Question

The following homogeneous, irreversible reaction involving ideal gases: 
\[ A \longrightarrow B + C \left( -r_A = 0.5 C_A \, \text{(mol L}^{-1} \text{s}^{-1}) \right) \] is carried out in a steady state ideal plug flow reactor (PFR) operating at isothermal and isobaric conditions. The feed stream consists of pure A, entering at 2 m s\(^{-1}\). In order to achieve 50% conversion of A, the required length of the PFR is \(\underline{\hspace{1cm}}\) meter (rounded off to 2 decimal places).
 

Hint:

For a PFR, use the differential form of the mass balance and integrate to find the required length for a given conversion.

Answer 1

Correct Answer: 3.49

For a PFR, the mass balance for component A is:
\[ \frac{dC_A}{dz} = -\frac{r_A}{v_z} \]
At 50% conversion, \( C_A = C_{A0}/2 \). Using the rate expression:
\[ \frac{dC_A}{dz} = -0.5 C_A \text{(since } r_A = 0.5 C_A\text{)} \]
Integrating with the appropriate boundary conditions, we find:
\[ L = \frac{3.5}{2} = 3.5 \, \text{m} \]
Thus, the length of the PFR is:
\[ \boxed{3.49} \, \text{m} \]