Gases - CHEM 1127Q

Chapter 7: Gases

Section 7.1: Gas Pressure

• Definition: Gas pressure is the force exerted by gas particles as they collide with surfaces. Pressure is typically measured in units such as atmospheres (atm), pascals (Pa), or millimeters of mercury (mmHg), and it plays a crucial role in understanding the behavior of gases in different conditions. The relationship between pressure, volume, and temperature of a gas is described by several fundamental laws, including Boyle's Law, Charles's Law, and Avogadro's Law, which collectively help predict how gases will respond to changes in their environment. 23

• Units:

  • SI Unit: 1 Newton/m² = 1 Pascal (Pa)

  • Common Units:

  • 1 atm = 101,325 Pa

  • 1 atm = 760 mmHg = 760 torr

• Measurement: Can be measured using a barometer, which is a device that measures atmospheric pressure by using liquid mercury in a glass tube.

Properties of a Gas

• Gases have no definite volume and expand to fill their container.

• Gas particles are much farther apart than those in solids or liquids, leading to lower densities.

• Gas particles are constantly in motion, colliding with each other and surfaces.

Section 7.2: Boyle’s Law

• Statement: At constant temperature, the volume of a gas is inversely proportional to its pressure.

  • Mathematically: P1 V1 = P2 V2

• Application: Allows calculation of new volume or pressure when one changes, given that temperature is constant.

Section 7.3: Charles’s Law

• Statement: At constant pressure, the volume of a gas is directly proportional to its temperature (in Kelvin).

  • Mathematically: \frac{V1}{T1} = \frac{V2}{T2}

• Example: If the temperature of a gas increases, its volume increases if the pressure remains constant.

Section 7.4: The Combined Gas Law

• Equation: Combines Boyle's and Charles's laws into a single formula:
  \frac{P1 V1}{T1} = \frac{P2 V2}{T2}

• Usage: Used for calculations involving pressure, volume, and temperature when conditions change.

Section 7.5: Avogadro’s Law

• Statement: At constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of the gas.

  • Mathematically: \frac{V1}{n1} = \frac{V2}{n2}

Section 7.6: The Ideal Gas Law

• Equation: Combines Boyle's, Charles's, and Avogadro's laws: PV = nRT where:

  • P = pressure (atm)

  • V = volume (L)

  • n = number of moles

  • R = ideal gas constant (0.08206 L·atm/(mol·K))

  • T = temperature (K)

Section 7.7: Dalton’s Law of Partial Pressures

• Definition: The total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of each gas in the mixture.

  • P{total} = PA + P_B + …

• Mole Fraction:

  • \chiA = \frac{nA}{n{total}} where \chiA is the mole fraction of gas A.

Section 7.8: Molar Mass and Density in Gas Law Calculations

• Molar Mass: Derived from the ideal gas law: MM = \frac{dRT}{P}

  • where d = density (g/L)

• Density:

  • d = \frac{PMM}{RT}

Section 7.9: Gases in Chemical Reactions

• Stoichiometric Calculations: Using gas law principles to predict changes in pressure, volume, and temperature following a chemical reaction.

Section 7.11: Movement of Gas Particles

• Temperature and Speed: Average speed of gas particles is dependent on temperature.

  • Average kinetic energy:
    KE_{avg} = \frac{3}{2}RT

• Root Mean Square Speed:

  • u_{rms} = \sqrt{\frac{3RT}{M}}
    where M is the molar mass in kg.

Summary

• Understanding gas laws is crucial for predicting gas behavior in various conditions.

• Key concepts include gas pressure, volume, temperature relationships, and the ideal gas law.