Chem. 312, Autumn '13
Problem Set 2
Problem Set #2, page 1
Due in class, Wednesday, October 9
1. Consider the graph of r22 at right. Which of
the following could this graph below to?
(i) 2s
(ii) 2p
(iii) 5f
(iv) 3p
(v) 4d
(vi) 3s
The correct answer could be zero, one, or more of
the above. Briefly explain.
2. (a) How many nodes are there in a 6dx2-y2 orbital? Describe each node.
(b) For an electron in a 6d orbital, give the possible range of each of the four quantum numbers
(n, l, ml, ms).
3. Draw the orbitals listed below. Indicate all nodes with dotted lines.
(a) 4s
(b) 4pz
(c) 5dx2-y2
4. On the last problem set, we determined that Fe3+ could have three possible configurations:
4s23d3, 4s13d4, or 3d5. Here you will figure out which one is likely the correct ground state.
(a) Let's do it one step at a time, starting with the configuration 3d3 since an Fe3+ ion must have
at least three 3d electrons. If an electron is added to this d3 ion, will it occupy a 4s orbital or ax
3d orbital? Answer this question by calculating the energy of the electron in each case, using
Slater’s rules, -(Z*)2/(n*)2. The electron will occupy the more stable orbital, the one with the
more negative energy.
(b) Now add the second electron, to the ion whose configuration you have just determined. Follow the
same procedure as in part (a) to determine if this electron occupies a 4s or a 3d orbital.
5.(a) Using Slater's rules and the approximate equation for the radius of an atom,
[r = ao(n*)2/(Z*)], order the atoms F, Ne, Na in terms of increasing size.
(b) Is the size difference between F and Ne greater or less than the difference between Ne and
Na? Briefly explain why this is (not just by restating your Slater's rules result).
6. Based on the trends we have discussed in class, for each pair of elements below, predict:
(a) Which has the larger covalent radius?
(b) Which has the larger electronegativity?
(c) Which has the larger first ionization energy (ionization potential)?
(i) C vs. Si
(ii) C vs. N
(iii) C vs. P
(iv) Si vs. P
Note: “I can’t predict” based on the trends could be the correct answer.
(d) Now look up the values for these parameters for these elements in the tables in the text.
Are the predictions based on the trends accurate?
Chem. 312, Autumn '13
Problem Set #2, page 2
7.
Now look up the first ionization energies of Ge and As.
(a) Are there larger changes on moving from the second period to the third (CSi, NP) or on
moving from the third period to the fourth (AlGa, SiGe)?
(b) Is this expected based on the simple trends taught in class?
(c) Discuss your answers to (a) and (b) in light of what Slater's Rules calculate: Calculate ESlater
= -(Z*)2/(n*)2 for the outermost electron in C, Si, and Ge.
(d) In a sentence or two explain why moving from C to Si is different than moving from Si to Ge.
8. You know about vertical relationships in the Periodic Table, for instance that C and Si are similar
because they are both in group 14. There are also similarities between elements that are
diagonally related (diagonal relationships).
(a) Based on your answers to problem 4, do you think that there are strong similarities between Si
and N or strong similarities between C and P?
(b) In general, do you think diagonal relationships will be “one down and one to the right" or "one
down and one to the left" within the Periodic Table? Explain, based on the trends.
(c) Based on your answer to problem 5, do you think these diagonal relationships will be closer
for second/third period combinations or third/fourth period combinations?
9. On the basis of the trends discussed in class,
(a) Order the following ions in order of increasing ionic radius: (i) Ti2+ (ii) Ti4+ (iii) Ca2+
(b) Order the ions below in order of increasing heat of hydration, Hhyd.
(i) Ti2+
(ii) Ca2+
(iii) Li+
(c) Order the ions in (b) in order of increasing acidity (decreasing pKa of aquo ions).
10. “Energy” is a hot topic these days, from the high price of gasoline to the environmental cost
(major or minor?) of oil drilling or fracking for natural gas (as described in the movie The
Promised Land).
(a) Briefly describe (a few sentences at most) roughly what “natural gas” is composed of
(chemically), and what process is described by the word “fracking.” Please look on the web, and
see if you find different perspectives on fracking.
(b) Some natural gas contains a fair amount of helium (this is where we get most of the He we
use). Based on your knowledge of nuclear chemistry (not geology or atmospheric science), can
you guess where this He comes from? [Hint: this answer is distantly related to the crustal
abundance discussed in class.]
(c) Briefly describe what the “Deepwater Horizon” was, what it did, what happened to it, and why
this was national news for months.
(d) Do you see any conceptual connection between the “Deepwater Horizon” and concerns over
fracking? Note that some people do and some don’t see any connection; I want your opinion.
11. In 2005, Inorganic Chemistry published a set of related papers (a “Forum”), on solar energy.
The Preface is still relevant today; please download and read: Overview of the Forum on Solar
and Renewable Energy by R. Eisenberg, D.G. Nocera Inorg. Chem. 2005, 44, 6799 – 6801.
(a) It is stated that global annual energy consumption in 1998 was “402 exajoules (12.7 TW [terawatts]).” Exa is the SI prefix for 1018 and tera is the prefix for 1012. Joules and watts are
different kinds of units. Explain why they are different and how the authors converted the
value in joules to one in watts. For some helpful links and some calibration, you might be
interested in: http://en.wikipedia.org/wiki/Orders_of_magnitude_(energy)
(b) According to this article, what is the U.S. fraction of global energy consumption? Do you
guess that the U.S. fraction is higher or lower today than it was in 2005? Can you estimate
Chem. 312, Autumn '13
Problem Set #2, page 3
(not given in the article) what is the U.S. fraction of global population? You might check the
U.S. Census Bureau for relevant numbers. Any comments?
(c) Summarize in one or two sentences the argument made in the long lower paragraph in the first
column of p. 6800. Do you find the analysis and conclusions convincing?
(d) Nuclear energy is a substantial part of electricity production. What major world even has
happened since 2005 that has changed the global view of nuclear power, at least for some?
12. Download: Long-Lived Luminogenic Probe for Detection of RNA in a Crude Solution of Living
Bacterial Cells, H. Saneyoshi, Yoshihiro Ito, and Hiroshi Abe J. Am. Chem. Soc. 2013, 135,
13632–13635. This is a complicated paper and I only expect you to look at parts of it, enough
to answer the questions below.
(a) Where was the work done? When was the paper submitted to the journal and when was it
published? Why do you think these dates are important?
(b) In one sentence, what broadly is the long-term goal of this research?
(c) What are “fluorescence” and “autofluorescence”? Why is it important that the fluorescence
from the authors’ compounds have a long lifetime?
(d) In one sentence and in very simple terms, what kind of experiments will be possible if the
authors succeed in this project?
(e) The authors use Eu3+ and Tb3+ as their luminescent material. What are the electronic
configurations of these ions. You can assume that their valence s and d orbitals are empty.
How many possible unpaired spins do the ground states of these ions have?
(f) Does the organic chemistry look simple to make the ligand, the molecule that binds the metal
ion? (See Scheme 1).
(g) One of the nice features of lanthanide ions is that their spectra and luminescence don’t vary
very much from one compound to another. Given what we’ve talked about in class about the
lanthanides, why do you think this is?