課程名稱︰普通化學甲上
課程性質︰必修
課程教師︰金必耀
開課學院：物理系 材料科學與工程學系
開課系所︰化學系
考試日期（年月日）︰103年11月21日
考試時限（分鐘）：160分鐘
試題 :
1.In a reproduction of the Millikan oil-drop experiment, a student obtains the
following values for the charges on nine different oil droplets.
6.653*10^-19 C 13.13*10^-19 C 19.71*10^-19 C 8.024*10^-19 C 16.48*10^-19 C
22.89*10^-19 C 11.50*10^-19 C 18.08*10^-19 C 26.18*10^-19 C
(a)Based on these data alone, what is your best estimate of the number of
electrons on each of the above droplets?(Hint: Begin by considering
differences in charges between adjacent data points, and see into what
groups these are categorized.)
(b)Based on these data alone, what is your best estimate of the charge on the
electron?
(c)Is it conceivable that the actual charge is half the charge you claculated
in (b)? What evidence would help you decide one way or the other?
2.Draw Lewis electron dot diagrams for the following species, indicating formal
charges and resonance diagrams where applicable.
(a)HNC (central N atom)
(b)SCN- (thiocyanate ion)
(c)H2CNN (the first N atom is bonded to the carbon and the second N)
3.(a)Predict the geometry of the SbCl5(2-) ion, using the VSEPR method.
(b)The ion SbCl6(3-) is prepared from SbCl5(2-) by treatment with Cl-.
Determine the steric number of the central antimony atom in this ion, and
discuss the extension of the VSEPR theory that would be needed for the
prediction of its molecular geometry.
4.The molecular ion S3N3- has the cyclic structure. All S-N bonds are
equivalent.
_
[ S ]
[ / \ ]
[ N N ]
[ | | ]
[ S S ]
[ \ / ]
[ N ]
(a)Give six equivalent resonance hybrid Lewis diagrams for this molecular ion
(b)Compute the formal charges on all atoms in th molecular ion in each of the
Lewis diagrams.
(c)Determine the charge on each atom in the polyatomic ion, assuming that the
true distribution of electrons is the average of the six Lewis diagrams
arrived at in parts (a) and (b).
(d)An advanced calculation suggests that the actual charge resident on each N
atom is -0.375 and on each S atom is +0.041. Show that this result is
consistent with the overall -1 charge on the molecular ion.
5.An interesting class of carbon-containing molecules called conjugated
molecules have structure that consist of a sequence of alternating single and
double bonds. These chainlike molecules are represented as zigzag structures in
which the angle between properties to be explored in later chapters indicate
that the electrons forming the double bonds are "delocalized" over the entire
chain. Such molecules absorb light in the visible and ultraviolet regions of
the electromagnetic spectrum. Many dyestuffs and molecules with biological
significance have these structures. The properties of these molecules can be
described approximately by the particle-in-a-box model in which we assume there
is no interaction between the electrons, the potential energy is constant along
the chain, and the potential energy is infinite at the ends of the chain.
Assume the length of the potential well is Nd, where N is the number of carbon
atoms in the chain, and d = 0.14 nm is half the sum of the lengths of a C-C
single bond and a C=C double bond. In a molecule of N atoms, there will be N
electrons involved in the double bonds.
The ground state n=N/2, the first transition n+1=N/2+1
(a)Write the equation for the energy levels of an electron in this potential
well.
(b)Write the equation for the wave function of an electron in this potential
well.
(c)Write the equation for the frequency of light that will cause the
transition.
(d)The molecule hexatriene has six carbon atoms with conjugated structure;
thus, N = 6. Calculate the wavelength of light in the first transition
of hexatriene.
(e)The molecular structure of vitamin A is conjugated with N = 10. Calculate
the wavelength of light in the first transition of vitamin A.
(f)The molecule Beta-carotene has N = 22. Calculate the wavelength of light
in the first transition of Beta-carotene.
6.When metallic sodium is dissolved in liquid sodium chloride, electrons are
released into the liquid. These dissolved electrons absorb light with a
wavelength near 800 nm. Suppose we treat the positive ions surrounding an
electron crudely as defining a three-dimensional cubic box of edge L, and we
assume that the absorbed light excites the electron from its ground state to
the first excited state. Calculated the edge length L in this simple model.
7.Label the orbitals described by each of the following sets of quantum numbers
(a)n = 3, l = 2
(b)n = 6, l = 3
(c)n = 7, l = 4
How many radial nodes and how many angular nodes does each of these orbitals
have?
8.Photoelectron spectroscopy studies have determined the orbital energies for
fluorine atoms to be epsilon(1s)= -689eV, epsilon(2s)=-34eV,
epsilon(2p)=-12eV. Estimate the value of Zeff for F in each of these orbitals
9.The first ionization energy of helium is 2370 kJ/mol, the highest for any
element.
(a)Define ionization energy and discuss why for helium it should be so high.
(b)Which element would you expect to have the highest second ionization
energy? Why?
(c)Suppose that you wished to ionize some helium by shining electromagnetic
radiation on it. What is the maximum wavelength you could use?
10.Consider the vanadium atom with the ground-state electronic configuration
[Ar](3d^3)(4s^2). Use the following interelectronic repulsion terms J and
one-electron ionization energy terms W:
J(3d,3d) = 17.36eV
J(3d,4s) = 11.16eV
J(4s,4s) = 8.68eV
W(3d) = 65.21eV
W(4s) = 46.86eV
(a)Calculate the excitation energy:
V(3d^3 4s^2)→V(3d^5)
(b)Calculate the ionization energy for removal of a 3d electron:
V(3d^3 4s^2)→(V^+)(3d^2 4s^2) + e-
(c)Calculate the ionization energy for removal of a 4s electron:
V(3d^3 4s^2)→(V^+)(3d^3 4s^1) + e-
(d)From your results in parts (b) and (c), which electron, 3d or 4s, has
the lower ionization energy?