar molecules).

  • Example: HCl, SO2

• Hydrogen Bonding:

  • Occurs when H is bonded to N, O, or F.

  • Strongest among small molecules.

  • Example: Water (H2O), ammonia (NH3)

• Ranking (Small Molecules):

  1. Hydrogen bonding (strongest)

  2. Dipole-dipole

  3. Dispersion (weakest)

Vapor Pressure

• Measurement: Vapor pressure is measured by sealing a liquid in a container and observing the equilibrium pressure of its vapor.

• Relation to Intermolecular Forces: Stronger intermolecular forces result in lower vapor pressure.

Enthalpy of Vaporization ($\Delta H_{\text{vap}}$)

• Definition: The energy required to convert one mole of liquid to vapor at constant pressure.

• Formula: $\Delta H_{\text{vap}}$ (units: kJ/mol)

• Applications: Water's high $\Delta H_{\text{vap}}$ is important for cooling (sweating), climate regulation, and steam engines.

Hydrogen Bonding in Living Systems

• Role: Hydrogen bonds stabilize DNA structure, proteins, and influence water's properties in biological systems.

Definition of a Foam

• Foam: A colloidal system where gas bubbles are dispersed in a liquid or solid.

Useful Constants

• Avogadro's Number: $N_a = 6.022 \times 10^{23}$

• Gas Constant: $R = 0.0821$ L·atm·mol–1·K–1 or $R = 8.314$ J·mol–1·K–1

• Planck's Constant: $h = 6.63 \times 10^{-34}$ J·s

• Speed of Light: $c = 3.00 \times 10^8$ m·s–1