Download kJ∙mol -1 - Chemistry

Atoms, Electrons and
Atomic/Electronic Energies
• The behavior of macroscopic objects/systems
can be adequately described using Newtonian
mechanics and thermodynamics. A train, a
hockey puck and an iceberg are all examples
of macroscopic objects. We might wish, for
example, to consider how the kinetic energy
of a hockey puck varies with velocity (goalies
do!) or to calculate how much heat/energy is
needed to melt an iceberg.
Pucks and Gas Molecules
• Hockey players who have studied physics know
that the kinetic energy of a puck varies with
velocity as described by the familiar equation.
• Ekinetic = ½ mv2
• During the course of a hockey game the puck will
move with a range of velocities and,
correspondingly, a range of kinetics energy
values. We assume that the kinetic energy of the
puck can be continuously varied. Why?
• In discussing gases one learns that the
pressure exerted by a gas results from the fact
that individual gas molecules have high
velocities. The rapidly moving gas molecules
have significant kinetic energy. At a given
temperature not all gas molecules have the
same velocity or kinetic energy. A range of
velocity/kinetic energy values is seen for a gas
at a particular temperature. As the gas
temperature increases the average kinetic
energy of gas molecules also increases.
• Atoms and molecules can possess energy in
addition to translational kinetic energy. Two
types of energy – rotational and vibrational –
will be considered later (for molecules).
Electronic energies will be considered first.
• The energies of individual atoms, electrons
and molecules are best studied experimentally
using spectroscopy (interaction of light with
matter). Key spectroscopic experiments tell us
that, for atoms and molecules, Newtonian
mechanics does not work!
Atomic and Molecular Energies
• Spectroscopic experiments show us that
atomic and molecular energies are not
continuously variable.
• Experiments show us that atomic and
molecular energies are quantized – only a
small number of energy values are observed.
The properties of light will be reviewed briefly.
The wave/particle “dual” character of light
(and electrons!) is particularly important.
Simple Frequency Wavelength
Conversion
• In spectroscopic experiments both frequency
and wavelength measurements are reported.
Conversions using the velocity of light are
needed. Example: What is the wavelength of
the 2.450 GHz radiation (light) used in a
typical microwave oven?
• Recognize Hz as equivalent to s-1.
• Then ν = 2.450 GHz = 2.450 x 109 s-1
• Use c = λν to get λ = c/ν
=(2.9979 x 108 m∙s-1/2.450 x 109 s-1)
=0.1224 m =12.24 cm
(mention quarter-wave plates?)
• Higher frequency light is more energetic than
lower frequency light. We know that infrared
light makes us feel warm. Visible light and UV
light on the other hand cause serious sunburn.
The energy transported per photon of light is
proportional to the frequency of light. The
relationship between light frequency and energy
was studied by Max Planck.
Photon Frequency (s-1) and Energy (J)
EPhoton
Slope = Planck’s Constant = h
= 6.626 x 10-34 J∙s
νPhoton (s-1)
• Example: How much energy is possessed by
(a) 1 photon and (b) NA photons of 16.6 GHz
electromagnetic radiation?
• EPhoton = hν = (6.626 x 10-34 J∙s)*(16.6 x 109 s-1)
= 1.10 x 10-23 J
• For one mole of photons
• (1.10 x 10-23 J/photon)*(6.022 x 1023 photons/mol) =
6.62 J
• This is a small amount of energy. It takes a lot of
microwave photons to heat up a cold cup of coffee!
We could calculate the number of photons needed
to heat a cup of coffee. How?
• Highly energetic/hot objects have a tendency
to lose energy/heat to the surroundings.
Atoms are no exception. Very hot atoms emit
only a few frequencies of light. These so-called
line spectra (together with E = hν and
sometimes c = λν) indicate that
atomic/electronic energies are quantized (not
continuously variable). “Cold” atoms readily
absorb light – as long as the energy of the
photon corresponds to the difference in
energy between two energy levels of the
atom.
