Chemistry Chapter 12: Gas Laws

Chapter 12: Exploring Gas Laws

• Gas laws describe how gases behave
• The Law of Combining Volumes states that when gases react, the volumes of reactants and products (measured at equal temperatures and pressures) are in whole number ratios.
• Joseph Louis Gay-Lussac formulated this law
• 2 volumes of hydrogen gas react with 1 volume of oxygen gas to produce 2 volumes of water vapor.

Chapter 11.1: The Ideal Gas Law

• The Law of Multiple Proportions states that the masses of elements combining can be expressed in small, whole-number ratios
• John Dalton formulated this law

Avogadro's Law

• Amedeo Avogadro (1776-1856) contributed to molecular theory (Avogadro's Law)
• This law combines Gay-Lussac's and Dalton's ideas
• The volume of a gas is related to the amount of gas present, calculated from the mass.
• Equal volumes of gases under the same temperature and pressure conditions contain equal numbers of molecules.
• Avogadro's law provides a mathematical relationship between the volume of a gas (V) and the number of moles of gas present (n).
• V ∝ n, or n = kV, or V₁/n₁ = V₂/n₂
• where n = number of moles, V = volume and k = a constant

Molar Volume

• One mole of any gas at the same temperature and pressure occupies the same volume
• Molar volume is the space occupied by one mole of a gas, expressed as L/mol

Example Calculation

• A 1.30 L container, with a mass of 7.43 g, has nitrogen gas added, until the pressure is 98.0 kPa at 22.0 °C. The total mass is 6.18 g. Calculate the molar volume of nitrogen gas at STP. (Solution provided)
  • Given values include initial pressure (P₁), initial volume (V₁), initial temperature (T₁), final pressure (P₂), and the mass added (m)
  • Find the volume of 1 mole of nitrogen at STP

Real Gases at STP

• At standard temperature and pressure (STP) gases behave like ideal gases.
• At high pressure and/or low temperatures, gas molecules no longer behave like ideal gases
  • Gas particles have their own volume
  • Gas particles attract each other
  • Collisions are not perfectly elastic (there is some energy loss)
• This is because gas molecules have their own volume and also that there is an attraction between them
• In these conditions molecules will have smaller volumes, be closer together and allow for gas particle attraction

### The Ideal Gas Law

- PV = nRT
- R is the universal gas constant (8.314 kPa·L/mol·K)

• Guidelines for using ideal gas law:
  • Convert temperature to Kelvin
  • Convert masses to moles
  • Convert volumes to liters
  • Convert pressures to kilopascals (kPa)

Universal Gas Constant, R

• One mole of a gas at STP has P=101.3 kPa, T=273 K, V=22.4L, n=1.00 mol
• Calculate R by substituting the values for P, V, n, and T into PV = nRT

Gas Law Stoichiometry

• Use Gay-Lussac's law of combining volumes to solve for stoichiometry problems involving gas-phase reactions when gases react with other gases
  • Balancing chemical equations is important
• Example: Calculate the volume of ammonia gas produced from 12.0 L of nitrogen gas, if there is excess hydrogen.
  • Balanced chemical equation
  • Ratio between nitrogen and ammonia (1 mol N₂ to 2 mol NH₃)

Using Ideal Gas Law for Stoichiometry

• To solve stoichiometry problems when gases are involved, convert volumes into moles first
• Compare the moles
• Convert back to volumes

Partial Pressure

• Reactions in solutions sometimes involve releasing gases
  • Gas release is often affected by the pressure of the water vapor
  • Dalton's partial pressure law can be used to correct for water vapor pressure.

  P<sub>gas</sub> = P<sub>total</sub> - P<sub>water vapor</sub>
  

  -Use a table of water vapor pressure to correct for these issues.

Homework

• Questions are provided on specific pages of a textbook

Explore the fascinating world of gas laws in this quiz. Delve into concepts such as the Law of Combining Volumes, the Ideal Gas Law, and Avogadro's contributions to molecular theory. Test your understanding of how gases behave under various conditions and their mathematical relationships.