Gas Laws and Properties of Gases: Study Notes

Gas Laws and Properties of Gases

Introduction to Gas Variables

Gases are described by four main variables: pressure (P), volume (V), temperature (T), and amount (n) (in moles). The relationships between these variables are governed by several fundamental gas laws.

• Pressure (P): The force exerted by gas particles per unit area.

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

• Temperature (T): Measured in Kelvin (K), affects the kinetic energy of gas particles.

• Amount (n): The number of moles of gas present.

Boyle's Law: Pressure-Volume Relationship

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

• Inverse Relationship: As pressure increases, volume decreases, and vice versa.

• Mathematical Expression: $P_1V_1 = P_2V_2$

• General Formula: $P imes V = ext{constant}$

• Example: If a gas at 0.950 atm occupies 35.0 L, what volume will it occupy at 0.750 atm? $(0.950 ext{ atm})(35.0 ext{ L}) = (0.750 ext{ atm})(V_2)$ $V_2 = 44.3 ext{ L}$

Charles's Law: Volume-Temperature Relationship

Charles's Law states that the volume of a fixed amount of gas at constant pressure is directly proportional to its temperature in Kelvin.

• Direct Relationship: As temperature increases, volume increases.

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

• Example: If a gas at 233 L and 295 K is heated to 219 K at constant pressure, what is the new volume? $\frac{233 ext{ L}}{295 ext{ K}} = \frac{V_2}{219 ext{ K}}$ $V_2 = 172.8 ext{ L}$

Avogadro's Law: Volume-Amount 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.

• Direct Relationship: As the amount of gas increases, volume increases.

• Mathematical Expression: $\frac{V_1}{n_1} = \frac{V_2}{n_2}$

• Example: If 3.22 mol of a gas occupies 491 mm Hg, what pressure will 6.36 mol exert at the same temperature and volume? $\frac{491 ext{ mm Hg}}{3.22 ext{ mol}} = \frac{P_2}{6.36 ext{ mol}}$ $P_2 = 970 ext{ mm Hg}$

Combined Gas Law

The Combined Gas Law incorporates Boyle's, Charles's, and Avogadro's laws to relate pressure, volume, temperature, and amount of gas.

• Mathematical Expression: $\frac{P_1V_1}{n_1T_1} = \frac{P_2V_2}{n_2T_2}$

• Application: Used when more than one variable changes.

Ideal Gas Law

The Ideal Gas Law provides a comprehensive relationship between all four variables for a gas under ideal conditions.

• Mathematical Expression: $PV = nRT$

• Gas Constant (R):

  • $R = 0.0821 \text{ L} \cdot \text{atm} / \text{mol} \cdot \text{K}$

  • $R = 62.364 \text{ L} \cdot \text{mm Hg} / \text{mol} \cdot \text{K}$

• Example: Calculate the number of moles in 14.0 L of gas at 395 mm Hg and 37°C. $PV = nRT$ $n = \frac{PV}{RT}$ $n = \frac{(14.0 \text{ L})(395 \text{ mm Hg})}{(62.364 \text{ L} \cdot \text{mm Hg} / \text{mol} \cdot \text{K})(310.2 \text{ K})} = 0.291 \text{ mol}$

Standard Temperature and Pressure (STP)

STP refers to a temperature of 0°C (273.15 K) and a pressure of 1 atm. At STP, one mole of an ideal gas occupies 22.4 L.

• Example: How many moles are in 3.5 L of CH4 at STP? $\frac{3.5 \text{ L}}{22.4 \text{ L/mol}} = 0.156 \text{ mol}$

Diatomic Gases

Common diatomic gases include H2, N2, O2, F2, and Cl2. These molecules consist of two atoms bonded together.

Partial Pressure and Dalton's Law

Dalton's Law of Partial Pressures states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of each individual gas.

• Mathematical Expression: $P_{\text{total}} = P_{A} + P_{B} + P_{C} + \ldots$

• Example: If $P_{He} = 73 \text{ mm Hg}$, $P_{Ar} = 835 \text{ mm Hg}$, $P_{Xe} = 111 \text{ mm Hg}$, then $P_{Ne} = P_{\text{total}} - (P_{He} + P_{Ar} + P_{Xe})$

Summary Table: Gas Laws

Law	Relationship	Formula	Variables Held Constant
Boyle's Law	Inverse (P & V)	$P_1V_1 = P_2V_2$	n, T
Charles's Law	Direct (V & T)	$\frac{V_1}{T_1} = \frac{V_2}{T_2}$	n, P
Avogadro's Law	Direct (V & n)	$\frac{V_1}{n_1} = \frac{V_2}{n_2}$	P, T
Combined Gas Law	All variables	$\frac{P_1V_1}{n_1T_1} = \frac{P_2V_2}{n_2T_2}$	None
Ideal Gas Law	All variables	$PV = nRT$	None

Key Concepts and Applications

• Always use Kelvin for temperature in gas law calculations.

• Convert pressure units as needed (atm, mm Hg, torr).

• Use the correct value of R for the units in your calculation.

• Gas laws are foundational for understanding chemical reactions involving gases, stoichiometry, and laboratory measurements.

Additional info: Some equations and relationships were expanded for clarity and completeness. Examples were inferred and solved based on the notes provided.