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 concepts.

• Gas Pressure: The force exerted by gas particles colliding with the walls of their container.

• Volume: The space occupied by a gas, typically measured in liters (L) or milliliters (mL).

• Temperature: A measure of the average kinetic energy of gas particles, usually in Kelvin (K).

• Amount (n): The quantity of gas, measured in moles.

Gas Pressure and Its Measurement

Defining Gas Pressure

Gas pressure is defined as the force per unit area exerted by gas molecules as they collide with the surfaces of their container.

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

• The Earth's atmosphere exerts pressure on its surface, known as atmospheric pressure.

Measuring Atmospheric Pressure

Atmospheric pressure is commonly measured using a barometer, an instrument invented by Torricelli in 1643.

• Standard atmospheric pressure: 1 atm = 760 mm Hg = 101.3 kPa

• Other units: Pascal (Pa), torr

Gas Laws

Boyle's Law

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

• Formula: $P_1 V_1 = P_2 V_2$

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

• Example: Compressing a balloon reduces its volume.

Charles's Law

Charles's Law relates the volume and temperature of a gas at constant pressure.

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

• Volume increases as temperature increases (direct relationship).

• Example: Heating a balloon causes it to expand.

Combined Gas Law

The Combined Gas Law combines Boyle's and Charles's Laws to relate pressure, volume, and temperature.

• Formula: $\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$

• Useful when all three variables change.

Ideal Gas Law

The Ideal Gas Law provides a relationship between pressure, volume, temperature, and amount of gas.

• Formula: $PV = nRT$

• $P$ = pressure (atm), $V$ = volume (L), $n$ = moles, $R$ = gas constant (0.08206 L·atm/mol·K), $T$ = temperature (K)

• Describes the behavior of ideal gases under various conditions.

Standard Temperature and Pressure (STP)

STP is a reference condition for gases: 0°C (273.15 K) and 1 atm pressure.

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

• Formula: $V = \frac{nRT}{P}$

Gas Density and Molar Mass

Calculating Density and Molar Mass

The density of a gas can be related to its molar mass using the ideal gas law.

• Formula: $M = \frac{dRT}{P}$

• $d$ = density (g/L), $M$ = molar mass (g/mol)

• Gas densities depend on temperature and pressure.

Gas Stoichiometry

Stoichiometric Calculations with Gases

Gas stoichiometry involves using the ideal gas law to relate volumes of gases to moles in chemical reactions.

• Balanced chemical equations are used to relate reactants and products.

• Example: Decomposition of sodium azide ($2\text{NaN}_3 \rightarrow 2\text{Na} + 3\text{N}_2$) to inflate 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 the sum of the partial pressures of each component.

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

• Each gas exerts a pressure proportional to its amount in the mixture.

Vapour Pressure

Vapour pressure is the pressure exerted by a vapor in equilibrium with its liquid phase.

• Vapour pressure increases with temperature.

• When collecting gases over water, the total pressure includes both the gas and water vapor pressures.

• Formula: $P_{\text{total}} = P_{\text{gas}} + P_{\text{H}_2\text{O}}$

Mole Fraction

Definition and Calculation

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

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

• Also defined as the ratio of partial pressure or volume of one component to the total.

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

Diffusion and Effusion of Gases

Graham's Law of Effusion

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

• Formula: $\text{Rate of effusion} \propto \frac{1}{\sqrt{M}}$

• Comparing two gases: $\frac{\text{Rate}_1}{\text{Rate}_2} = \sqrt{\frac{M_2}{M_1}}$

• Lighter gases effuse and diffuse faster than heavier gases.

Diffusion

Diffusion is the spreading of a gas throughout a space or another gas.

• Rate of diffusion is also inversely proportional to the square root of molar mass.

• Example: Natural gas spreading in a room.

Summary Table: Gas Laws and Relationships

Law	Relationship	Formula	Variables Held Constant
Boyle's Law	P vs. V (inverse)	$P_1 V_1 = P_2 V_2$	T, n
Charles's Law	V vs. T (direct)	$\frac{V_1}{T_1} = \frac{V_2}{T_2}$	P, n
Combined Gas Law	P, V, T	$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$	n
Ideal Gas Law	P, V, n, T	$PV = nRT$	None
Dalton's Law	Total Pressure	$P_{\text{total}} = P_1 + P_2 + \ldots$	Volume, T

Example Problems

Sample Calculations

• Calculate the mass of a gas sample given its volume, pressure, and temperature using the ideal gas law.

• Determine the partial pressure of each gas in a mixture using Dalton's Law.

• Find the density or molar mass of a gas from experimental data.

• Apply Graham's Law to compare rates of effusion for two gases.

Additional info: These notes expand on the original slides and problems, providing definitions, formulas, and context for all major gas laws and concepts relevant to a General Chemistry course.