Question

The following isothermal autocatalytic reaction: 
\[ A + B \longrightarrow 2B \left( -r_A = 0.1 C_A C_B \, \text{(mol L}^{-1} \text{s}^{-1}) \right) \] is carried out in an ideal continuous stirred tank reactor (CSTR) operating at steady state. Pure A at 1 mol L\(^{-1}\) is fed, and 90% of A is converted in the CSTR. The space time of the CSTR is \(\underline{\hspace{1cm}}\) seconds.
 

Hint:

For CSTRs, space time \( \tau = \frac{V}{F} \), and mass balances help to determine the conversion and space time.

Answer 1

Correct Answer: 100

For a CSTR, the space time \( \tau \) is given by:
\[ \tau = \frac{V}{F} \]
The mass balance at steady state for component A is:
\[ F(C_{A0} - C_A) = -r_A V \]
Substitute the given values: \( C_{A0} = 1 \, \text{mol L}^{-1} \), \( C_A = 0.1 \, \text{mol L}^{-1} \), and \( r_A = 0.1 \cdot C_A \cdot (C_{A0} - C_A) \):
\[ F(1 - 0.1) = 0.1 \cdot 0.1 \cdot (1 - 0.1) V \]
Simplifying:
\[ F \times 0.9 = 0.009 \times V \]
Solving for space time:
\[ \tau = \frac{100}{1} = 100 \, \text{seconds} \]