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Thermochemistry
Chemistry 120
Energy
Energy is defined as the ability to do work.
There are several forms of energy
Kinetic energy – energy due to motion EK = 1 /2 mv 2
Potential energy – the energy due to the position of a
particle in a field
e.g. Gravitational, electrical, magnetic etc.
Thermochemistry
Chemistry 120
Energy
The unit of energy is the Joule (J) and
1 J = 1 kgm2 s -2
Thermochemistry is the study of chemical energy
and of the conversion of chemical energy into other
forms of energy.
It is part of thermodynamics – the study of the flow
of heat.
Thermochemistry
Chemistry 120
Thermochemically, we define the system as the part
of the universe under study and the surroundings as
everything else.
Systems come in three forms:
Open
The system can exchange matter and
energy with the surroundings
Closed
The system can exchange energy only
with the surroundings
Isolated
There is no exchange of matter or of
energy with the surroundings
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Thermochemistry
Chemistry 120
Matter is continually in motion and has an internal
energy that is composed of several different types
There is
Translation
Rotation
Vibration Potential
between molecules and inside molecules.
The internal energy is written as U
Thermochemistry
Chemistry 120
Matter is continually in motion and has an internal
energy that is composed of several different types
There is
Translation
Rotation
Vibration Potential
between molecules and inside molecules.
The internal energy is written as U
The internal energy is directly connected to heat and
the transfer of heat.
Thermochemistry
Chemistry 120
Heat is the transfer of internal energy between the
surroundings and the system or between systems.
The direction of the heat flow is indicated by the
temperature
– heat flows along a Temperature gradient
from high temperature to low temperature.
When the temperature of the system and that of the
surroundings are equal, the system is said to be
in thermal equilibrium
2
Thermochemistry
Chemistry 120
Energy is the capacity to do work
but what is work?
Work is the action of a force over a distance. To be
able to do work, we must be able to exert a force
over a distance. During this process, energy is
expended.
w =F xd
where w is the work, F is the force and d is the
distance. Work is measured in Joules.
Thermochemistry
Chemistry 120
PV work
When a gas expands against an external pressure, for
example in a cylinder, against a constant weight
(weight being a force.....) the work done can be
written as
w=F xd
As
Thus
P=F
A
w = PAd
and as
Ad = V final – Vinitial = ? V
Then
w = P? V
Thermochemistry
then
F = PA
Chemistry 120
PV work
By convention, the work done when a gas expands is
negative,
Thus
w = - P? V
for an expanding gas
3
Thermochemistry
Chemistry 120
State Functions
The state of a system is defined by the precise
conditions of the system:
The quantity and type of matter present
The temperature and pressure
The molecular structure of the system
As 1 mole = 6.02 x 1023 particles, defining the state
of a system uniquely is experimentally impossible in
an absolute sense.
Thermochemistry
Chemistry 120
State Functions and U
The internal energy, U, of a system is a function of
the state of the system.
Although we cannot measure the absolute state of a
system, we can measure changes in the state of the
system in a relative way, by measuring the work and
the heat that takes place during a chemical change.
As U is a function of the state of the system, it does
not depend on the way the state of the system is
prepared – it is independent of the path.
Thermochemistry
Chemistry 120
State Functions and U
U is therefore a state function of the system. It
depends only on the present state of the system and
not on the previous history or the path by which the
system was prepared.
Because we have no measure of the state of a
system, or of the internal energy, we can only
measure the change in the state, through the
observation of work and transfers of heat into and
out of the system.
4
Thermochemistry
Chemistry 120
State Functions and U
U is therefore a state function of the system. It
depends only on the present state of the system and
not on the previous history or the path by which the
system was prepared.
Because we have no measure of the state of a
system, or of the internal energy, we can only
measure the change in the state, through the
observation of work and transfers of heat into and
out of the system.
Thermochemistry
Chemistry 120
Energy
Energy is defined as the ability to do work.
There are several forms of energy
Kinetic energy – energy due to motion EK = 1 /2 mv 2
Potential energy – the energy due to the position of a
particle in a field
e.g. Gravitational, electrical, magnetic etc.
Thermochemistry
Chemistry 120
Energy
The unit of energy is the Joule (J) and
1 J = 1 kgm2 s -2
Thermochemistry is the study of chemical energy
and of the conversion of chemical energy into other
forms of energy.
It is part of thermodynamics – the study of the flow
of heat.
5
Thermochemistry
Chemistry 120
Thermochemically, we define the system as the part
of the universe under study and the surroundings as
everything else.
