# Difference between revisions of "Assignment 1 - 2013"

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

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• 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

#. :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?

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

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 seconds 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

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 :math:0.1\,\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 :math:0.1\,\text{mol.L}^{-1}.

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

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 (is this a reasonable assumption?). 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.

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 material:
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>