Question

The reaction A → B is carried out isothermally on a porous catalyst. The intrinsic reaction rate is $k C_A^2$, where $k$ is the rate constant and $C_A$ is the concentration of A. If the reaction is strongly pore-diffusion controlled, the observed order of the reaction is

• A. 1
• B. 2
• C. 3/2
• D. $\sqrt{2}$

Hint:

When internal diffusion limits a catalytic reaction, the observed order becomes $(n+1)/2$ for an intrinsic $n$-th order reaction. This helps identify diffusion limitation experimentally.

Answer 1

The Correct Option is C

In porous catalysts, the overall reaction rate may not follow the intrinsic kinetic order if strong internal diffusion resistance exists. When diffusion is slow compared to reaction, the concentration profile inside the pores becomes steep, and the "effective rate" is determined by the combined effect of kinetics and diffusion. For a reaction with intrinsic rate proportional to $C_A^n$, the observed order under strong pore-diffusion control becomes $(n+1)/2$. This result comes from solving the diffusion–reaction equation inside a spherical or cylindrical pore, where diffusion and reaction simultaneously occur.

Step 1: Intrinsic order
Given intrinsic rate $r = k C_A^2$, the intrinsic reaction order is $n = 2$.

Step 2: Observed order under pore-diffusion control
For strong diffusion limitation, the Thiele modulus is large. The rate is then proportional to the surface concentration multiplied by the effectiveness factor, which scales as $1/\phi$ for large $\phi$. The effective reaction rate behaves as: \[ r_{\text{obs}} \propto C_A^{(n+1)/2}. \] Substituting $n = 2$ gives \[ \frac{n+1}{2} = \frac{2+1}{2} = \frac{3}{2}. \]

Step 3: Conclusion
Thus, the observed reaction order is 3/2 instead of the intrinsic value of 2 when the reaction is strongly pore-diffusion controlled.