Systems come in three forms:
Open
The system can exchange matter and
energy with the surroundings
Closed
The system can exchange energy only
with the surroundings
Isolated
There is no exchange of matter or of
energy with the surroundings
Thermochemistry
Chemistry 120
Matter is continually in motion and has an internal
energy that is composed of several different types
There is
Translation
Rotation
Vibration Potential
between molecules and inside molecules.
The internal energy is written as U
Thermochemistry
Chemistry 120
Matter is continually in motion and has an internal
energy that is composed of several different types
There is
Translation
Rotation
Vibration Potential
between molecules and inside molecules.
The internal energy is written as U
The internal energy is directly connected to heat and
the transfer of heat.
6
Thermochemistry
Chemistry 120
Heat is the transfer of internal energy between the
surroundings and the system or between systems.
The direction of the heat flow is indicated by the
temperature
– heat flows along a Temperature gradient
from high temperature to low temperature.
When the temperature of the system and that of the
surroundings are equal, the system is said to be
in thermal equilibrium
Thermochemistry
Chemistry 120
Energy is the capacity to do work
but what is work?
Thermochemistry
Chemistry 120
Energy is the capacity to do work
but what is work?
Work is the action of a force over a distance. To be
able to do work, we must be able to exert a force
over a distance. During this process, energy is
expended.
7
Thermochemistry
Chemistry 120
Energy is the capacity to do work
but what is work?
Work is the action of a force over a distance. To be
able to do work, we must be able to exert a force
over a distance. During this process, energy is
expended.
w =F xd
where w is the work, F is the force and d is the
distance. Work is measured in Joules.
Thermochemistry
Chemistry 120
PV work
When a gas expands against an external pressure, for
example in a cylinder, against a constant weight
(weight being a force.....) the work done can be
written as
w=F xd
As
Thus
P=F
A
w = PAd
and as
Ad = V final – Vinitial = ? V
Then
w = P? V
Thermochemistry
then
F = PA
Chemistry 120
PV work
By convention, the work done when a gas expands is
negative,
Thus
w = - P? V
for an expanding gas
8
Thermochemistry
Chemistry 120
State Functions
The state of a system is defined by the precise
conditions of the system:
The quantity and type of matter present
The temperature and pressure
The molecular structure of the system
As 1 mole = 6.02 x 1023 particles, defining the state
of a system uniquely is experimentally impossible in
an absolute sense.
Thermochemistry
Chemistry 120
State Functions and U
The internal energy, U, of a system is a function of
the state of the system.
Although we cannot measure the absolute state of a
system, we can measure changes in the state of the
system in a relative way, by measuring the work and
the heat that takes place during a chemical change.
As U is a function of the state of the system, it does
not depend on the way the state of the system is
prepared – it is independent of the path.
Thermochemistry
Chemistry 120
State Functions and U
U is therefore a state function of the system. It
depends only on the present state of the system and
not on the previous history or the path by which the
system was prepared.
Because we have no measure of the state of a
system, or of the internal energy, we can only
measure the change in the state, through the
observation of work and transfers of heat into and
out of the system.
9
Thermochemistry
Chemistry 120
State Functions and U
U is therefore a state function of the system. It
depends only on the present state of the system and
not on the previous history or the path by which the
system was prepared.
Because we have no measure of the state of a
system, or of the internal energy, we can only
measure the change in the state, through the
observation of work and transfers of heat into and
out of the system.
Thermochemistry
Chemistry 120
Internal Energy, U and State Functions
Energy, and therefore the capacity to do work is
present in all matter.
This internal energy is stored in translational,
rotational, vibrational and potential forms or modes
in the material.
The exact distribution of energy defines the state of
the system, together with external variables such as
pressure, temperature.
Thermochemistry
Chemistry 120
Internal Energy, U and State Functions
U is a function of the state of the material only, not
of the history of the sample or the path taken to
prepare the state of the sample.
Heat is the transfer of energy between the
surroundings and the sample
- the symbol for heat is q
Work is the result of a force acting over a distance
- the symbol for work is w
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Thermochemistry
Chemistry 120
Internal Energy, U and State Functions
Heat and work are the only two ways of changing
the internal energy of a system.
Temperature is defined by the direction of the flow
of heat, which is always from high temperature to
low temperature.
When the the temperature of the system and the
surroundings are the same, the system is at thermal
equilibrium with it’s surroundings.
Thermochemistry
Chemistry 120
The sign conventions of thermochemistry
When the internal energy of the system rises, this
energy change has a positive sign.
