PRELIMS

Behavior of Gases

The behavior of gases is defined by physical laws relating pressure (P), volume (V), temperature (T), and quantity (n).

Standard Gas Laws

1. Boyle's Law (1662): At constant temperature (T), .
   • Equation: .
2. Charles’s Law (1787): At constant pressure (P), (Absolute temperature in Kelvin).
   • Equation: .
3. Gay-Lussac’s Law (1802): At constant volume (V), (in Kelvin).
   • Equation: .
4. Avogadro’s Law: At constant T and P, the volume of a gas ( ) is directly proportional to the number of molecules ( ).
   • Equation: .

Ideal Gas Equation

Ideal gas is a hypothetical gas that obeys all gas laws exactly.

• Formula: .
• Gas Constant (R):

Standard and Normal Conditions (STP & NTP)

• At S.T.P. (Standard Temperature and Pressure):
  • Volume ( ): 22.4 liters for 1 mole of any gas.
  • Pressure ( ): 1 atm = 760 mm Hg = 76 cm Hg.
  • Temperature ( ): 273 K ( ).
• Confused Pair — STP vs. N.T.P.: Older texts use STP and NTP interchangeably (0°C, 1 atm). IUPAC's current STP is 0°C and 1 bar (100 kPa), giving a molar volume of ~22.7 L; NTP is commonly defined as 25°C (298 K) and 1 atm. For UPSC purposes, the classical value 22.4 L/mole at 0°C, 1 atm remains the standard expected answer unless the question specifies IUPAC's newer definition.

Kinetic Theory of Gases (Postulates)

• Gas consists of tiny particles in continuous, random motion.
• Molecules are point masses with negligible volume compared to the container.
• No force of attraction/repulsion between molecules (ideal gas assumption).
• Collisions are perfectly elastic (no energy loss).
• Pressure is due to collisions of molecules with the walls of the container.
• Average kinetic energy of gas molecules is directly proportional to absolute temperature.

Diffusion of Gases

Diffusion is the spontaneous intermixing of gases regardless of density.

• Graham’s Law of Diffusion: The rate of diffusion ( ) is inversely proportional to the square root of its density ( ) or molecular mass ( ).
  • Equation: .
• Link: Molecular Mass = 2 Vapour Density ( ).

Dalton’s Law of Partial Pressure

The total pressure ( ) exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures each gas would exert if it filled the container alone at the same temperature.

• Formula:

UPSC Relevance

Gas laws explain various physical and industrial phenomena.

• Practical Examples: The working of a pressure cooker (Gay-Lussac's Law) or the behavior of a balloon in cold weather (Charles's Law).
• Calculation Constants: Knowing that 1 mole of any ideal gas occupies 22.4 L at STP is essential for solving S&T numericals.
• Diffusion: Explains why lighter gases (like Hydrogen) diffuse faster than heavier gases (like Oxygen).