Gas Laws

Combined Gas Law

The Combined Gas Law integrates the relationships between pressure, volume, and temperature for a fixed amount of gas. It is useful for predicting how changes in two variables affect the third, provided the number of moles remains constant.

• Formula:

• Variables:

  • P: Pressure (in atm, mmHg, etc.)

  • V: Volume (in L, mL, etc.)

  • T: Temperature (in Kelvin)

• Application: Used when both temperature and pressure change, but the amount of gas (n) 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 calculated using the combined gas law.

Avogadro’s Law: Volume and Moles

Avogadro’s Law describes the relationship between the volume of a gas and the number of moles present, assuming constant temperature and pressure. The volume is directly proportional to the number of moles.

• Formula:

• Variables:

  • V: Volume (in L)

  • n: Number of moles

• Application: Used to determine how the volume changes when the amount of gas changes, with 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 is a set of standard conditions used for comparing gases. It allows for the calculation of molar volume and conversion between moles and volume.

• STP Conditions:

  • Temperature: 273 K (0°C)

  • Pressure: 1 atm (760 mmHg)

• Molar Volume: At STP, 1 mole of any gas occupies 22.4 L.

• Conversion Factors:

  • 1 mole gas = 22.4 L (STP)

  • 22.4 L (STP) = 1 mole gas

• Example: The volume at STP of 4.0 moles of CH4 is 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. Each gas in a mixture behaves independently and contributes to the total pressure according to its own partial pressure.

• Formula:

• Application: Used to calculate the total pressure in a mixture or to find the partial pressure of a component gas.

• Example: In a scuba tank with a total pressure of 8.00 atm, if oxygen has a partial pressure of 1280 mmHg, the partial pressure of helium can be found by subtracting the oxygen pressure (converted to atm) from the total pressure.

• Air Composition: Typical air contains 21% oxygen, 78% nitrogen, and 1% other gases.

Summary Table: Gas Laws and Their Relationships

Additional info: The notes are based on Timberlake, K. (2018), "Chemistry: Introduction to general, organic and biological chemistry (13th ed.)" Pearson Education.