Assignment 1: Introduction to Models
This is an individual assignment and is marked out of 36 (as given below).
It will contribute 12% to your total mark for CHEM 3X23
The assignment is due 23:59 Sunday Week 6 (11th September 2022)
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community. In this situation, acting with respect and integrity involves a commitment to our performance on
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confirm that you have acted in line with your responsibilities as outlined in the Student Charter.
Preamble:
Euler’s model can be used to numerically propagate chemical rate equations. It can also be
used to model the thermalisation of molecules via collisions.
In the atmosphere, acetaldehyde, CH3CHO, can absorb a near ultra violet solar photons in
the range 300-340 nm. This corresponds to energies between approximately 350 and 400
kJ/mol, and this energy drives the following chemical reactions involving acetaldehyde,
CH3CHO, vinyl alcohol, CH2CHOH, and the carbene, methylhydroxycarbene, CH3COH:
CH3CHO → CH3 + HCO; 1
CH3CHO → CH4 + CO; 2
CH3CHO ? CH2CHOH; 3, ?3
CH2CHOH ? CH3COH; 4, ?4
With respect to the energy of ground state CH3CHO, the thresholds for these reactions are
350 kJ/mol for formation of both the CH3 + HCO and the CH4 + CO products, 282 kJ/mol for
formation of CH2CHOH, and 310 kJ/mol for formation of CH3COH.
The Jupyter notebooks for ‘Model 3’ and ‘Model 3 with Collisions’ from Lecture 6 contains a
number of useful Python functions:
functions that determine the rate coefficients for these reactions per nanosecond as
a function of energy, in kJ/mol.
a function to determine, for a given temperature and pressure, the collision rate per
nanosecond between the C2H4O isomers and atmospheric N2 or O2.
a program that uses Euler’s method to propagate solutions to these reactions that
includes loss of internal energy of dE = 1.8 kJ/mol per collision, when the CH3CHO,
CH2CHOH and CH3COH molecules collide with atmospheric N2 and O2 molecules.
You can use these functions to do your assignment or write your own. If you are
adventurous, you could do a stochastic rather than a deterministic simulation. There are no
additional marks for doing this, however. If you do write your own code, please upload a
python notebook, as an .ipynb file, together with your assignment.
Assignment Questions:
1. In the absence of collisions, it is relatively easy to model these reactions using numerical
iterative, matrix or stochastic models. Discuss the relative strengths and weaknesses of
these models. (6 marks)
2. In the absence of collisions what, in general, will be the long-term outcome of the
system of reactions? (Hint: if you are not sure, you could run a simulation with k_coll=
0.0). (2 marks)
3. For an initial energy of E0 = 375 kJ/mol, using the functions/functional forms provided,
determine the rate coefficients, per nanosecond, k1, k2, k3, k_3, k4 and k_4. On the basis
of these values, suggest an appropriate time step and total time for the simulation of
the system of reactions. Give reasons for your answers. (6 marks)
4. Using the last two digits of your SID (I’ve indicated these as “XX” below), choose a
pressure of 0.XX atmospheres. (NB if the last two digits are both zero, use the last two
digits that include a non-zero digit). Determine the collision frequency, k_coll, per
nanosecond at this pressure and at a temperature of 300 K. On the basis of this value,
should the time step or total simulation time be modified, from your answer to question
3. If so, to what values. Give reasons for your answer. (3 marks)
5. Choosing an appropriate time step, dt, and total time, Total_time, simulate the system of
reactions at the pressure chosen in Q4, using either the Python code provided or code
you write yourself. Include a publication quality plot or plots of the mole fraction of the
6 ‘species’ (that is, CH3CHO, CH3+HCO, CH4+CO, CH2CHOH and CH3COH as a function of
time. Also make sure you provide the final, equilibrium, mole fractions of the 6 species.
(13 marks)
6. Describe the differences you observe in your simulation in question 5, compared to
what would have been observed at a pressure of 1.5 atm. (Hint: if you are not sure, you
could run a simulation with Pressure = 1.5 atm). (2 marks)
7. If energy loss were significantly more efficient, for example, if dE = 5.0 kJ/mol, describe
how this would this change your results from question 5. Rationalise these changes in
terms of the reaction thresholds. (Hint: if you are not sure, you could run a simulation
with dE = 5.0 kJ/mol). (2 marks)
8. If the initial solar photon were 300 nm, providing the CH3CHO with approximately 400
kJ/mol internal energy, how would this change your results from question 5? (Hint: if
you are not sure, you could run a simulation with E0 = 400.0 kJ/mol). (2 marks)