Gas Laws

Avogadro's law states that the volume of a gas is directly proportional to the number of moles of gas at constant temperature and pressure. Mathematically:
V ∝ n
This law holds true for an ideal gas where the gas particles do not interact with each other and occupy no volume. It is based on the assumption of perfect behavior in gases, which is a characteristic of ideal gases.

Answer: ideal gas

This problem can be solved using Graham's Law of Diffusion, which states that the rate of diffusion (or effusion) of a gas is inversely proportional to the square root of its molar mass (M), given constant temperature and pressure. Comparing two gases (1 = Hydrocarbon (HC), 2 = SO₂): The rate of diffusion ( ) is the volume diffused ( ) per unit time ( ).

• Hydrocarbon (HC): cm³, minutes.
  cm³/min.
• Sulfur Dioxide (SO₂): cm³, hour = 60 minutes.
  cm³/min.

Now, substitute the rates into Graham's Law: So, We need the molar mass of SO₂: M(S) 32 g/mol, M(O) 16 g/mol. Substitute into the equation: Square both sides: Solve for the molar mass of the hydrocarbon ( ): Now, we find the hydrocarbon from the options with a molar mass of 16 g/mol:

• (A) CH₄: M = 12 + 4(1) = 16 g/mol
• (B) C₂H₆: M = 2(12) + 6(1) = 24 + 6 = 30 g/mol
• (C) C₂H₄: M = 2(12) + 4(1) = 24 + 4 = 28 g/mol
• (D) C₂H₂: M = 2(12) + 2(1) = 24 + 2 = 26 g/mol

The calculated molar mass (16 g/mol) matches Methane (CH₄), which is option (A).