Question

A unimolecular, irreversible liquid-phase reaction \(A \rightarrow P\) is carried out in an ideal batch reactor at temperature \(T\). The rate of reaction \((-r_A)\) (in \(\text{mol}\,\text{m}^{-3}\,\text{s}^{-1}\)) measured at different conversions \(X_A\) is given: \[ \begin{array}{c|cccccc} X_A & 0 & 0.1 & 0.2 & 0.4 & 0.6 & 0.8\\\hline -r_A & 0.45 & 0.35 & 0.31 & 0.18 & 0.11 & 0.05 \end{array} \] The reaction is also carried out in an ideal CSTR at the same \(T\) with a feed concentration \(C_{A0}=1\ \text{mol}\,\text{m}^{-3}\) under steady state. For a conversion of \(0.8\), the space time (in s) of the CSTR is ____________ (in integer).

Hint:

For CSTR design at a specified conversion, use the exit rate at that conversion: \(\tau=C_{A0}X_A/(-r_A)_{\text{exit}}\).
The batch data table directly provides \((-r_A)\) vs. \(X_A\), so interpolation at the target \(X_A\) (if needed) gives the required exit rate.

Answer 1

Correct Answer: 16

Step 1: For a steady-state CSTR, \[ \tau=\frac{C_{A0}X_A}{-r_A\big|_{\text{exit}}}. \] Step 2: At the desired conversion \(X_A=0.8\), the exit rate from the table is \((-r_A)=0.05\ \text{mol}\,\text{m}^{-3}\,\text{s}^{-1}\). Step 3: Substitute \(C_{A0}=1\ \text{mol}\,\text{m}^{-3}\): \[ \tau=\frac{1\times 0.8}{0.05}=16\ \text{s}. \] \[ \boxed{16} \]