The liquid-phase reaction follows an elementary rate law and is carried out isothermally in a flow system. The concentrations of the A and B feed streams are 2 M before mixing. The volumetric flow rate of each stream is 5 dm 3 /min, and the entering temperature is 300 K. The streams are mixed immediately before entering. Two reactors are available. One is a gray, 200.0-dm 3 CSTR that can be heated to 77 C or cooled to 0 C, and the other is a white, 800.0-dm 3 PFR operated at 300 K that cannot be heated or cooled but can be painted red or black. Note that k 0.07 dm 3 /mol min at 300 K and E 20 kcal/mol.

a) Which reactor would and what conditions do you recommend? Explaining the reason for your choice. Back up your reasoning with calculations.

b) How long would it take to achieve 90% conversion in a 200 dm3 batch reactor with initial concentrations of A and B at 1 mol/L and operated at 77 °C?

c) What would be your answer to part (b) if at 0 °C?

d) What conversion would be obtained if the CSTR and PFR were operated at 300 K and connected in series? In parallel with 5 dm min of the mixture to each?

e) What can you say about the various reactor types based on the above?

a) The CSTR operating at 77 °C is recommended since it attain a higher conversion (96.2%).

b) 1.05 minutes.

c) 3474.9 minutes.

d)

- Series: 96%

- Parallel: 86%

e) The highest conversion was obtained in the first single 200-dm³ CSTR.

Explanation:

Hello,

At first, it is convenient to know that the initial flow rates of both A and B are equal since their volumetric rates and concentrations are equal:

Hence, we proceed.

a) In this case, one could select the answer by comparing the obtained conversion of A in the PFR and in the CSTR as shown below:

- PFR: the design equation is:

So the rate, as it is an elemental reaction, we have:

Integrating as shown below:

Thus, the achieved conversion is the 95.7% which looks promising under its operation conditions.

- CSTR: the design equation is:

In this case, the greater rate constant is selected as shown below:

In such a way, it is better at 77 °C

Therefore, the conversion is found by solving the design equation with solver as:

Thus, the achieved conversion is the 96.2% which looks promising under its operation conditions.

Therefore, the CSTR operating at 77 °C is recommended since it attain a higher conversion.

b) In this case, the rate constant is 8.55 dm³mol⁻¹min⁻¹ as previously computed, so the design equation is:

As long as there is no change in volume by cause of the state at which the reaction is carried out, that is liquid. Thereby, integrating and solving for time for a 90% conversion we obtain:

c) In this case, the rate constant is 0.00259 dm³mol⁻¹min⁻¹ as previously computed, so the time turns out:

d)

- Series: the first CSTR will provide the following conversion, considering that the rate constant is at 300K:

Consequently, the inlet concentration and flow rate to the PFR are:

In this manner, the new integration yields the following conversion:

And the overall conversion is:

- Parallel:

In this case, the initial flow rate to each reactor is 5 mol/min as the feed is divided, thus, the CSTR will provide the following conversion:

And the PFR:

Thus, the outlet A's flow rate from the CSTR and the PFR is:

Thus, the outlet flow rate is 1.4 mol/mol, so the overall conversion is:

e) The results showed that a simple CSTR is more than enough to attain a high conversion since the reaction is second-order, because if it would be first order a higher change in the conversion will be related with a higher volume for both CSTR and PFR, as well as it is the smallest one (cheaper one).

Best regards.