Difference between revisions of "Assignment 1 - 2013"
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:grading: 10 | :grading: 10 | ||
#. :math:`\displaystyle \int{ \frac{1}{x} \,dx}` | #. :math:`\displaystyle \int{ \frac{1}{x} \,dx} =` | ||
#. :math:`\displaystyle \int{ \frac{1}{x^2} \,dx}` | #. :math:`\displaystyle \int{ \frac{1}{x^2} \,dx} =` | ||
#. :math:`\displaystyle \int{ \frac{1}{ax+b} \,dx}` | #. :math:`\displaystyle \int{ \frac{1}{ax+b} \,dx} =` | ||
#. :math:`\displaystyle \int{ \frac{1}{\sqrt{x}} \,dx}` | #. :math:`\displaystyle \int{ \frac{1}{\sqrt{x}} \,dx} =` | ||
#. When do we require an integration constant; and when do we not require it? | #. When do we require an integration constant; and when do we not require it? | ||
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#. 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 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. | #. 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? | ||
.. question:: | .. question:: | ||
:grading: 10 | :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 | 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}}`. | 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}}`. | ||
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-r_A = \frac{0.1 C_A}{1+0.5 C_A } \left[\dfrac{\text{mol}}{\text{L.min}}\right] | -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 | 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 | 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 | ||
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3. PFR | 3. PFR | ||
to achieve an exit concentration of A of | 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? | 4. Which of the CSTR or PFR require a smaller volume? | ||
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:math:`k = 2\,\text{L.mol}^{-1}\text{.min}^{-1}`. | :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: | 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 partial pressure due to A in the reactor | ||
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:grading: 10 | :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 | 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: | ||
.. math:: | .. math:: |
Revision as of 13:40, 14 January 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 14.7 psi and 1340°F. The reactor volume is :math:`290\,\text{ft}^3`. How many mols are in the system, assuming an ideal gas?
.. 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 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
.. 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 :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?
.. 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 (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.
.. 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 material:
.. 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>