Ideal Flow Reactors CSTR and PFR Questions and Answers

Answer: C

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

Both are true and the reason is the mechanism. An autocatalytic rate is low at the start, because there is little product to catalyse it, rises to a maximum and falls again as reactant is consumed. A CSTR can be operated with its entire contents sitting at that maximum, whereas a PFR must pass through the slow initial region. That is why the optimal arrangement is often a CSTR to the rate maximum followed by a PFR to finish.

Answer: D

The area under the curve gives the plug flow volume and a rectangle gives the CSTR volume. Reading the two off the same plot makes the comparison between reactor types immediate. The plot is drawn from measured kinetic data.

Answer: A

Both are true and the reason gives the construction, and the difference between the rectangle and the area is exactly the volume penalty a CSTR carries. For a zero order reaction the two coincide. Reading both off one plot is the point of it.

Answer: B

Correct answer: 45 minutes

For a first order reaction in a CSTR, \[ \tau = \frac{X}{k(1-X)} = \frac{0.9}{0.2\times0.1} = \frac{0.9}{0.02} = 45\ \mathrm{min}. \] The 11.5 minutes offered is the PFR answer, \( -\ln(0.1)/0.2 \) - and the comparison is worth noting: at 90 per cent conversion the CSTR needs almost four times the volume, exactly the penalty described in the first item of this topic.

Answer: C

Correct answer: a concentration gradient along it

A gradient is precisely what an ideal CSTR does not have; perfect mixing means the composition is uniform and equal to the exit stream. Steady state, uniform temperature and perfect mixing are the three assumptions that define the ideal. A gradient along the length is the defining feature of the plug flow reactor instead.

Answer: D

The first two are correct and together define plug flow as an idealisation. The third describes a stirred tank and is the direct opposite of the first statement, so no reactor can satisfy both at once and the two models sit at opposite ends of the range.

Answer: A

Correct answer: uniform composition throughout the vessel

Uniform composition throughout describes a CSTR. The plug flow ideal is the opposite: a gradient along the length, no mixing in the axial direction, and complete uniformity across each cross-section, so that every element spends the same time in the reactor and sees the same history.

Answer: B

Correct answer: True

Turbulence mixes vigorously across the tube, which is what plug flow requires, while a large length-to-diameter ratio makes axial dispersion negligible compared with the distance travelled. The two conditions together are what make a long turbulent tube a good approximation, and it is why laminar flow in a short tube is a poor one - the parabolic profile gives fluid at the centre a much shorter residence time than fluid at the wall.

Answer: C

Correct answer: the well mixed contents control temperature

The vigorous mixing keeps the whole vessel at one temperature and puts the entire contents in contact with the heat transfer surface, so there is nowhere for a hot spot to develop. That is the CSTR’s decisive advantage for a strongly exothermic reaction, and it is bought at the cost of volume - the reactor is larger than a PFR of the same duty, not more productive.

Answer: D

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. Near the inlet the reactant concentration is at its highest, so heat is generated fastest there while the cooling capacity per unit length is the same all along. If generation outruns removal the local temperature rises, which raises the rate further - a positive feedback that can run away. Diluting the feed, staging the inlet or grading the catalyst activity are the usual remedies.