Download Chemistry 1000 Lecture 9: Periodic trends

Chemistry 1000 Lecture 9: Periodic trends
Marc R. Roussel
A qualitatively correct result of the Bohr theory
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Some results of the Bohr theory are qualitatively correct, even
for multi-electron atoms, but need to be reinterpreted.
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Recall, from Bohr theory, rn ∝ n2 .
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We call a set of orbitals with the same n a shell.
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The average distance of the electrons from the nucleus is
roughly proportional to n2 , so the Bohr theory is qualitatively
correct.
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This average distance however increases slightly with `, which
the Bohr theory doesn’t predict.
Screening
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Suppose that we consider two shells with different n.
The shell with the larger n has most of its electron density
outside the shell with smaller n.
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Electrons in the small-n shell therefore screen the electrons in
the large-n shell from the nucleus relatively effectively.
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Electrons in higher-n shells have an effect on lower-n electrons
(because the high-n orbital does have some density “inside”
the low-n orbital), but it’s small.
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If there are other electrons in the same shell, these also have
some screening effect on each other.
Effective nuclear charge
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The effective nuclear charge experienced by an electron takes
into account the screening by other electrons.
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Effective nuclear charges can be calculated numerically using
quantum chemical methods.
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The effective nuclear charge is slightly different for orbitals of
different ` values within a shell because of slightly different
average distances to the nucleus.
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As we go across a period, the effective nuclear charge
increases because the charge of the nucleus is increasing, but
there is only partial screening by additional electrons added to
the valence shell.
The core electron configuration doesn’t change across a
period.
Effective nuclear charge
Trend along a period
8
7
3s
3p
Zeff
6
5
4
3
2
Na
Mg
Al
Si
P
S
Cl
Ar
Atomic size
Orbitals don’t have a sharp cut-off.
They are “spongy”.
So how can we define an atomic size?
Covalent radius: From compounds with single covalent bonds,
whether network solids (e.g. diamond) or molecular
compounds (e.g. F2 )
For
the
For
the
elements, the radius is half the distance between
nuclei.
compounds, the distance between the nuclei is
sum of the radii.
Atomic size
Metallic radius: Same idea as the covalent radius, but in a metal.
What’s the difference, then?
In a covalent compounds, some of the valence
electrons are shared between two atoms.
In a metallic compound, the valence electrons are
shared throughout the metal.
van der Waals radius: Mostly for noble gases, based on shortest
distance between atoms in a solid crystal in which
the atoms are not bonded to each other.
Important note: These radii are not strictly comparable to each
other, so we should always try to compare
measurements of the same kind.
Atomic size
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Atomic size increases as we move down a group because we
are adding shells and r ∝ n2 /Zeff .
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In a period, for the main-group elements, Zeff increases as we
move from left to right, so atomic size decreases.
Atomic size
Trend down a group
280
260
r/pm
240
220
200
180
160
140
Li
Na
K
Rb
Cs
Atomic size
Trend across a period
200
190
180
170
r/pm
160
150
140
130
120
110
100
90
Na
Mg
Al
Si
P
S
Cl
Ionic radius
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Measured analogously to covalent radius, but using crystals of
an ionic compound.
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Bootstrapping problem: You need one radius in order to be
able to assign the rest.
Convention: r (O2− ) = 1.40 Å
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Generally, similar trends observed as for atomic radii.
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Removing electrons (esp. if a shell is emptied) results in
cations being smaller than the neutral atoms from which they
are formed.
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The smallest ion in an isoelectronic series has the highest Z .
Ionic radius
Example: Put the following ions in order of increasing size:
O2− , F− , Na+ , Mg2+
Answer: Mg2+ (72 pm), Na+ (102 pm),
F− (133 pm), O2− (140 pm)
Ionization energy
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Ionization energy = 1st ionization energy = I1
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Ionization energy decreases as we go down a group because
the outer electrons are farther from the nucleus and thus more
loosely held.
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As an overall trend, ionization energy increases as we move
from left to right across a period because the effective nuclear
charge increases and the size of the atom decreases, both of
which increase the electrostatic force between the valence
electrons and the nucleus.
Ionization energy (continued)
We must also consider electronic configuration.
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Going from an ns2 to an ns2 np1 configuration, the ionization
energy decreases in the first few periods because the p orbital
is higher in energy than the s.
