Question

Reaction A → B follows first-order elementary kinetics and the reaction rate constant for A is 0.01 per min.

The time taken to reduce the concentration of A from 100 M to 10 M in a batch reactor is ______ min (rounded off to one decimal place).

Hint:

Use the integrated first-order batch reactor equation C = C0 e^(-kt) and solve for t after substituting the given concentrations and rate constant.

Answer 1

Correct Answer: 230.3

Step 1: Write the governing rate equation for a first-order batch reaction.
For \(A \rightarrow B\) following first-order kinetics in a batch reactor, \[-\frac{dC_A}{dt} = kC_A\] which on integration between the initial concentration \(C_{A0}\) and the concentration \(C_A\) at time \(t\) gives \[C_A = C_{A0}\,e^{-kt}\]

Step 2: Substitute the known values.
Here \(C_{A0}=100\ M\), \(C_A=10\ M\), and \(k = 0.01\ min^{-1}\). So \[10 = 100\,e^{-0.01t}\]

Step 3: Solve for time.
Dividing both sides by 100 gives \(e^{-0.01t} = 0.1\). Taking the natural log of both sides: \[-0.01t = \ln(0.1) = -2.302585\] \[t = \frac{2.302585}{0.01} = 230.2585\ min\]

Step 4: Round the result.
Rounding to one decimal place, \(t \approx 230.3\ min\), which falls right in the expected 225-235 minute band.