Catalysis

Step 1: Understanding the relation.
The effectiveness factor and thiele modulus are related in catalytic reactions occurring in porous media. The relationship for a first-order isothermal catalytic reaction in an infinitely long cylindrical pore is given by: This relationship reflects the behavior of the catalyst effectiveness depending on the diffusion and reaction rates.
Step 2: Analyzing the options.
(1) : This is the correct relationship for a first-order reaction occurring in an infinitely long cylindrical pore.
(2) : This is incorrect because it does not match the expected relationship.
(3) : This is incorrect because it does not account for the influence of the thiele modulus.
(4) : This is incorrect as it does not reflect the correct relationship for the given scenario.
Step 3: Conclusion.
The correct answer is , as it matches the established relationship for this reaction type.