Gas Laws

Combined Gas Law

The Combined Gas Law integrates Boyle’s, Charles’s, and Gay-Lussac’s laws to relate pressure, volume, and temperature of a fixed amount of gas. It is useful for predicting the effect of changing two variables on the third, provided the number of moles remains constant.

• Formula:

• Variables: P = pressure, V = volume, T = temperature (in Kelvin)

• Application: Used to solve problems where two of the three variables (P, V, T) change and the amount of gas is constant.

Example: If a sample of helium gas has a volume of 0.180 L, a pressure of 0.800 atm, and a temperature of 29°C, and is changed to a volume of 90.0 mL and a pressure of 3.20 atm, the new temperature can be found using the combined gas law (convert all units to standard first).

Avogadro’s Law: Volume and Moles

Avogadro’s Law states that the volume of a gas is directly proportional to the number of moles of gas, provided temperature and pressure are constant. This law is essential for understanding how changing the amount of gas affects its volume.

• Formula:

• Variables: V = volume, n = number of moles

• Application: Used to calculate the new volume when the amount of gas changes at constant temperature and pressure.

Example: A weather balloon with a volume of 44 L is filled with 2.0 moles of helium. If 3.0 moles are added (total 5.0 moles), the final volume can be calculated using Avogadro’s Law.

Standard Temperature and Pressure (STP)

STP (Standard Temperature and Pressure) provides a reference for comparing gases. At STP, one mole of any ideal gas occupies the same volume, known as the molar volume.

• STP Conditions:

  • Temperature: 273 K (0°C)

  • Pressure: 1 atm (760 mmHg)

  • 1 mole of gas = 22.4 L (molar volume at STP)

• Conversion Factors:

  • 1 mole gas = 22.4 L (at STP)

  • 22.4 L (at STP) = 1 mole gas

Example: To find the volume at STP of 4.0 moles of CH4, multiply the number of moles by the molar volume: L.

Dalton’s Law of Partial Pressures

Dalton’s Law of Partial Pressures describes the behavior of mixtures of gases. Each gas in a mixture exerts its own pressure, called a partial pressure, and the total pressure is the sum of all partial pressures.

• Formula:

• Application: Used to determine the total pressure of a gas mixture or the partial pressure of an individual component.

• Example: In a scuba tank with a total pressure of 8.00 atm, if the partial pressure of oxygen is 1280 mmHg, the partial pressure of helium can be found by converting units and subtracting from the total.

Key Points:

• Gas particles in a mixture behave independently.

• The total pressure results from the sum of all individual gas pressures.

References: Timberlake, K. (2018). Chemistry: Introduction to general, organic and biological chemistry (13th ed.). Pearson Education.