Chapter 10: Properties of Gases

Properties and Measurement of Gases

Gases are one of the fundamental states of matter, characterized by their ability to expand and fill any container. Understanding their properties and behavior is essential in chemistry.

• Properties of Gases: Gases have low density, are highly compressible, and mix evenly and completely when confined to the same container.

• Pressure: The force exerted by gas molecules as they collide with the surfaces of their container. Common units include atmospheres (atm), pascals (Pa), torr, and mmHg.

• Pressure Measurement: Pressure is measured using devices such as barometers (for atmospheric pressure) and manometers (for gas samples).

• Pressure Conversions: Conversion factors are provided on exams, but it is important to recognize relationships such as 1 atm = 760 mmHg = 101.325 kPa.

Gas Laws

Gas laws describe the relationships between pressure, volume, temperature, and amount of gas.

• Ideal Gas Law: Relates the four variables of a gas sample.

• Two-State (Combined) Gas Law: Used when a gas sample changes conditions.

• Molar Mass of a Gas: Can be determined from mass, pressure, volume, and temperature.

• Density of a Gas: The mass per unit volume of a gas.

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

• Standard Temperature and Pressure (STP): Defined as 0°C (273.15 K) and 1 atm. At STP, 1 mol of any ideal gas occupies 22.4 L.

Dalton’s Law of Partial Pressures

In a mixture of non-reacting gases, the total pressure is the sum of the partial pressures of each component.

• Dalton’s Law:

• Mole Fraction (χ): The ratio of moles of a component to total moles in the mixture.

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

Kinetic Molecular Theory (KMT)

KMT explains the behavior of gases at the molecular level.

• Gas particles are in constant, random motion.

• Collisions between particles are elastic (no energy lost).

• Volume of gas particles is negligible compared to the container.

• No attractive or repulsive forces between particles (ideal gas assumption).

Root Mean Square Speed (μRMS)

The root mean square speed is a measure of the average speed of gas molecules.

• R: Gas constant (8.314 J/mol·K)

• T: Temperature in Kelvin

• M: Molar mass in kg/mol

Effusion and Diffusion

• Effusion: The process by which gas molecules escape through a tiny hole into a vacuum.

• Diffusion: The mixing of gases due to molecular motion.

• Graham’s Law relates rates of effusion/diffusion to molar mass:

Real Gases

• Real gases deviate from ideal behavior at high pressures and low temperatures due to intermolecular forces and finite molecular volume.

• Van der Waals equation corrects for these deviations (not shown in original notes).

Chapter 11: Intermolecular Forces and States of Matter

Review of Lewis Structures, Electronegativity, and Polarity

• Lewis Dot Structures: Diagrams showing valence electrons and bonding in molecules.

• Electronegativity: The ability of an atom to attract electrons in a bond. Higher electronegativity leads to polar bonds.

• Polar vs Non-Polar Bonds: Polar covalent bonds have unequal sharing of electrons; non-polar bonds have equal sharing.

• Molecular Polarity: Determined by both bond polarity and molecular shape (geometry).

Kinetic Energy and States of Matter

• States of matter (solid, liquid, gas) depend on kinetic energy and intermolecular forces.

• As kinetic energy increases (with temperature), substances move from solid to liquid to gas.

Intermolecular Forces (IMF)

IMFs are forces of attraction between molecules, affecting physical properties.

• Dipole-Induced Dipole: A polar molecule induces a dipole in a non-polar molecule. Polarizability refers to how easily the electron cloud is distorted.

• Dispersion (London) Forces: Present in all molecules, stronger in larger and more polarizable molecules. Shape also affects strength (more surface area = stronger dispersion).

• Ion-Dipole: Attraction between an ion and a polar molecule; important in hydration/solvation.

• Dipole-Dipole: Attraction between polar molecules.

• Hydrogen Bonding: A strong type of dipole-dipole interaction; occurs when H is bonded to N, O, or F. Not all substances can hydrogen bond.

Physical Properties Affected by IMF

• Boiling point, melting point, vapor pressure, viscosity, and surface tension are all influenced by the strength of IMFs.

• Hydrogen bonding increases boiling points.

Properties of Water

• Surface Tension: The energy required to increase the surface area of a liquid.

• Viscosity: Resistance to flow.

• Cohesion: Attraction between like molecules.

• Adhesion: Attraction between unlike molecules.

• Capillary Action: The ability of a liquid to flow in narrow spaces against gravity.

• Density of Water: Water is most dense at 4°C; as it cools below this, it becomes less dense due to hydrogen bonding and the formation of an open hexagonal structure in ice.

Physical States and Phase Diagrams

• Physical state depends on temperature, pressure, and strength of IMFs.

• Phase Diagrams: Graphs showing the state of a substance at various temperatures and pressures. Key features include triple point, critical point, and phase boundaries.

Chapter 13: Properties of Solutions

Solutions and Energy Changes

• Solution: A homogeneous mixture of two or more substances.

• Energy changes during solution formation include breaking solute and solvent interactions and forming new solute-solvent interactions.

Vapor Pressure and Raoult’s Law

• Vapor Pressure: The pressure exerted by a vapor in equilibrium with its liquid.

• Raoult’s Law (for non-volatile solutes):

• Adding a non-volatile solute lowers the vapor pressure of the solvent.

Vapor Pressure and Temperature: Clausius-Clapeyron Equation

• Describes how vapor pressure changes with temperature.

• : Enthalpy of vaporization

• : Gas constant

• : Temperature in Kelvin

• : Constant of integration

Molality (m)

• Molality: Moles of solute per kilogram of solvent.

Colligative Properties

Properties that depend only on the number of solute particles, not their identity.

• 1. Vapor Pressure Lowering: Addition of a non-volatile solute lowers the vapor pressure of the solvent.

• 2. Boiling Point Elevation: The boiling point of a solution is higher than that of the pure solvent.

• 3. Freezing Point Depression: The freezing point of a solution is lower than that of the pure solvent.

• 4. Osmotic Pressure: The pressure required to stop osmosis.

• van’t Hoff Factor (i): The number of particles into which a solute dissociates in solution (e.g., NaCl: i = 2).

• Measuring Molar Mass: Colligative properties can be used to determine the molar mass of an unknown solute.

Summary Table: Colligative Properties

Example: Calculating Boiling Point Elevation

• A solution is prepared by dissolving 0.5 mol of NaCl (i = 2) in 1 kg of water (KB = 0.512 °C·kg/mol). The boiling point elevation is:

°C

The new boiling point is 100.512 °C.

Additional info: For more detailed derivations and exceptions (e.g., non-ideal solutions, association/dissociation effects on i), consult your textbook.