Question

What is the Knudsen diffusion coefficient for cumene at 510°C through the pores of a catalyst of porosity 0.51 and density 1.14 g/cm³? The specific surface area is 342 m²/g.

• A. 2.46 cm²/sec
• B. \( 6.46 \times 10^{-3} \) cm²/sec
• C. \( 8.46 \times 10^{-3} \) cm²/sec
• D. \( 1.05 \times 10^{-4} \) cm²/sec

Hint:

The Knudsen diffusion coefficient helps determine the rate of molecular diffusion in porous materials. It is influenced by factors like porosity and surface are(A)

Answer 1

The Correct Option is B

- The Knudsen diffusion coefficient is given by: \[ D_K = \frac{2}{3} \times \frac{d_p^2}{r} \times \frac{1}{\epsilon} \] where \( d_p \) is the pore diameter, \( r \) is the gas viscosity, and \( \epsilon \) is the porosity. - Substituting the given values, we can calculate the Knudsen diffusion coefficient to be \( 6.46 \times 10^{-3} \) cm²/se(C) 
Conclusion: The Knudsen diffusion coefficient for cumene is \( 6.46 \times 10^{-3} \) cm²/sec, as given by option (B).