Homework Assignment for CHEM 4511
Professor J. M. Weber
Office: JILA A709; Phone 303-492-7841; email: [email protected]
________________________________________________________________________
Problem Set 11
To be returned before class on Wednesday, April 22, 2015. Please slide it under my
office door or bring it to class.
1. Rate Laws
a.) Calculate the integrated rate law for the product concentration in the unimolecular
reaction A  P. Start from the rate law to do so, and assume that there is no product
present at time zero.
(4 credits)
b.) N2O decomposes according to
2 N2O(g)  2 N2(g) + O2(g).
Under certain conditions, the rate of the reaction is 6.1610-6 molL-1s-1. Calculate the
values of d[N2O]/dt, d[N2]/dt and d[O2]/dt.
c.) The reaction
(3 credits)
SO2Cl2(g)  SO2(g) + Cl2(g)
is first order and has a rate constant of kr = 2.2410-5 s-1 at 320C. Calculate the halflife of the reaction. What fraction of the reactant remains after being heated for 5.00
hours at 320C? How long will a sample of SO2Cl2 need to be maintained at 320C
for decomposition of 92% of the initial amount present?
(3 credits)`
d.) In biochemistry, radioactive labeling is often used in kinetics experiments and as
markers in gel electrophoresis. You order a sample of Na3PO4 containing the
radioisotope 32P (t1/2 = 14.3 days). If the shipment in transit is delayed for two weeks,
how much of the initial activity will remain when you finally receive the sample?
(3 credits)
e.) In geology and archaeology, potassium-argon dating is used to date sedimentary
rocks. 40K decays by two pathways:
40
K  40Ca + electron
40
K  40Ar + positron
The overall half-life of 40K is 1.3109 years. Estimate the age of sedimentary rocks
with a 40Ar:40K ratio of 0.0102.
(4 credits)
1
Homework Assignment for CHEM 4511
Professor J. M. Weber
Office: JILA A709; Phone 303-492-7841; email: [email protected]
________________________________________________________________________
A  products
f.) Consider a reaction
d [ A]
 kr [ A]n ,
dt
that obeys the rate law
where n is the reaction order and can have any value except n = 1. Show that for such
a reaction the half-life is given by
t1 / 2 
1 1 2 n1  1
·
·
.
kr n  1 [ A]0n 1
(4 credits)
2. Simulating Reaction Kinetics
Getting integrated rate laws can be mathematically challenging even for relatively simple
reactions, particularly if there are consecutive reactions, or if reactions are close to
equilibrium. In this problem, you will learn how to set up simulations of reaction kinetics
without resorting to integrated rate laws. This is easy to set up in Microsoft Excel or any
similar program. The setup instructions here are for Excel. Start by populating the first
few cells of an Excel sheet as shown below:
1 A Reaction B C AB 2 3 Rate Law vr = k[A] t [A] D E F G t / s 1
[A]0 / mol 1
k / s‐1 0.1
[B]0 / mol 0
k‐1 / s‐1 0.1
4 5 H [B] You will now set up a simulation for a very simple unimolecular reaction of the type
AB
which is first order in both directions. The rate constants are called k for the forward
reaction and k-1 for the back reaction.
2
Homework Assignment for CHEM 4511
Professor J. M. Weber
Office: JILA A709; Phone 303-492-7841; email: [email protected]
________________________________________________________________________
Populate the first three cells in row 6 as follows:
0
=$H$1
=$H$2
The first entry gives the time at the start of the reaction (here defined as zero), and the
other two entries define the concentrations at time zero.
Now enter in the first three cells in row 7 the following:
Into cell A7: =A6+$E$1
increases time by t as defined in cell E1
Into cell B7: =B6-$E$2*B6*$E$1+$E$3*$E$1*C6
according to
[A]previous + [A] = [A]previous – k·[A]previous·t + k-1·[B]previous·t
Into cell C7: =C6-$E$3*$E$1*C6+$E$2*$E$1*B6
according to
calculates [A] at this time
calculates [B] at this time
[B]previous + [B] = [B]previous + k·[A]previous·t – k-1·[B]previous·t
Now copy and paste the contents of cells A7, B7 and C7 into the cells below, so you get
to 50 time steps total (populate all up to row 56). Now you have calculated the
concentrations of A and B for 50 time steps. You can now play with the initial conditions
(cells H1 and H2), the rates (cells E2 and E3) and the time resolution of the simulation
(cell E1). Plot the concentrations of A and B to get the plot shown below:
OK, now you are (hopefully) ready to tackle the following problems:
3
Homework Assignment for CHEM 4511
Professor J. M. Weber
Office: JILA A709; Phone 303-492-7841; email: [email protected]
________________________________________________________________________
a.) Change the initial concentration of B to 1 mol. Describe in one sentence what
happens.
(1 credit)
b.) Change the initial concentration of B to 0.5 mol. What are the concentrations of A
and B in the limit of t?
(2 credits)
c.) Set the initial concentration of B to zero. Now increase both rates in steps of 0.1 s-1.
At what value do you stop getting meaningful results? Why (one sentence)? What can
you do to make the simulation meaningful again, keeping the same rates (one
sentence)?
(4 credits)
d.) Now, you will take the next step: on a new sheet, implement a simulation for the
2A  B.
reaction
This is 2nd order in the forward direction and 1st order in the backward direction. You
can check your results on the way by doing two things:
i.
Make a new column that contains the sum of the concentrations of A and B.
This column must always be the same as the sum of the concentrations at time
zero.
ii.
For long times, the equilibrium constant K must be the ratio of the forward
and backward rate constants. The concentrations must behave accordingly.
Set the initial concentration of A to 1 mol, B to zero, t to 1 s, and use 0.1 s-1 for both
rates. What are the final concentrations for A and B (3 significant figures)? Plot the
graph of your simulation.
(6 credits)
e.) Use the same settings as in (e), except for the initial concentration of B, which you set
to 0.2 mol. What are now the final concentrations of A and B (3 significant figures)?
Plot the graph of your simulation.
(2 credits)
f.) Use the following settings:
t = 2 s;
k = 0.1 s-1;
k-1 = 0.01 s-1; [A]0 = 1 mol; [B]0 = 0.
What are the final concentrations of A and B (3 significant figures)? Plot the graph of
your simulation.
(2 credits)
We will continue with more simulations in the last problem set of the semester (PS 12),
so please make every effort to get this working.
4