Gas Laws and Properties of Gases

States of Matter

• Matter exists in three states: solid, liquid, and gas.
• Gaseous molecules have:
  • Large intermolecular spaces/distances.
  • Weak intermolecular forces of attraction.

Properties of Gases

• The property of gases depends on three variables:
  1. Temperature
  2. Pressure
  3. Volume

Units of Variables

1. Temperature:

   • 0°C = 273K
   • Note: Temperature is always expressed in Kelvin (K) for calculations.

2. Pressure:

   • 1 atm = 760 mmHg = 76 cmHg = 101.32 kPa

3. Volume:

   • 1 L = 1000 ml = 1 dm³ = 1000 cm³

Standard Temperature and Pressure (STP)

• Standard temperature = 273K
• Standard pressure = 1 atm

Boyle’s Law (Pressure-Volume Relationship)

• States that at constant temperature, the volume of a gas is inversely proportional to its pressure:
  • $P<em>1 V</em>1 = P<em>2 V</em>2$
  • When pressure doubles, volume decreases to ½.
  • When pressure decreases to ¼, volume increases by four times.

Real-Life Applications of Boyle’s Law:

1. Syringe:
   • Decreasing the volume increases pressure; increasing volume decreases pressure.
2. Respiration:
   • Inhaling increases lung volume, decreasing pressure; exhaling reduces lung volume, increasing pressure.
3. Bicycle Pump:
   • Pushing down decreases volume, increasing pressure; pulling up increases volume, decreasing pressure.

Charles’s Law (Volume-Temperature Relationship)

• States at constant pressure, the volume of a given quantity of gas increases or decreases by $rac{1}{273}$ of its volume at 0°C for every 1°C rise or fall in temperature.

Real-Life Applications of Charles’s Law:

1. Hot Air Balloon:
   • Increasing temperature causes volume to increase, allowing it to ascend.
2. Baking:
   • Increased oven temperature increases cake volume, making it fluffier.
3. Spray Can:
   • Heating can lead to an explosion due to increased volume.
4. Breathing:
   • Low temperature makes breathing difficult as lung volume cannot expand; high temperature enhances lung volume expansion.

Avogadro’s Law (Volume-Number of Moles Relationship)

• Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.
• Volume of gas is directly proportional to the number of moles under similar conditions:
  • 1 mole = $6.023 imes 10^{23}$ molecules
  • 1 mole = 22.4 L (molar volume).

Gay-Lussac’s Law

• States that at constant volume, pressure is directly proportional to temperature:
  • $P ext{ } ext{ is proportional to } T$

Real-Life Applications of Gay-Lussac’s Law:

1. Pressure Cooker:
   • Heating increases temperature, which raises pressure, cooking food faster.
2. Heating a Spray Can:
   • Increased temperature raises pressure, risk of explosion.
3. Tyre Burst:
   • Friction increases temperature, raising pressure and potentially causing a burst.

Ideal Gas Equation

• Combines Boyle’s Law, Charles’s Law, and Avogadro’s Law into a single equation:

$PV = nRT$

• Where:
  • $V$ = volume (litres)
  • $P$ = pressure (atm)
  • $T$ = temperature (Kelvin)
  • $n$ = number of moles (mol)
  • $R$ = gas constant (0.0821 L atm / K mol)

Important Note

• Ensure to always convert temperature to Kelvin when performing gas law calculations to maintain accuracy and consistency in results.