Study Notes: Gases and Gas Laws (General Chemistry I, Chapter 5)

Gases: Characteristics and Properties

General Properties of Gases

Gases are one of the fundamental states of matter, characterized by their unique physical properties. Understanding these properties is essential for studying gas behavior and the gas laws.

• Low Density: Gases have much lower densities compared to solids and liquids.

• Compressibility: Gases are highly compressible; their volume can decrease significantly under pressure.

• Expansion: Gases expand spontaneously to fill the volume of their containers.

• Homogeneity: Gases form homogeneous mixtures with each other regardless of the identity or proportions of the component gases.

• Occupy Full Volume: Gases occupy about 0.1% of the volume of their containers, with the rest being empty space between particles.

• Nonmetallic Elements: Most gases are nonmetals and have low molar masses.

• Vapors: Substances that are normally solids or liquids at room temperature can exist in the gaseous state as vapors.

Example: Gas Behavior with Temperature Change

When the temperature of a gas in a sealed container is lowered, the gas particles move closer together, resulting in a decrease in volume (if pressure is constant) or an increase in pressure (if volume is constant).

Pressure and Its Measurement

Definition of Pressure

Pressure (P) is defined as the force (F) exerted per unit area (A):

$P = \frac{F}{A}$

The SI unit for pressure is the pascal (Pa):

$1\ \text{Pa} = 1\ \text{N}/\text{m}^2 = 1\ \text{kg}/(\text{m} \cdot \text{s}^2)$

Atmospheric pressure is the pressure exerted by the weight of the atmosphere and can be measured using a mercury barometer.

Common Units of Pressure

Pressure can be expressed in several units. The following table summarizes the most common units and their relationships:

Pressure Measured in	Unit	Standard Pressure
pascal	Pa	100,000 Pa
kilopascal	kPa	100 kPa
torr (mmHg)	torr	760.0 torr
atmosphere	atm	0.98692 atm
pounds per square inch	psi	14.504 psi

Standard pressure is defined by IUPAC as 100,000 Pa (1 bar).

The Gas Laws

The behavior of gases can be described by several empirical laws that relate pressure (P), volume (V), temperature (T), and the number of moles (n) of a gas.

Variables Defining the State of a Gas

• Temperature (T): Measured in Kelvin (K).

• Pressure (P): Measured in units such as Pa, atm, or torr.

• Volume (V): Measured in liters (L) or cubic meters (m3).

• Number of moles (n): Amount of gas present.

Boyle's Law: Pressure-Volume Relationship

Boyle's Law states that at constant temperature and number of moles, the volume of a gas is inversely proportional to its pressure.

$V \propto \frac{1}{P}$

or

$V = \frac{\text{constant}}{P}$

or

$PV = \text{constant}$

• If the volume decreases, the pressure increases, provided temperature and amount of gas remain constant.

• The relationship is represented graphically as a hyperbola (P vs. V).

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

Charles's Law: Volume-Temperature Relationship

Charles's Law states that at constant pressure and number of moles, the volume of a gas is directly proportional to its absolute temperature (in Kelvin).

$V \propto T$

or

$\frac{V}{T} = \text{constant}$

• As temperature increases, the volume of the gas increases (if pressure is constant).

• Temperature must be measured in Kelvin: $T_{\text{Kelvin}} = T_{\text{Celsius}} + 273.15$

Example: Heating a balloon causes it to expand as the gas inside increases in volume.

Avogadro's Law: Volume-Mole Relationship

Avogadro's Law states that at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gas present.

$V \propto n$

or

$\frac{V}{n} = \text{constant}$

• Adding more gas (increasing n) increases the volume, provided temperature and pressure are constant.

• All gases at the same temperature and pressure have the same molar volume (approximately 22.4 L at STP for 1 mol).

Example: Filling a balloon with more gas increases its size.

Concept Checks and Applications

Concept Check: Gas Density

Given four common atmospheric gases (N2, O2, Ar, CO2) at equal size, temperature, and pressure, the gas with the highest density is the one with the highest molar mass (CO2).

Concept Check: Changing Conditions

• Decreasing the temperature of a gas at constant volume decreases the pressure.

• Increasing the number of moles of gas at constant temperature and pressure increases the volume.

Summary Table: Gas Laws

Law	Relationship	Variables Held Constant	Mathematical Form
Boyle's Law	P ∝ 1/V	n, T	$PV = \text{constant}$
Charles's Law	V ∝ T	n, P	$\frac{V}{T} = \text{constant}$
Avogadro's Law	V ∝ n	P, T	$\frac{V}{n} = \text{constant}$

Key Definitions

• Pressure (P): Force per unit area exerted by gas particles colliding with container walls.

• Volume (V): The space occupied by a gas.

• Temperature (T): A measure of the average kinetic energy of gas particles; must be in Kelvin for gas law calculations.

• Mole (n): The amount of substance; 1 mole = $6.022 \times 10^{23}$ particles.

Additional info:

• For ideal gases, the combined gas law and the ideal gas law ($PV = nRT$) can be derived from these relationships, but derivation is not required for this section.

• Standard Temperature and Pressure (STP) is defined as 0°C (273.15 K) and 1 bar (100,000 Pa).