Question

In a binary gas mixture at low pressures, the diffusion coefficient is ______

• A. inversely proportional to pressure
• B. proportional to square of the pressure
• C. independent of pressure
• D. directly proportional to the pressure

Hint:

Remember that while gas diffusivity is inversely proportional to pressure (\( D_{AB} \propto P^{-1} \)), liquid diffusivity is independent of pressure because liquids are incompressible.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks how the binary gas diffusion coefficient (\( D_{AB} \)) depends on the system pressure at low pressure conditions.
This is a standard transport property relationship in mass transfer.

Step 2: Key Formula or Approach:
According to the Chapman-Enskog kinetic theory of gases, the binary diffusion coefficient for a gas pair A and B is given by:
\[ D_{AB} = \frac{0.001858 \cdot T^{3/2} \cdot \sqrt{\frac{1}{M_A} + \frac{1}{M_B}}}{P \cdot \sigma_{AB}^2 \cdot \Omega_D} \]
where \( T \) is temperature, \( M_A, M_B \) are molecular weights, \( P \) is total pressure, \( \sigma_{AB} \) is collision diameter, and \( \Omega_D \) is the collision integral.

Step 3: Detailed Explanation:

• Pressure Dependence Analysis: From the Chapman-Enskog analytical equation, we can see that:
\[ D_{AB} \propto \frac{1}{P} \]
This means the binary gas diffusivity is inversely proportional to the total pressure at low to moderate pressures.

• Physical Explanation: Diffusion in gases occurs via random molecular collisions.
If the pressure is increased, the gas molecules are compressed closer together, which decreases their mean free path.
With more frequent collisions, the rate of molecular transport (diffusion) is reduced, resulting in a lower diffusion coefficient.
Conversely, lowering the pressure increases the mean free path, allowing molecules to diffuse faster.


Step 4: Final Answer:
In a binary gas mixture at low pressures, the diffusion coefficient is inversely proportional to the pressure.