Properties and Behavior of Gases

Characteristics of Common Gases

Many simple molecules such as H2, He, Ne, N2, O2, F2, Cl2, CO, NO, N2O, HCN, CO2, NH3 share certain properties:

• Small molecular size and low molecular mass

• Nonpolar or weakly polar (except for some like NH3 and HCN)

• Exist as gases at room temperature due to weak intermolecular forces

• Examples: Noble gases (He, Ne), diatomic molecules (O2, N2), simple compounds (CO, NH3)

Pressure and Gas Molecules

Pressure is a fundamental property of gases, resulting from collisions of gas molecules with the walls of their container.

• Definition: Pressure is the force exerted per unit area by gas molecules striking the container walls.

• Example: In a closed sphere, gas molecules move randomly and collide with the walls, creating pressure.

• Formula: , where P is pressure, F is force, and A is area.

Measuring Gas Pressure

Devices for Measuring Pressure

Gas pressure is commonly measured against atmospheric pressure using devices such as barometers and manometers.

• Barometer: Measures atmospheric pressure using a column of mercury. If atmospheric pressure decreases, the height of the Hg column decreases.

• Manometer: Measures the pressure of a gas sample relative to atmospheric pressure. The difference in mercury levels indicates the pressure of the gas.

• Units: Common units include atmospheres (atm), millimeters of mercury (mmHg), and pascals (Pa).

Gas Laws and Relationships

Boyle's Law

Boyle's Law describes the relationship between pressure and volume for a fixed amount of gas at constant temperature.

• Statement: As pressure increases, volume decreases (inverse relationship).

• Mathematical Expression: (at constant n and T)

• Graph: Pressure vs. Volume is a hyperbola.

Charles's Law

Charles's Law describes the relationship between volume and temperature for a fixed amount of gas at constant pressure.

• Statement: As temperature increases, volume increases (direct relationship).

• Mathematical Expression: (at constant n and P)

• Graph: Volume vs. Temperature is a straight line.

• At 0 K: Theoretically, volume would be zero, but this is not physically realistic because gases condense or solidify before reaching absolute zero.

Avogadro's Law and Stoichiometry

Avogadro's Law states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

• Statement: Volume is proportional to the number of moles of gas.

• Mathematical Expression:

• Application: Used in reaction stoichiometry to relate volumes and moles of gases.

The Ideal Gas Law

Equation of State

The Ideal Gas Law combines Boyle's, Charles's, and Avogadro's Laws into a single relationship:

• Formula:

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

• Gas constant: L·atm/(mol·K) or J/(mol·K)

• Density: , where M is molar mass

Using the Ideal Gas Law

• To solve problems: Identify which variables are held constant and which change.

• Combined Gas Law: (for a fixed amount of gas)

• Key considerations: Use for single-state problems; use the combined gas law for changes between states.

Partial Pressures and Mole Fractions

Dalton's Law of Partial Pressures

In a mixture of gases, each gas exerts a pressure independently of the others.

• Formula:

• Mole Fraction (X):

• Partial Pressure:

Non-Ideal Gases: Deviations from Ideality

Conditions for Ideal Gas Behavior

• Best conditions: High temperature and low pressure favor ideal behavior.

• Assumptions: Gases are point masses (no volume), no attractive forces, random motion.

Deviations from Ideality

• Volume effects: At high pressure, the volume occupied by gas molecules becomes significant.

• Attractive forces: At low temperature, intermolecular attractions reduce pressure.

Note: CO2 and NH3 deviate more due to stronger intermolecular forces.

van der Waals Equation

The van der Waals equation corrects for non-ideal behavior by accounting for molecular volume and intermolecular forces:

• Equation:

• a: Correction for attractive forces

• b: Correction for molecular volume

Observation: Larger values of "b" correspond to larger molecules.

Kinetic Molecular Theory and Gas Speeds

Average Molecular Speed

The kinetic molecular theory relates the temperature of a gas to the average speed of its molecules.

• Formula:

• Variables: R = 8.314 J/(mol·K), T = temperature (K), MM = molar mass (kg/mol)

• Applications: Used to calculate speed, diffusion, and effusion rates.

Diffusion and Effusion

• Diffusion: Movement of molecules from high to low concentration.

• Effusion: Escape of gas molecules through a small opening.

• Rate of Diffusion/Effusion:

Worked Examples and Applications

Stoichiometry and Gas Laws

• Example: Calculate grams of NH3 at given conditions using .

• Example: Identify an unknown gas from its density and pressure using .

Partial Pressures in Mixtures

• Example: Calculate partial pressures and mole fractions for a mixture of N2 and H2 forming NH3.

Non-Ideal Gas Calculations

• Example: Compare predicted pressures using the ideal gas law and van der Waals equation for CH4 at 0°C in a 250.0 mL flask.

Summary Table: Key Gas Laws

Additional info: Some context and explanations have been expanded for clarity and completeness, including definitions, formulas, and applications relevant to a General Chemistry course.