CM2004
Useful information:
k = 1.381×10-23 J K-1
c = 2.998×108 m s-1
ASSIGNMENT 1
1 D = 3.336×10-30 C m
h = 6.626×10-34 J s
ε0 = 8.854×10-12 C-2 J-1 m-1
1.
Cs is the least electronegative element and F is the most electronegative. Assume
that in CsF the Cs atom donates its outermost electron to F. The ionic diameters of
Cs and F are respectively 330 pm and 270 pm. What is the dipole moment in D of
CsF in the gas phase?
2.
What is the force between Mg2+ and Cl- ions when:
a) separated by 10.0 Å in vacuum
b) separated by 7.0 Å in benzene (εr = 2.3)
c) separated by 5.0 Å in water (εr = 78)
3.
Which medium in the above question will best keep these ions separate and why?
[Answer within 2 lines.]
4.
What is the dipole moment of a hypothetical molecule in which partial charges of
±0.40e are separated by 0.30 Å ?
5.
Calculate the induced dipole (in D) of benzene in a field of strength 1.0×109 V m-1.
Benzene is nonpolar and has a polarizability volume, α′ = 10.3 Å3.
6.
What is the ion-dipole potential energy of interaction of Na+ with CH3Cl, if they are
separated by 5.0 Å and the dipole is at an angle of 30° to the line between the ioni
and the dipole? CH3Cl has a dipole of 1.87 D. How does this interaction compare
with the thermal energy of molecules at 30 ºC?
7.
What is the dipole-dipole interaction potential of HBr and HI at a separation of
6.0 Å and at a temperature of 273 K? The dipole of HBr is 0.80 D and HI is 0.42 D.
8.
Compare the above dipole-dipole interaction to the dipole-induced dipole
interactions for HBr and HI at the same separation. The polarizability volumes of
HBr and HI are respectively 3.61 Å3 and 5.45 Å3.
9.
Na+ and Cl- are separated by 8.0 Å in vacuum.
a) What is their Coulombic potential energy relative to infinite separation?
b) How does the above potential energy compare to thermal energy at 150ºC?
10. Based on molecular structure and the different electronegativities of different
nuclei, state whether the following molecules are polar or non-polar.
[No calculations necessary, although a sketch of the molecules may be helpful]
a) CO
b) CO2
c) CHCl3
d) CH2Cl2
e) C6H6
f) p-C6H4Cl2
g) m-C6H4Cl2
h) C6H5Cl
CM2004
ASSIGNMENT 1
11. Use the Boltzmann distribution to calculate the number of molecules of H2 (in a
total sample of 108) that will be in the first excited vibrational level at a temperature
of 100ºC. The ground vibrational level of H2 is at 2200 cm-1 and the first excited
vibrational level is at 6600 cm-1. Convert joules [J] to wavenumbers [cm-1] by
dividing by hc, where h is Plank’s constant and c is the speed of light in the correct
units.
12. Rotationally averaged dipole-dipole interactions do not sum to zero because more
molecules are found in the most favourable energy configuration compared to the
least favourable configuration. Use the Boltzmann distribution to calculate the ratio
of molecules in the lowest energy configuration compared to the highest energy
configuration if the difference in energy is 3×10-21 J. The temperature of the sample
is 20°C.
TEASER: Optional question for fun or test your understanding – will not be marked…
13. Imagine the potential energy of two CH4 molecules is described by the Lennard12
6
Jones potential (also called the 12,6 potential): V  4  / R    / R  ,
where R is the separation of the molecules, and ε/k = 124 K-1 and σ = 3.42 Å for
Ar. (k is the Boltzmann constant).
a. Using Excel or another spreadsheet program, sketch and print this
intermolecular potential
b. At what intermolecular separation will the molecules be moving fastest
relative to each other if the molecules are initially stationary and
separated by 10Å?
c. What will the velocity of each molecule be at this distance?
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