Question

If the conversion of a first-order liquid phase reaction occurring in a CSTR is 75%, molar feed rate is 5 mol/min, the rate of the reaction is 5 $\frac{mol}{litre \cdot min}$ then the volume of the reactor (in litre) is?

• A. 0.33
• B. 0.4
• C. 0.75
• D. 0.5

Hint:

Remember that for a CSTR, the rate of reaction is evaluated at the exit conditions (which are the same as the conditions inside the reactor due to perfect mixing). The conversion \(X_A\) is defined as the moles of \(A\) reacted per mole of \(A\) fed.

Answer 1

The Correct Option is C

Step 1: Understand the characteristics of a CSTR and a first-order liquid phase reaction.

Continuous Stirred Tank Reactor (CSTR): A CSTR is an ideal reactor where the contents are perfectly mixed, leading to a uniform concentration and temperature throughout the reactor. The exit stream has the same properties as the fluid inside the reactor.

First-order liquid phase reaction: For a first-order reaction \(A \rightarrow \text{products}\) in the liquid phase, the rate of reaction \(-r_A\) is proportional to the concentration of the reactant \(A\):

\(-r_A = k C_A\)

where \(k\) is the rate constant and \(C_A\) is the concentration of \(A\).

Step 2: Apply the design equation for a CSTR.

The design equation for a CSTR in terms of the molar flow rate of the reactant \(F_{A0}\), the conversion \(X_A\), and the rate of reaction \(-r_A\) is:

\( V = \frac{F_{A0} X_A}{-r_A} \)

where \(V\) is the volume of the reactor.

Step 3: Identify the given parameters.

From the problem statement, we have:

• Conversion \(X_A = 75\% = 0.75\)
• Molar feed rate \(F_{A0} = 5\) mol/min
• Rate of the reaction \(-r_A = 5\) mol/(litre·min)

Step 4: Substitute the values into the design equation and solve for the volume \(V\).

Plugging the given values into the CSTR design equation:

\( V = \frac{(5 \, \text{mol/min}) \times (0.75)}{5 \, \text{mol/(litre} \cdot \text{min})} \)

\( V = \frac{3.75 \, \text{mol/min}}{5 \, \text{mol/(litre} \cdot \text{min})} \)

\( V = 0.75 \, \text{litre} \)

Therefore, the volume of the reactor is 0.75 litre.

Step 5: Match the calculated volume with the given options.

The calculated volume \(0.75\) litre matches option (3).