Going from an ns2 np3 to an ns2 np4 configuration, the
ionization energy decreases because pairing electrons in an
orbital increases electron-electron repulsion, thus making it
easier to remove one.
Ionization energy
Trend down a group
1400
1300
1200
I1/kJ mol
-1
1100
1000
900
800
700
600
500
400
300
H
Li
Na
K
Rb
Cs
Ionization energy
Trend across a period for the 1st IE
1600
1400
I1/kJ mol
-1
1200
1000
800
600
400
Na
Mg
Al
Si
P
S
Cl
Ar
Second ionization energy
The second ionization energy is the energy required to remove a
second electron from an atom, i.e. the energy
required to remove an electron from X+ forming X2+ .
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Second ionization energies can be understood using the same
principles as first ionization energies, but you have to take
into account the electron configuration of the singly ionized
ion that is the starting point.
Second ionization energy
Trend across a period for the 2nd IE
5000
4500
I2/kJ mol
-1
4000
3500
3000
2500
2000
1500
1000
Na
Mg
Al
Si
P
S
Cl
Ar
Enthalpy of electronic attraction
This is called electron affinity in the textbook.
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∆ea H is the enthalpy change for the process A + e− → A− in
the gas phase.
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∆ea H is generally negative.
A more negative value means a stronger attraction for
electrons.
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Some elements have essentially no ability to accept an
additional electron.
Examples: Be, Mg, N, noble gases. Why?
Trend across a period
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∆ea H tends to become more negative as we go from left to
right in a period because of increasing effective nuclear charge
and decreasing atomic radius.
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Exceptions to the previous observation can generally be
rationalized in terms of the electron configurations of the
atom and anion.
Enthalpy of electronic attraction
Trend across a period
0
-50
∆eaH/kJ mol
-1
-100
-150
-200
-250
-300
-350
-400
Na
Mg
Al
Si
P
S
Cl
Ar
Enthalpy of electronic attraction
Group trends
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∆ea H tends to become less negative as we move down a
group because of increasing atomic radius, but there are many
exceptions.
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Second-period elements tend to have less negative ∆ea values
than the corresponding third-period element because of the
small size of the former which concentrates the electrons in a
small region of space and makes it energetically less favorable
to add another electron.
The trend is reversed in groups with low ∆ea H values.
Enthalpy of electronic attraction
Group 1 is “normal”.
-45
∆eaH/kJ mol
-1
-50
-55
-60
-65
-70
-75
H
Li
Na
K
Rb
Enthalpy of electronic attraction
Group 14 shows the off-trend second-period element.
-20
6eaH/kJ mol-1
-40
-60
-80
-100
-120
-140
C
Si
Ge
Sn
Pb
Is there any special stability to noble-gas configurations?
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We often see claims that the propensity of atoms to form ions
with noble-gas configurations is due to some special stability
of the noble-gas electron configuration.
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If that were the case, it should be difficult to remove an
electron from the F− ion.
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The amount of heat (enthalpy) required to do so is −∆ea H,
which turns out to be 328 kJ mol−1 for F− .
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As ionization energies go, this is not a particularly large value.
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The context for studying issues of stability always has to be a
balanced reaction in which we consider reactants and
products.
Avoid thinking in terms of any special stability properties of
octets (even though that is often the end result in reactions
involving main-group elements).
Electronegativity
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Usual symbol: χ
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An empirical measure of the tendency of an atom to attract
electrons
There are in fact several electronegativity scales.
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The Mulliken electronegativity scale is linearly related to
I − ∆ea H.
(Recall, ∆ea H is negative if an electron can be added to an
atom.)
The more commonly used Pauling scale is based on bond
dissociation energies, but correlates very well with the
Mulliken scale.
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Electronegativity decreases as we go down a group.
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Electronegativity increases as we go from left to right across a
period.
Electronegativity
Trend down a group for χ
2.2
2
1.8
χ
1.6
1.4
1.2
1
0.8
0.6
H
Li
Na
K
Rb
Cs
Fr
Electronegativity
Trend across a period for χ
3.5
3
χ
2.5
2
1.5
1
0.5
Na
Mg
Al
Si
P
S
Cl
Knowing the periodic table
Important: You are expected to learn the names, symbols, and
positions in the periodic table of all the elements in
the first four periods (up to and including Kr).