Gases: Properties, Laws, and Calculations – General Chemistry Study Notes

Properties and Behavior of Gases

Introduction to Gases

Gases are one of the fundamental states of matter, characterized by their ability to expand and fill any container. Their properties and behavior are governed by several physical laws and measurable quantities.

• Compressibility: Gases can be compressed easily due to the large spaces between particles.

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

• Negligible Intermolecular Forces: In ideal conditions, forces between gas particles are considered negligible.

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

• Variables: The behavior of gases is described by pressure (P), volume (V), temperature (T), and amount in moles (n).

Gas Pressure and Measurement

Definition and Measurement

Gas pressure is the force exerted by gas particles per unit area on the walls of a container. Atmospheric pressure is the pressure exerted by the Earth's atmosphere.

• Pressure Formula: $\text{Pressure} = \frac{\text{Force}}{\text{Area}}$

• Standard Atmospheric Pressure: 1 atm = 760 mm Hg = 101.3 kPa

• Barometer: Device invented by Torricelli to measure atmospheric pressure using a column of mercury.

Unit	Symbol	Value
Atmosphere	atm	1 atm
Millimeter of Mercury	mm Hg	760 mm Hg
Pascals	Pa	101,325 Pa

Gas Laws

Ideal Gas Law

The ideal gas law relates pressure, volume, temperature, and amount of gas in moles.

• Equation: $PV = nRT$

• P: Pressure (atm)

• V: Volume (L)

• n: Moles of gas

• R: Gas constant ($0.08206$ L·atm/mol·K)

• T: Temperature (K)

Standard Temperature and Pressure (STP): $T = 0^\circ C = 273.15\,K$, $P = 1\,atm$

• Molar Volume at STP: $V = 22.4\,L$ for 1 mole of ideal gas

Boyle's Law

Describes the relationship between pressure and volume at constant temperature.

• Equation: $P_1V_1 = P_2V_2$

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

Charles's Law

Describes the relationship between volume and temperature at constant pressure.

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

• Volume increases as temperature increases (direct relationship).

Combined Gas Law

Combines Boyle's and Charles's laws to relate pressure, volume, and temperature.

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

Gas Density and Molar Mass

The density and molar mass of a gas can be determined using the ideal gas law.

• Density Formula: $d = \frac{PM}{RT}$

• Molar Mass Formula: $M = \frac{dRT}{P}$

Gas Stoichiometry

Stoichiometric Calculations with Gases

Gas stoichiometry involves using the ideal gas law and balanced chemical equations to relate volumes, masses, and moles of reactants and products.

• Use $PV = nRT$ to convert between gas volume and moles.

• Balanced chemical equations provide mole ratios.

Example: Decomposition of NaN3 to produce N2 gas for airbags.

Dalton's Law of Partial Pressures

Partial Pressure in Gas Mixtures

Dalton's law states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each component.

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

• Each gas exerts pressure independently of the others.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor above its liquid in a closed system. It increases with temperature.

• Example: Vapor pressure of water at 22°C is 19.8 mm Hg; at 50°C is 92.5 mm Hg.

Mole Fraction

Definition and Calculation

The mole fraction is the ratio of the number of moles of one component to the total number of moles in a mixture.

• Equation: $X_A = \frac{n_A}{n_{\text{total}}}$

• Can also be defined as the ratio of partial pressure or volume of one component to the total.

• Equation: $X_A = \frac{P_A}{P_{\text{total}}} = \frac{V_A}{V_{\text{total}}}$

• The sum of mole fractions in a mixture is 1.

Graham's Law of Effusion

Effusion and Molecular Mass

Graham's law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.

• Equation: $\text{rate of effusion} \propto \frac{1}{\sqrt{M}}$

• Lighter gases effuse more rapidly than heavier gases.

• Comparative Equation: $\frac{\text{rate}_1}{\text{rate}_2} = \sqrt{\frac{M_2}{M_1}}$

Diffusion

Definition and Rate

Diffusion is the spreading of a gas in an open space where it mixes with another gas. The rate of diffusion is also inversely proportional to the square root of molar mass.

• Lighter gases diffuse faster than heavier gases.

• Diffusion is generally slower than effusion due to collisions with other particles.

Examples and Applications

Sample Problems

Typical problems involve calculating gas volumes, pressures, densities, molar masses, and partial pressures using the laws and equations above.

• Calculate the volume of a gas at different temperatures and pressures.

• Determine the mass or molar mass of a gas sample from density and pressure data.

• Find the partial pressure of each component in a gas mixture.

• Apply stoichiometry to reactions involving gases.

Example: A mixture of gases contains 0.75 mol O2, 0.22 mol CO2, and 0.15 mol CO. If the total pressure is 0.98 atm, what is the partial pressure of each component?

Summary Table: Key Gas Laws

Law	Equation	Variables Held Constant
Boyle's Law	$P_1V_1 = P_2V_2$	Temperature, amount
Charles's Law	$\frac{V_1}{T_1} = \frac{V_2}{T_2}$	Pressure, amount
Combined Gas Law	$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$	Amount
Ideal Gas Law	$PV = nRT$	None
Dalton's Law	$P_{\text{total}} = \sum P_i$	None
Graham's Law	$\frac{\text{rate}_1}{\text{rate}_2} = \sqrt{\frac{M_2}{M_1}}$	None

Additional info: These notes expand on the original slides and questions by providing full definitions, equations, and context for each law and concept, suitable for exam preparation in a General Chemistry course.