Tutorial 4 - 2013

From Introduction to Reactor Design: 3K4
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Due date(s): All questions due as assignment 3A
Nuvola mimetypes pdf.png (PDF) Tutorial questions

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    • Assignment objectives**:

* To demonstrate your understanding of chemical equilibrium in system with and without change in volume. * To use the reactor design equations in terms of conversion.

.. question:: :grading: 5

Consider the reversible reaction of A going to 2B, with only pure A fed to the flow reactor at 340K and 202.6 kPa. The equilibrium constant at 340K is :math:`K_C = 100\,\text{mol.m}^{-3}`.

Show that the equilibrium conversion, :math:`X_\text{eq}`, leaving the reactor is :math:`X_\text{eq} = 0.51`.

.. question:: :grading: 4

Consider the system producing product, D, from raw materials A and B in the reversible reaction:

.. math::

\text{A} + \text{B} \mathop{\rightleftharpoons}_{k_{-A}}^{k_A} \text{D}

If the equilibrium constant, :math:`K_C` has a value of 40 at room temperature, 25°C:

#. What are the units of :math:`K_C`? #. What is the value of :math:`K_C` at 50°C, if the heat of reaction is :math:`150\,\text{kJ.mol}^{-1}`? #. Draw of a plot of the equilibrium constant against temperature.

.. question:: :grading: 20

At your company there is an existing glass-lined, and well-mixed CSTR. With the inlet and outlet valves closed it becomes a batch reactor. The volume of this vessel is 1800 L. The temperature of the vessel is easily controlled.

You are working to produce a product, D, from raw materials A and B in the reaction:

.. math::

\text{A} + \text{B} \mathop{\longrightarrow}^{k_A} \text{D}

which is a liquid-phase reaction system that operates with the following kinetics: :math:`-r_A = k_A C_A`, where :math:`k_A = 0.18\,\text{hour}^{-1}` helpfully determined by your company's laboratory, at room temperatures of 25°C.

Your boss is giving you, the engineering team lead, the task of determining how to maximize production of species D. Because there is such a high demand for it, you must figure out how to produce the most amount of D within a regular production shift in that vessel. Species A is available in pure form at 50 mol per litre, and species B is available at 70 mol per litre.

There is only one constraint: you must operate at room temperature, because the product is extremely temperature sensitive and starts to degrade rapidly at temperatures exceeding 30°C. Also consider that you want the stream leaving the reactor to have a high purity, so you can minimize the amount of downstream separation of D from A and B.

Describe *clearly and concisely to your operators* how to produce product D and how much of D will be produced in a 12 hour period. You must show all your calculation steps to obtain full grade.

.. question:: :grading: 12

The following gas phase reaction is taking place: :math:`\text{A} \longrightarrow 3\text{B}` at 350K and 900 kPa; the equilibrium constant is :math:`0.20\,\text{mol}^2\text{.L}^{-6}` at these conditions. Calculate (a) the equilibrium concentration of A, (b) the equilibrium concentration of B, and (c) the conversion of A, for the following 3 cases:

#. The material is reacting in a flow reactor. #. The material is reacting in a constant volume batch reactor. #. The material is reacting in a constant pressure batch reactor.


4. Compare the above answers for the 3 situations and explain why they make sense/do not make sense. In particular, explain any differences in the equilibrium concentration of A among the 3 reactors.