Chapter 11: Gases – Study Guide and Key Concepts

Gases

Major Gas Laws

The behavior of gases is described by several fundamental gas laws, each relating different variables such as pressure, volume, temperature, and amount of gas. Understanding these laws is essential for predicting and explaining gas behavior under various conditions.

• Boyle's Law: At constant temperature, the pressure and volume of a gas are inversely related. $P_1V_1 = P_2V_2$

• Charles's Law: At constant pressure, the volume of a gas is directly proportional to its temperature (in Kelvin). $\frac{V_1}{T_1} = \frac{V_2}{T_2}$

• Gay-Lussac's Law: At constant volume, the pressure of a gas is directly proportional to its temperature (in Kelvin). $\frac{P_1}{T_1} = \frac{P_2}{T_2}$

• Avogadro's Law: At constant temperature and pressure, the volume of a gas is directly proportional to the number of moles. $\frac{V_1}{n_1} = \frac{V_2}{n_2}$

• Ideal Gas Law: Combines all the above relationships into a single equation. $PV = nRT$

Example: If 2.0 moles of a gas occupy 44.8 L at STP, what is the pressure?

Additional info: The Combined Gas Law ($\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$) is also used for calculations involving changes in multiple variables.

Kinetic Molecular Theory (KMT)

The Kinetic Molecular Theory explains the behavior of gases based on the motion of their particles. It provides a molecular-level understanding of gas laws.

• Gas particles are in constant, random motion.

• Collisions between gas particles and container walls cause pressure.

• Gas particles are assumed to have negligible volume and no intermolecular forces (ideal gas assumption).

• Temperature is proportional to the average kinetic energy of the particles.

Example: Increasing temperature increases the speed of gas particles, raising the pressure if volume is constant.

Pressure and Its Units

Pressure is defined as the force exerted per unit area by gas particles colliding with the walls of their container.

• Common units: Atmospheres (atm), Pascals (Pa), millimeters of mercury (mmHg), and torr.

• Conversions: 1 atm = 101,325 Pa = 760 mmHg = 760 torr

Example: Convert 2 atm to mmHg: $2 \times 760 = 1520$ mmHg.

Deviations from Ideal Gas Law

Real gases deviate from ideal behavior at high pressures and low temperatures due to intermolecular forces and the finite volume of gas particles.

• Van der Waals equation: Adjusts the ideal gas law for real gases. $(P + a\frac{n^2}{V^2})(V - nb) = nRT$

• Ideal gas law is most accurate at low pressure and high temperature.

Example: At very high pressure, gas molecules are closer together, and their volume cannot be ignored.

Ideal Gas Law Equation and Constant

The ideal gas law is a central equation in gas chemistry, relating pressure, volume, temperature, and amount of gas.

• Equation: $PV = nRT$

• R (gas constant): 0.0821 L·atm/(mol·K) or 8.314 J/(mol·K) depending on units used.

• Units: Pressure (atm), Volume (L), n (moles), Temperature (K)

Example: Calculate the volume occupied by 1 mole of gas at STP using $PV = nRT$.

Standard Temperature and Pressure (STP)

STP is a reference point for gas measurements, defined as 1 atm pressure and 0°C (273 K) temperature.

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

• Used for comparing gas volumes and calculations involving molar volume.

Example: At STP, 2 moles of gas occupy $2 \times 22.4 = 44.8$ L.

Summary Table: Gas Laws and Relationships

Law	Equation	Variables	Relationship
Boyle's Law	$P_1V_1 = P_2V_2$	P, V	Inverse
Charles's Law	$\frac{V_1}{T_1} = \frac{V_2}{T_2}$	V, T	Direct
Gay-Lussac's Law	$\frac{P_1}{T_1} = \frac{P_2}{T_2}$	P, T	Direct
Avogadro's Law	$\frac{V_1}{n_1} = \frac{V_2}{n_2}$	V, n	Direct
Ideal Gas Law	$PV = nRT$	P, V, n, T	Combined

Pressure Unit Conversion Table

Unit	Equivalent
1 atm	101,325 Pa
1 atm	760 mmHg
1 atm	760 torr