Chemistry Homework: Analyzing Dissociation Energy and Molecular Modes

This document presents solutions to a chemistry assignment focusing on two main problems. The first problem involves calculating the dissociation energy of the upper electronic state of O2 using the Schumann–Runge band data and constructing a Birge–Sponer plot. The solution details the process of arranging the wavenumber data and determining the dissociation energy. Furthermore, it uses additional information about the excited state and ground state dissociation to calculate the ground-state O2 dissociation energy. The second problem addresses a planar, T-shaped molecule of C2v symmetry, asking for the number and irreducible representations of its vibrational modes. The solution indicates that there are six vibrational modes, which can be reduced to four due to double degeneracy, providing a structural representation of the molecule and citing relevant references.

SOLUTIONS
1. A transition of particular importance in O2 gives rise to the
‘Schumann– Runge band’ in the ultraviolet region. The
wavenumbers ( in cm-1) of transitions from the ground state to the
vibrational levels of the first excited state ( 3Su
-) are
50,062.6 50,725.451,369.0 51,988.6 52,579.0 53,143.4 53,679.6
54,177.0 54,641.8 55,078.2 55,460.0 55,803.1 56,107.3 56,360.3
56,570.6
(a) What is the dissociation energy of the upper electronic state
as determined by constructing a Birge– Sponer plot?
Ans:
In this case, we need to obtain the independent variable (x-variables) against the
given dependent variable (wave numbers) and this is done as follows but first we
arrange the values:
v G(v)
14 50,062.6
13 50,725.4
12 51,369.0
11 51,988.6
10 52,579.0
9 53,143.4
8 53,679.6
7 54,177.0
6 54,641.8
5 55,078.2

4 55,460.0
3 55,803.1
2 56,107.3
1 56,360.3
0 56,570.6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0
10000
20000
30000
40000
50000
60000
v
G(v)
Figure 1: The Birge-Sponor plot
The dissociation energy is the sum of energy levels from v=0 to v= 15
Hence De= 807745.9Jmol-1
(b) The same excited state is known to dissociate into one
ground state O atom and one excited state atom with an
energy 190 kJ mol-1 above the ground state. (This excited
atom is responsible for a great deal of photochemical
reactivity in the atmosphere.) Ground state O2 dissociates
into two ground- state atoms. Use this information to
calculate the dissociation energy of ground- state O2 from the
Schumann– Runge data.

At 190kJmol-1, we can deduce the De from the given data as provided by
Yoshimo et al (1984) hence it is 11.0kJmol-1
2. Consider a planar, T-shaped molecule of C2v symmetry. (ClF3
has approximately this geometry). How many vibrational modes
are there in this molecule and to what irreducible representations
do they transform?
Based on its planar symmetry, the vibrational modes in the molecule are 6. The molecule
can be oriented in any of the identifiable symmetrical planar directions during vibratory
mode. However, this can be reduced to 4 as two of these are doubly degenerate (Bellucci,
2013)
Figure 2: Structural representation of the molecule (Courtesy of Bellucci, 2013)
REFERENCE
Bellucci, J.C. (2013).Housecroft Inorganic Chemistry 3e. Available at:
http://www.ebah.com.br/content/ABAAAA44sAH/housecroft-inorganic-chemistry-3e?
part=7
Yoshimo, D.E, Freeman & Parkinson, W.H. (1984). Atlas of the Schumann-Runge
Absorption Bands Of O2 in the Wavelength Region 175-205nm. Online Journal of
Physical chemistry