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 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: Pressure increases in a sealed container when heated.

• 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 amount of gas doubles the volume (at constant T and P).

• 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: $PV = nRT$

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

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

• Example: In a mixture with gases at 200, 400, and 600 kPa, total pressure is 1200 kPa.

Standard Temperature and Pressure (STP)

STP is a reference point used in gas calculations.

• Standard Temperature: 0°C (273 K)

• Standard Pressure: 1 atm (101.3 kPa or 760 mm Hg)

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

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.

Stoichiometry and Gas Calculations

Stoichiometry with Gases

Stoichiometry involves using balanced chemical equations to calculate the relationships between reactants and products. When gases are involved, the ideal gas law and molar volume at STP are often used.

• Use $PV = nRT$ to find moles, volume, or pressure of gases.

• At STP, use molar volume: 1 mol = 22.4 L.

• Volume ratios in reactions can be determined from coefficients in balanced equations (Gay-Lussac's Law).

Sample Calculations

• Finding Volume at STP: $V = n \times 22.4$ L

• Using Ideal Gas Law: $n = \frac{PV}{RT}$

• Partial Pressure: $P_{\text{gas}} = P_{\text{total}} - P_{\text{water vapor}}$

• Temperature Conversion: $K = ^\circ C + 273.15$

Useful Constants and Conversion Factors

Selected Prefixes

Prefix	Symbol	Value
kilo-	k	103
centi-	c	10-2
milli-	m	10-3
micro-	μ	10-6
nano-	n	10-9

Selected Constants

Constant	Value
Avogadro's Number ($N_A$)	$6.022 \times 10^{23}$ mol-1
Gas Constant ($R$)	$0.0821$ L·atm/mol·K

Selected Conversion Factors

Conversion	Value
1 atm	101.3 kPa
1 atm	760 mm Hg
1 atm	14.7 psi
1 mm Hg	1 torr

Equations and Problem-Solving Strategies

Key Equations

• Ideal Gas Law: $PV = nRT$

• Boyle's Law: $P_1V_1 = P_2V_2$

• Charles's Law: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$

• Gay-Lussac's Law: $\frac{P_1}{T_1} = \frac{P_2}{T_2}$

• Combined Gas Law: $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

• Avogadro's Law: $\frac{V_1}{n_1} = \frac{V_2}{n_2}$

• Dalton's Law: $P_{\text{total}} = P_1 + P_2 + \ldots$

Problem-Solving Tips

• Always convert temperatures to Kelvin: $K = ^\circ C + 273.15$

• Check units for pressure, volume, and R.

• Use stoichiometry for reactions involving gases.

• Apply the correct law based on which variables are held constant.

Summary Table: Gas Laws Comparison

Law	Equation	Variables Held Constant	Relationship
Boyle's Law	$P_1V_1 = P_2V_2$	Temperature, moles	Pressure inversely with volume
Charles's Law	$\frac{V_1}{T_1} = \frac{V_2}{T_2}$	Pressure, moles	Volume directly with temperature
Gay-Lussac's Law	$\frac{P_1}{T_1} = \frac{P_2}{T_2}$	Volume, moles	Pressure directly with temperature
Avogadro's Law	$\frac{V_1}{n_1} = \frac{V_2}{n_2}$	Pressure, temperature	Volume directly with 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.

• Prefixes and conversion factors are essential for unit conversions in gas law calculations.

• Stoichiometry with gases often uses molar volume at STP and the ideal gas law.