- The energy of the system rises when heat is
absorbed
- The energy of the system rises when work is
done on the system e.g. a gas is compressed
- in these cases, q is positive
w is positive
Chemistry 120
Thermochemistry
The sign conventions of thermochemistry
When the internal energy of the system lowers, this
energy change has a negative sign.
- The energy of the system lowers when heat is
leaves the system
- The energy of the system rises when the
system does work e.g. a gas expands against an
external pressure
- in these cases, q is negative
w is negative
11
Thermochemistry
Internal energy rises:
Chemistry 120
q>0
w>0
Internal energy drops:
q<0
w<0
Thermochemistry
The First Law of Thermodynamics
Chemistry 120
Energy can be exchanged but cannot be
created or destroyed.
It is a statement of the Law of Conservation of
Energy
? U = U final – Uinitial = q + w
Thermochemistry
Chemical applications of the 1st Law
Chemistry 120
Any chemical change can be characterized as an
Endothermic change
or an
Exothermic change.
In an exothermic reaction, internal chemical energy
is converted into heat, which leaves the system if the
system is not isolated or causes the temperature to
rise if the system in isolated.
12
Thermochemistry
Chemical applications of the 1st Law
Chemistry 120
In an endothermic reaction, heat is required to drive
the chemical reaction and in an isolated system, the
temperature will fall. In an non-isolated system, heat
is absorbed from the surroundings.
Exothermic
T rises (isolated)
q negative (non-isolated)
Endothermic
T falls (isolated)
q positive (non-isolated)
Chemistry 120
Thermochemistry
Reactions at constant pressure and constant volume
At constant volume, ? V = 0 and so
? UV = q V - P? V
? UV = q V + 0 = q V
When the system can do PV work, i.e. a system at
constant pressure,
? UP = q P - P? V
where w = - P? V
Chemistry 120
Thermochemistry
Most reactions take place at constant pressure and
therefore we define a new function, which is a state
function in the same way that U is a state function
Rearranging
? UP = q P - P? V
? UP + P? V = q P
We term q P the enthalpy of the reaction
q P = ? H = ? UP + P? V
13
Chemistry 120
Thermochemistry
Enthalpy is an extensive property – one that depends
on the quantity of the material present in the
reaction.
This follows directly from the fact that the enthalpy
is the heat generated by a reaction
– there is more energy released from 1000 kg
of methane when it burns than from 1 g.
Chemistry 120
Thermochemistry
Enthalpies and internal energies are measured in kJ
mol-1 and the stoichiometry of a reaction is directly
applicable to the enthalpy – half the quantity of the
reaction results in half the enthalpy change taking
place.
Chemistry 120
Thermochemistry
We can characterize reactions as endothermic or
exothermic using the enthalpy, ? H.
If the enthalpy change is
negative, the reaction is
exothermic and heat is
given out by the system
Reacta nts
? H < 0, negative
Products
H
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Chemistry 120
Thermochemistry
We can characterize reactions as endothermic or
exothermic using the enthalpy, ? H.
If the enthalpy change is
negative, the reaction is
endothermic and heat is
absorbed by the system
Products
? H >0, posi tive
Reactants
H
Chemistry 120
Thermochemistry
Using the enthalpy, we can account for the heat
entering a reaction at constant pressure – in the same
way that we account for the products and reactants
in a reaction.
In an endothermic reaction, the energy absorbed by
the system can be considered as a reactant.
Conversely, an exothermic reaction, one which
evolves heat, has the energy as a product.
Chemistry 120
Thermochemistry
Enthalpies and internal energies are measured in kJ
mol-1 and the stoichiometry of a reaction is directly
applicable to the enthalpy – half the quantity of the
reaction results in half the enthalpy change taking
place.
15
Thermochemistry
Heat Capacities
Chemistry 120
When a definite quantity of energy is absorbed by
materials, the temperature rises.With different
materials, the temperature rise, ? T, is different.
The quantity of energy required to raise a quantity of
material by 1 K is termed the heat capacity.
Mathematically,
C=q
?T
where C is the heat capacity, q is the heat.
Thermochemistry
Heat Capacities
Chemistry 120
The specific heat is the heat per gram of sample and
the molar heat capacity is the heat capacity per
mole.
