Gas Laws

Introduction to Gas Laws

The gas laws describe the behavior of gases in relation to pressure, volume, temperature, and amount (moles). These laws are foundational in both general and organic chemistry, providing the basis for understanding reactions involving gases and the quantitative relationships between reactants and products.

The Mole: Review

Definition and Importance

• Mole (mol): The standard chemical unit for describing the amount of substance, defined as containing exactly 6.022 × 10^23 particles (Avogadro's number).

• Avogadro's Number: particles per mole.

• The mass of a substance (solid or liquid) can be calculated using the relationship between moles, mass, and molar mass:

• The volume of a gas is most easily found by measuring the volume it occupies under specific conditions.

Molar Volume of a Gas

Concept and Application

• Molar Volume: The volume occupied by one mole of any gas at a specified temperature and pressure.

• At standard temperature and pressure (STP: 0°C, 100 kPa), 1 mole of any ideal gas occupies the same volume, regardless of its chemical identity.

• If the amount of gas (number of moles) in a syringe is doubled, the volume doubles, provided temperature and pressure are constant.

• This relationship is consistent for all ideal gases.

Standard Molar Volume at STP:

• STP conditions: 0°C (273 K), 100 kPa

• 1 mole of any gas occupies 22.71 L at STP

Avogadro's Law

Statement and Implications

• Avogadro's Law: Equal volumes of all gases, at the same temperature and pressure, contain the same number of particles (molecules).

• Mathematically, for a fixed temperature and pressure:

• At STP, any gas occupies 22.71 L per mole.

Example Table: Molar Volume at STP

Worked Example: Calculating Moles from Gas Volume at STP

• Given: 4.39 L of hydrogen gas produced at STP.

• Reaction: Zn + 2HCl → ZnCl2 + H2

• Calculate moles of H2:

mol

Practice Problem

• Find the volume occupied by 0.24 mol of nitrogen gas at STP.

• Solution: L

Ideal Gas Law

General Gas Law for Non-STP Conditions

The ideal gas law relates the pressure, volume, temperature, and amount of gas under any conditions, not just STP.

• Equation:

• P = pressure (kPa)

• V = volume (L)

• n = amount (mol)

• R = universal gas constant ()

• T = temperature (K)

Always convert temperature to Kelvin by adding 273 to the Celsius value.

Boyle's Law

Pressure-Volume Relationship

At constant temperature, the volume of a given mass of gas is inversely proportional to the applied pressure.

• Equation:

• P = pressure

• V = volume

• As pressure increases, volume decreases, and vice versa (at constant temperature).

Worked Example: Volume-Temperature Relationship

• Given: A sample of gas is collected at 58°C. What volume would this sample occupy at 25°C?

• Convert temperatures to Kelvin: 58°C = 331 K, 25°C = 298 K

• Use the relationship:

• Substitute values and solve for the unknown volume.

Summary Table: Key Gas Laws

Additional info: Charles's Law is referenced in the worked example, though not explicitly named in the slides. The summary table includes Charles's Law for completeness and context.