Gas Laws and Stoichiometry: Study Notes for General Chemistry

Gas Laws and Their Applications

Introduction to Gas Laws

Gas laws describe the relationships between pressure, volume, temperature, and amount of gas. These laws are fundamental in understanding the behavior of gases under various conditions and are essential for solving problems in stoichiometry and chemical reactions involving gases.

• Pressure results from gas particles moving and colliding with the walls of their container.

• Volume is the space a gas occupies.

• Temperature affects the kinetic energy of gas particles.

• Amount of gas is measured in moles.

Key Gas Laws

• Boyle's Law: At constant temperature, pressure and volume are inversely related.

  • Equation: $P_1V_1 = P_2V_2$

  • Example: If the volume of a gas doubles, its pressure halves (at constant temperature).

• Charles's Law: At constant pressure, volume and temperature are directly related.

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

  • Example: Heating a balloon causes it to expand.

• Gay-Lussac's Law: At constant volume, pressure and temperature are directly related.

  • Equation: $\frac{P_1}{T_1} = \frac{P_2}{T_2}$

  • Example: Increasing temperature in a rigid container increases pressure.

• Avogadro's Law: At constant temperature and pressure, volume and moles are directly related.

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

  • Example: Doubling the number of moles doubles the volume.

• Combined Gas Law: Relates pressure, volume, and temperature for a fixed amount of gas.

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

• Ideal Gas Law: Relates pressure, volume, temperature, and moles of gas.

  • Equation: $PV = nRT$

  • R is the gas constant, typically $0.0821$ L·atm/(mol·K).

Standard Temperature and Pressure (STP)

STP is a reference point for gas measurements:

• Temperature: 0°C (273 K)

• Pressure: 1 atm (760 mm Hg)

• Molar volume at STP: 1 mole of any ideal gas occupies 22.4 L

Dalton's Law of Partial Pressures

Dalton's Law states that the total pressure of a mixture of gases is the sum of the partial pressures of each individual gas.

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

• Application: Used to calculate the pressure exerted by each gas in a mixture.

Kinetic Molecular Theory

The Kinetic Molecular Theory explains the behavior of gases based on the motion of their particles.

• Gas particles are in constant, random motion.

• Collisions between particles and container walls cause pressure.

• Most of the volume of a gas is empty space.

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

Conversions and Units

• Pressure units: 1 atm = 760 mm Hg = 101.3 kPa

• Temperature: Always use Kelvin in gas law calculations. $K = ^\circ C + 273$

• Volume: Usually measured in liters (L)

• Moles: Amount of substance, $n$

Stoichiometry with Gases

Stoichiometry involves using balanced chemical equations to relate quantities of reactants and products. For reactions involving gases, use the molar volume at STP or the ideal gas law to convert between volume and moles.

• Example: In the reaction $2H_2 + O_2 \rightarrow 2H_2O$, the volume ratio of $H_2$ to $O_2$ is 2:1.

• Use $PV = nRT$ to find moles or volume when conditions are not at STP.

Sample Calculations

• Finding volume at new conditions:

  • Use the combined gas law: $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

  • Example: A balloon contains 40.0 L of helium at 18°C. If the temperature rises to 42°C at constant pressure, what is the new volume?

• Calculating moles from gas data:

  • Use the ideal gas law: $n = \frac{PV}{RT}$

  • Example: If 2.0 mol of gas at 300 K exerts a pressure of 4.82 atm, what is its volume?

Summary Table: Major Gas Laws

Law	Equation	Constant Variable	Relationship
Boyle's Law	$P_1V_1 = P_2V_2$	Temperature, moles	Pressure ∝ 1/Volume
Charles's Law	$\frac{V_1}{T_1} = \frac{V_2}{T_2}$	Pressure, moles	Volume ∝ Temperature
Gay-Lussac's Law	$\frac{P_1}{T_1} = \frac{P_2}{T_2}$	Volume, moles	Pressure ∝ Temperature
Avogadro's Law	$\frac{V_1}{n_1} = \frac{V_2}{n_2}$	Pressure, Temperature	Volume ∝ Moles
Combined Gas Law	$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$	Moles	Relates P, V, T
Ideal Gas Law	$PV = nRT$	None	Relates P, V, T, n

Additional info:

• Some questions reference the kinetic molecular theory, which is foundational for understanding gas behavior.

• Stoichiometry questions involve using gas laws to relate reactant and product volumes.

• Extra credit and calculation-based questions require application of the combined gas law and ideal gas law.