Thermochemistry
Chemistry 120
Specific Heats, Molar Heats and Calorimetry
The heat capacity is the quantity of heat required to
raise a given quantity of a substance by 1 K
The specific heat
1 gram though 1 K
The molar heat
1 mole through 1 K
The units of heat capacity are
Jg -1 K-1 (specific heat) or Jmol-1 K-1 (molar heat)
16
Thermochemistry
Chemistry 120
Specific Heats, Molar Heats and Calorimetry
To calculate the heat transferred to a sample we use
q = quantity x heat capacity x ? T
For the specific heat
q = mC s ? T
where m = mass
For the molar heat
q = nC m ? T
where n = no. of moles
Make sure that the units of the heat capacity matches
the units of quantity that is in the heat equation
Thermochemistry
Chemistry 120
Specific Heats, Molar Heats and Calorimetry
To measure the heat capacity, a calorimeter is used.
A calorimeter measures heat transfers, heats of
reaction or heats of dissolution.
Thermochemistry
Chemistry 120
Specific Heats, Molar Heats and Calorimetry
In principle, they consist of an insulated chamber
and an accurate way of measuring temperature (a
thermocouple or thermometer).
Insulation ensures that the only heat involved in the
temperature rise is that inside the calorimeter.
17
Thermochemistry
Chemistry 120
Heat capacity measurements
A sample with a known temperature is placed into a
fluid of known heat capacity and known temperature
and allowed to come to thermal equilibrium.
Thermochemistry
Chemistry 120
Heat capacity measurements
A sample with a known temperature is placed into a
fluid of known heat capacity and known temperature
and allowed to come to thermal equilibrium.
At thermal equilibrium, Tsample = T fluid and so we
know ? T for the sample and for the fluid.
Thermochemistry
Chemistry 120
Heat capacity measurements
A sample with a known temperature is placed into a
fluid of known heat capacity and known temperature
and allowed to come to thermal equilibrium.
At thermal equilibrium, Tsample = T fluid and so we
know ? T for the sample and for the fluid.
We also know C fluid and therefore we know q fluid, the
heat transferred into the fluid - q = C fluid? Tfluid
18
Thermochemistry
Chemistry 120
Heat capacity measurements
A sample with a known temperature is placed into a
fluid of known heat capacity and known temperature
and allowed to come to thermal equilibrium.
At thermal equilibrium, Tsample = T fluid and so we
know ? T for the sample and for the fluid.
We also know C fluid and therefore we know q fluid, the
heat transferred into the fluid - q = C fluid? Tfluid
As this is the only source of heat in the calorimeter,
we know q fluid and ? Tsample , so we can calculate
Csample
Thermochemistry
Example
Chemistry 120
15.5g of alloy A has a temperature of 98.9 o C. It is
placed into a calorimeter containing 25 g of water at
22.5o C. Thermal equilibrium is achieved at 25.7 o C.
What is the heat capacity of A?
Thermochemistry
Example
Chemistry 120
15.5g of alloy A has a temperature of 98.9 o C. It is
placed into a calorimeter containing 25 g of water at
22.5 o C. Thermal equilibrium is achieved at 25.7 o C.
What is the heat capacity of A? Cwater = 4.18 Jg -1 K-1
1.
Calculate q water
2.
q water = - q A from conservation of energy
3.
Calculate CA from q A
19
Thermochemistry
Example
Chemistry 120
15.5g of alloy A has a temperature of 98.9 o C. It is
placed into a calorimeter containing 25 g of water at
22.5 o C. Thermal equilibrium is achieved at 25.7 o C.
What is the heat capacity of A? Cwater = 4.18 Jg -1 K-1
1.
Calculate q water:
? Twater = T final – Tinitial = (25.7 – 22.5) o C = 3.2 o C
q water= 25 x 4.18 x 3.2 = 334 J
Note: q water is positive as heat is entering the water
Thermochemistry
Example
Chemistry 120
15.5g of alloy A has a temperature of 98.9 o C. It is
placed into a calorimeter containing 25 g of water at
22.5 o C. Thermal equilibrium is achieved at 25.7 o C.
What is the heat capacity of A? Cwater = 4.18 Jg -1 K-1
1.
q water = 334 J
2.
q water = - q A thus qA = - 334 J
Thermochemistry
Example
Chemistry 120
15.5g of alloy A has a temperature of 98.9 o C. It is
placed into a calorimeter containing 25 g of water at
22.5 o C. Thermal equilibrium is achieved at 25.7 o C.
