Study Notes: Chapter 11 – Gases (CHMI032 Pre-Test 4)

Gases: Properties, Laws, and Calculations

Introduction to Gases

Gases are one of the fundamental states of matter, characterized by their ability to expand and fill any container, low density, and high compressibility. Understanding the behavior of gases is essential in chemistry, as it allows us to predict and explain phenomena in both laboratory and real-world contexts.

• Compressibility: Gases can be compressed easily, unlike solids and liquids.

• Independence of Particles: Gas particles move independently and are far apart compared to solids and liquids.

• Pressure: Gases exert pressure on the walls of their container due to collisions of particles.

Kinetic Molecular Theory

The Kinetic Molecular Theory explains the behavior of gases based on the motion of their particles.

• Postulates:

  • Gas particles are in constant, random motion.

  • The volume of individual gas particles is negligible compared to the volume of the container.

  • There are no significant attractive or repulsive forces between gas particles.

  • Collisions between gas particles and container walls are perfectly elastic.

  • The average kinetic energy of gas particles is proportional to the temperature in Kelvin.

• Implications: Explains properties such as pressure, temperature, and volume relationships.

Gas Pressure and Units

Pressure is a measure of the force exerted by gas particles colliding with the walls of a container.

• Definition: $P = \frac{F}{A}$, where P is pressure, F is force, and A is area.

• Common Units:

  • Atmosphere (atm)

  • Millimeters of mercury (mm Hg)

  • Torr

  • Pascals (Pa)

• Conversions:

  • 1 atm = 760 mm Hg = 101,325 Pa

  • 1 mm Hg = 1 torr

Gas Laws

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

• Boyle's Law: At constant temperature, the volume of a gas is inversely proportional to its pressure.

  • $P_1V_1 = P_2V_2$

  • Example: Compressing a gas in a syringe decreases its volume as pressure increases.

• Charles's Law: At constant pressure, the volume of a gas is directly proportional to its temperature (in Kelvin).

  • $\frac{V_1}{T_1} = \frac{V_2}{T_2}$

  • Example: A balloon expands when heated.

• Avogadro's Law: At constant temperature and pressure, the volume of a gas is directly proportional to the number of moles.

  • $\frac{V_1}{n_1} = \frac{V_2}{n_2}$

  • Example: Doubling the amount of gas doubles the volume.

• Combined Gas Law: Combines Boyle's, Charles's, and Gay-Lussac's laws.

  • $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

• Ideal Gas Law: Relates pressure, volume, temperature, and number of moles.

  • $PV = nRT$

  • Where $R = 0.08206$ L·atm/(mol·K)

  • Example: Calculating the amount of gas in a container at known conditions.

Standard Temperature and Pressure (STP)

STP is a reference point for gas measurements.

• Conditions: 0°C (273 K) and 1 atm (760 mm Hg)

• Molar Volume: At STP, 1 mole of an ideal gas occupies 22.4 L.

Dalton's Law of Partial Pressures

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

• Formula: $P_{\text{total}} = P_1 + P_2 + P_3 + \ldots$

• Application: Used to calculate the pressure of dry gases collected over water by subtracting vapor pressure.

Gas Density and Molar Mass

The density of a gas can be calculated using its mass and volume, and is related to molar mass.

• Formula: $d = \frac{PM}{RT}$, where d is density, P is pressure, M is molar mass, R is the gas constant, and T is temperature in Kelvin.

• Example: Determining the molar mass of an unknown gas from its density.

Sample Calculations and Applications

• Volume and Temperature Changes: Use Charles's Law to find final volume or temperature when one changes.

• Pressure Changes: Use Boyle's Law to calculate new pressure or volume after a change.

• Gas Collection Over Water: Subtract vapor pressure of water from total pressure to find pressure of dry gas.

• Stoichiometry of Gases: Use molar volume at STP to relate moles of gas to volume in reactions.

Important Tables

Pressure Unit Conversions

Unit	Equivalent Value
1 atm	760 mm Hg
1 atm	101,325 Pa
1 mm Hg	1 torr

STP Conditions

Parameter	Value
Temperature	0°C (273 K)
Pressure	1 atm (760 mm Hg)
Molar Volume	22.4 L/mol

Summary Table: Gas Laws

Law	Relationship	Equation
Boyle's Law	$P \propto \frac{1}{V}$ (at constant T, n)	$P_1V_1 = P_2V_2$
Charles's Law	$V \propto T$ (at constant P, n)	$\frac{V_1}{T_1} = \frac{V_2}{T_2}$
Avogadro's Law	$V \propto n$ (at constant P, T)	$\frac{V_1}{n_1} = \frac{V_2}{n_2}$
Combined Gas Law	All variables	$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$
Ideal Gas Law	All variables	$PV = nRT$

Additional info:

• Some questions referenced the periodic table, which is used to determine molar masses for gas calculations.

• Sample problems included calculations involving changes in temperature, pressure, and volume, as well as gas stoichiometry and density.