Simple Two Energy Level System
EHIGH
Energy
per
Atom (J)
ΔEAbsorption
ELOW
ΔEEmission
• For the previous slide conservation of energy
dictates that
• ΔEAbsorption + ΔEEmission = 0
• Careful measurements of light frequencies (or
wavelengths) absorbed or emitted enables a
“pattern” of atomic or molecular energy levels
to be determined. In a few cases the energy
level pattern and corresponding
absorption/emission spectra can be described
using simple equations.
Bohr Theory for the Hydrogen Atom
• Bohr attempted to use the existing physics of
the early 20th century and a set of quantum
numbers to model the observed absorption
and emission spectra of the H atom.
• Tenets of the Bohr Theory:
• (1) Energies of the H atom/electron are
quantized.
• (2) The electron in a H atom moves around
the nucleus in a circular orbit.
• (3) The angular momentum of the electron in a H
atom is quantized.
• (4) Energy and angular momentum values for the
electron in a H atom are calculated using a
quantum number, n. The quantum number (n)
has integer values 1, 2, 3, 4, 5….. infinity.
• Angular momentum = nh/2π
• Radius of orbit = n2ao = rn
• Electron energy = En = -RH/n2
• Notes: En is always negative. Why? The quantity
ao is called the Bohr radius and specifies the
radius of the electron orbit for the lowest energy
state of the H atom.
Bohr Theory and the
Ionization Energy of Hydrogen
1
ΔE = RH ( 2
ni
–
1
) = h
2
nf
As nf goes to infinity for hydrogen starting in the ground state:
1
h = RH ( 2 ) = RH
ni
This also works for hydrogen-like species such as He+ and Li2+.
-Z2
En = RH ( 2 ) = -Z2RH
ni
Copyright © 2011 Pearson
Canada Inc.
General Chemistry: Chapter 8
Slide 15 of 50
Bohr Picture/Theory
• The Bohr theory has several shortcomings. It
implies that the electrons circle the nucleus in
regular orbits. This picture, reminiscent of
Newtonian mechanics, is incorrect. The Bohr
picture does account for atomic energies – but
only for one electron species such as H (and D
and T), He+, Li2+, Be3+ and so on – a not
insignificant problem.
The Rydberg Constant
• The equations presented on an earlier slide
assume that the Rydberg constant has energy
units (kJ∙mol-1 or J∙atom-1). Thus RH values of
1312 kJ∙mol-1 or 2.179 x 10-18 J∙atom-1 are
seen. Historically, from optical spectroscopy,
the Rydberg constant value was first
expressed in “wavenumbers” (109679 cm-1 or
1.09678 x 107 m-1). (Text, Chapter 11, Page
512. Slightly different equations.)
Bohr Theory and Ionization Energies
• The equations presented earlier suggest that
we can use ionization energies for one
electron species to calculate values for the
Rydberg constant (or vice versa). The
ionization energy for a one electron species is
the energy required to move the electron
from the n=1 level to n=∞ (free electron).
Calculations presented on the next slide take
ionization energies from webelements.com.
Bohr Theory and Ionization Energies
Species
Ionization Energy
(kJ∙mol-1)
Atomic
Number, Z
Z2
RH Estimated
(kJ∙mol-1)
H
1312.0
1
1
1312.0
He+
5250.5
2
4
1312.6
Li2+
11815.0
3
9
1312.78
Be3+
21006.6
4
16
1312.91
B4+
32826.7
5
25
1313.07
C5+
47277.0
6
36
1313.25
Bohr Theory and Ionization Energies
• The results of the previous slide suggest that
the Bohr picture, of an electron circling a
“stationary” nucleus, has shortcomings. The
small differences in calculated RH values in the
table can be understood using a reduced mass
calculation with the reduced mass defined as
μ = memNucleus/(me + mNucleus)
• This effect will be considered in one of the
Chemistry 2302 labs (H, D and T spectra).
Bohr Theory and Ionization Energies
Species
Ionization Energy
(kJ∙mol-1)
Atomic
Number, Z
Z2
RH Estimated
(kJ∙mol-1)
H
1312.0
1
1
1312.0
He+
5250.5
2
4
1312.6
Li2+
11815.0
3
9
1312.78
Be3+
21006.6
4
16
1312.91
B4+
32826.7
5
25
1313.07
C5+
47277.0
6
36
1313.25