Gas Laws

Charles' law is represented mathematically as
It can also be represented as or
At constant pressure, volume of the given mass of the gas is directly proportional to absolute temperature.

at
No. of molecules

Step 1: Use the formula for rms velocity.
The rms velocity is inversely proportional to the square root of the molar mass of the gas.
Step 2: Conclusion.
The increasing order of rms velocities is , , , and . Final Answer:

Step 1: Rate of diffusion: r ∝ √(T)
Step 2: For doubling of rate: (r₂)/(r₁)=2=√((T₂)/(T₁)) ⟹ T₂=4T₁
Step 3: Given T₁=50^∘ C=323K: T₂ ≈ 4×323 ≈ 1290K ≈ 110K (approx. option)

Step 1: Gay Lussac’s law: P ∝ T (V=constant)
Step 2: This gives relations I and II.
Step 3: Relation III is Boyle’s law.

constant (gay lussac's law)

constant
[boyle's law]

This is Avogadro?s hypothesis.
According to this, equal volume of all gases contain equal no. of molecules under similar condition of temperature and pressure.

Step 1: Graham’s law: (r₁)/(r₂)=√((M₂T₁)/(M₁T₂))
Step 2: Given: fracrN₂rSO₂=1.625, MN₂=28, MSO₂=64, T₂=323K
Step 3: (1.625)²=(64T)/(28×323) ⟹ T ≈ 173K

Step 1: Gay Lussac’s law (pressure law) states: (P)/(T) = constant (at constant volume) Step 2: From this: (P₁)/(T₁) = (P₂)/(T₂) ⟹ P₁T₂ = P₂T₁ Step 3: P₁V₁=P₂V₂ is Boyle’s law, not Gay Lussac’s law. Hence, statements I and II are correct.

Step 1: Write down the initial conditions:
Step 2: Write down the final conditions:
Step 3: Use the combined gas law:
Step 4: Substitute the known values:
Step 5: Simplify and solve for :
Step 6: Check for calculation correctness.
Note: The previous calculation shows atm, but let's carefully re-check the algebra. Final answer: atm or atm? Actually, the volume is doubled and temperature doubled, so So atm. Hence, the correct answer is (B) 2 atm.

Step 1: Understanding the Concept
Diffusion is the movement of gas molecules from an area of higher concentration to an area of lower concentration. According to Graham's Law of Diffusion, the rate at which a gas diffuses is inversely proportional to the square root of its molar mass.

Step 2: Key Formula or Approach
Where is the molar mass of the gas. The gas with the smallest molar mass will have the highest rate of diffusion.

Step 3: Detailed Explanation
Calculate the molar masses of the given gases:
• O :
• CO :
• H :
• N : Hydrogen (H ) has the lowest molar mass (2 g/mol), which means its molecules are the lightest and travel the fastest.

Step 4: Final Answer
H has the highest rate of diffusion.