Assignment 1 - 2013

Due date(s):	21 January 2013
(PDF)	Assignment questions

<rst> <rst-options: 'toc' = False/> <rst-options: 'reset-figures' = False/>

• • Assignment objectives**: math refresher; chemistry refresher; review mol balances

* Always state assumptions in this assignment, midterms and exams. * Never use an equation by just writing it down; state its origin and all simplifying assumptions. *For example*: using the general mol balance in a batch reactor, under the assumption of a well-mixed and constant volume system, we have: :math:`\dfrac{dN_j}{dt} = r_jV`

.. question:: :grading: 10

#. :math:`\displaystyle \int{ \frac{1}{x} \,dx}` #. :math:`\displaystyle \int{ \frac{1}{x^2} \,dx}` #. :math:`\displaystyle \int{ \frac{1}{ax+b} \,dx}` #. :math:`\displaystyle \int{ \frac{1}{\sqrt{x}} \,dx}` #. When do we require an integration constant; and when do we not require it?

.. question:: :grading: 10

#. A vessel contains a gas of concentration :math:`20\,\text{mol.m}^{-3}`. The gas is stored at 375°C. Assuming this is an ideal gas, what is the pressure in the vessel measured in kPa? What assumption are you making (apart from the ideal-gas law)?

#. A constant volume batch reactor operates at 14.7psi and 1340°F. The reactor volume is :math:`290\,\text{ft}^3`. How many mols are in the system, assuming an ideal gas?

.. question:: :grading: 10

Milk is pasteurized if it is heated to 63°C for 30 min, but if it is heated to 74°C it only needs 15 sec for the same result. Find the activation energy of this sterilization process.

Recall the activation energy for a chemical reaction is the :math:`E` term, and the rate constant in is given by :math:`k = k_0 e^{\frac{-E}{RT}}`.

*Hint*: assume pasteurization proceeds via first-order kinetics; what is the "reactant"?

.. Solution

See Vida's solution

.. question:: :grading: 13

The fermentation of an active ingredient :math:`A` is to be carried out in a reactor. The reaction kinetics are given by:

.. math::

A \longrightarrow R

-r_A = \frac{0.1 C_A}{1+0.5 C_A } \left[\dfrac{\text{mol}}{\text{L.min}}\right]

1. Consider a batch reactor filled with 750 L of reactant at :math:`C_{A,0} = 2 \text{mol.L}^{-1}`. How long must the reactor be operated to achieve an exit concentration of A of 0.1 :math:`\text{mol.L}^{-1}`?

If the feed rate is continuously fed at :math:`25\,\text{L.min}^{-1}`, with :math:`C_{A,0} = 2\,\text{mol.L}^{-1}`. Determine the volume required for a

2. CSTR 3. PFR

to achieve an exit concentration of A of 0.1 :math:`\text{mol.L}^{-1}`.

4. Which of the CSTR or PFR require a smaller volume?

.. question:: :grading: 7

The gas phase reaction:

.. math::

A \longrightarrow B + C

is carried out at 100°C in a 20 L constant-volume, sealed batch reactor, at atmospheric pressure. The reaction is second order: :math:`-r_A = k C_A^2` where :math:`k = 2\,\text{L.mol}^{-1}\text{.min}^{-1}`.

One mole of pure A is initially placed in the reactor, which is well mixed. Determine:

#. the partial pressure due to A in the reactor #. the concentration of A in the reactor after 5 minutes have elapsed #. the partial pressure due to A in the reactor after 5 minutes have elapsed.

.. question:: :grading: 10

Consider a municipal water treatment plant for a smallish community. Waste water at :math:`32,000\,\text{m}^3\text{.day}^{-1}`, flows through the treatment plant with a mean residence time of 8 hours. Air is bubbled through the tanks, and microbes in the tank attack and break down the organic materia

.. math::

\text{Organic waste} + \text{O}_2 \xrightarrow{\text{microbes}} \text{CO}_2 + \text{H}_2\text{O}

A typical entering feed has a BOD (biological oxygen demand) of :math:`200\,(\text{mg O}_2)\text{.L}^{-1}`, the effluent has a negligible BOD. Find the average rate of reaction, or decrease in BOD, in the treatment tanks. </rst>