Ideal Flow Reactors CSTR and PFR Questions and Answers

Answer: A

Perfect mixing means every point in the vessel is at the exit composition, so the reaction proceeds at the lowest rate in the whole conversion range. This single fact explains most of the differences from a plug flow reactor.

Answer: B

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the reason is the cause. A CSTR is perfectly mixed, so the whole vessel sits at the exit composition and therefore at the lowest rate anywhere in the process. A PFR passes through the whole range of compositions, working at high rate near the inlet, so it achieves the same conversion in less volume. The gap widens with the reaction order and with the conversion demanded.

Answer: C

Correct answer: a batch reactor with time replaced

Both integrate the same expression: \[ t = \int_0^{X}\frac{C_{A0}\,dX}{-r_A} \quad\text{and}\quad \tau = \int_0^{X}\frac{C_{A0}\,dX}{-r_A}. \] In the batch reactor the composition changes with time in a fixed volume; in the PFR it changes with position as a fluid element travels. A batch result can therefore be carried straight over to a PFR by reading time as space time.

Answer: D

Both are true and the reason gives the correspondence: the only difference is that the batch clock is replaced by position along the tube, which is why the two design equations take the same form. Batch data transfer directly to plug flow design.

Answer: A

It has units of time and is the time to process one reactor volume of feed. Space velocity is its reciprocal and is often quoted per hour instead. The two are reciprocals of one another. Both describe how hard the reactor is worked.

Answer: B

Five hundred divided by fifty is ten minutes. Space time equals the mean residence time only when the volumetric flow does not change through the reactor. For liquids the two are almost always equal. Gas phase expansion breaks the equality.

Answer: C

Correct answer: True

Space time is \( \tau = V/v_0 \), the reactor volume divided by the *entering* volumetric flow rate. When the density is constant the volumetric flow does not change through the reactor, so every element takes the same time to pass and the mean residence time equals \( \tau \). Where the number of moles changes in the gas phase the two diverge, and space time remains the design quantity because it is defined on the inlet.

Answer: D

Correct answer: A-2, B-4, C-1, D-3

Each reactor is characterised by how composition varies. A CSTR is uniform and equal to the exit stream. A PFR has a gradient along its length and none across it. A batch reactor varies with time but not position, since it is well mixed and closed. A semi-batch has one reactant fed in while nothing is withdrawn, which is how a reaction with a dangerous exotherm or an unwanted side reaction is controlled.

Answer: A

Correct answer: 1 and 2 only

Statements 1 and 2 are correct: for normal kinetics the PFR gives more conversion per unit volume, and the CSTR’s uniform contents make it far easier to hold at temperature. Statement 3 overstates the case in the opposite direction - the CSTR is generally the *larger*, and it is smaller only in the special cases such as autocatalysis considered elsewhere in this topic.

Answer: B

The CSTR carries the mixture quickly past the slow initial region where there is no product to catalyse the reaction. The PFR then finishes the job efficiently where the rate is falling. The combination beats either reactor alone.