Question

The elementary gas-phase reaction A+ B → C + D takes place isothermally at 300 K in a packed bed reactor in which the initial concentrations for A and B are both 1 mol/dm3. Currently, 60% conversion is achieved in a reactor with 80 kg of catalyst for a volumetric flow rate 120dm3/min. The pressure-drop parameter, a is 0.007 kg¹¹. If the activation energy is 50 kJ/mol, what is the specific reaction rate constant at 400 K?

Answer 1

The specific reaction rate constant, also known as the rate constant, can be determined using the Arrhenius equation, which relates the rate constant to the activation energy and the temperature. The Arrhenius equation is given by:

k = A * exp(-Ea / (R * T))

where:

k is the rate constant,

A is the pre-exponential factor,

Ea is the activation energy,

R is the gas constant (8.314 J/(mol·K)), and

T is the temperature in Kelvin.

In this case, we are given that the reaction is taking place at 300 K. To find the specific reaction rate constant at 400 K, we need to calculate the rate constant at both temperatures and compare the values.

Given:

Initial concentration of A = 1 mol/dm³

Initial concentration of B = 1 mol/dm³

Conversion = 60%

Catalyst mass = 80 kg

Volumetric flow rate = 120 dm³/min

Pressure-drop parameter (a) = 0.007 kg¹¹

Activation energy (Ea) = 50 kJ/mol

First, let's calculate the specific reaction rate constant at 300 K using the given information. Since we have the conversion and the catalyst mass, we can calculate the space-time (