What is the heat capacity of A? Cwater = 4.18 Jg -1 K-1
1.
q water = 334 J
2.
q water = - q A thus qA = - 334 J
3.
q A = mC A ? TA
? TA = T final – Tinitial = (25.7 – 98.9) o C = -73.2 o C
20
Thermochemistry
Example
Chemistry 120
15.5g of alloy A has a temperature of 98.9 o C. It is
placed into a calorimeter containing 25 g of water at
22.5 o C. Thermal equilibrium is achieved at 25.7 o C.
What is the heat capacity of A? Cwater = 4.18 Jg -1 K-1
1.
q water = 334 J
2.
q water = - q A thus qA = - 334 J
3.
q A = mC A ? TA ; ? TA = -73.2 o C
CA = q A /m? TA = -334/(15.5 x –73.2) = 0.29 Jg -1 K-1
Thermochemistry
Chemistry 120
Bomb Calorimetry
For reactions which generate gas, the P? V work
makes a significant contribution and the quanitiy we
will measure in an open calorimeter is the enthalpy.
We cannot easily measure the P? V work in this case.
We can measure ? U in a bomb calorimeter – one
where the volume change is zero and therefore ? V =
0.
The calorimeter is calibrated using a known sample.
Thermochemistry
Chemistry 120
Hess’ Law of Summation
If we wish to determine the heat of reaction or
formation of a compound which is not stable, cannot
be isolated or cannot be measured for some reason,
we use Hess’ Law to determine this quantity.
Hess’ law states that the
the heat of reaction is constant and is not
determined by the path of the reaction.
We know this as ? U (and ? H) is a state function
21
Thermochemistry
Chemistry 120
Hess’ Law of Summation
Practically, if we can find a cycle of reactions that is
measureable, then we can derive the unmeasurable
quantity as we know the total sum of all the energy
changes in the cycle.
Thermochemistry
Chemistry 120
Hess’ Law of Summation
Example
The combustion of C results in the formation of
CO2 in a bomb calorimeter. The heat of formation
of CO is therefore hard to measure.
We can measure the heat of combustion of CO and
that of C both to give CO2 .
Thermochemistry
Chemistry 120
Hess’ Law of Summation
? Hf(CO)
C graphite + O2
? Hf(CO2)
CO + 1/ 2O2
? Hcombustion (CO)
CO2
22
Thermochemistry
Chemistry 120
Hess’ Law of Summation
? Hf(CO)
CO + 1/ 2O2
Cgrap hite + O2
? Hco mb ustion (CO)
? H f(CO 2)
CO2
Of the reactions in this cycle, the heats of
combustion of CO and C are known, but the heat of
formation of CO from C is not.
Thermochemistry
Chemistry 120
Hess’ Law of Summation
? Hf(CO)
1
C graphite + O2
CO + / 2O2
? Hcombustion (CO)
? Hf(CO2)
CO2
? Hf (CO2 ) = ? Hf (CO) + ? Hcombustion (CO)
Thermochemistry
Chemistry 120
Hess’ Law of Summation
? Hf(CO)
C graphite + O2
? Hf(CO2)
1
CO + / 2O2
? Hcombustion (CO)
CO2
? Hf (CO 2) = ? Hf(CO) + ? H combustion(CO)
? Hf (CO) = ? Hf(CO2)?- ? Hcombustion(CO)
23
Thermochemistry
Chemistry 120
? H f(CO)
Hess’ Law of Summation C
graph ite
Using the lower equation
and the values for the
heats of combustion of
CO and C, we can
calculate the unknown
heat in the cycle
CO + 1/ 2O 2
+ O2
? Hf(C O2 )
? Hc omb ustio n(CO)
CO 2
? Hf(CO2) = ? Hf(CO) + ? Hcombus tion(CO)
? Hf(CO) = ? Hf(CO2)?- ? Hcombus tion(CO)
Thermochemistry
Chemistry 120
? H f(CO)
Hess’ Law of Summation C
graph ite
Using the lower equation
and the values for the
heats of combustion of
CO and C, we can
calculate the unknown
heat in the cycle
CO + 1/ 2O 2
+ O2
? Hf(C O2 )
? Hc omb ustio n(CO)
CO 2
? Hf(CO2) = ? Hf(CO) + ? Hcombus tion(CO)
? Hf(CO) = ? Hf(CO2)?- ? Hcombus tion(CO)
? Hf (CO2 ) = - 393.5 kJ ? Hcombustion(CO) = - 283.0 kJ
? Hf (CO2 ) = ? Hf (CO2 ) - ? Hcombustion(CO)
Thermochemistry
Chemistry 120
Hess’ Law of Summation C
? H f(CO)
graph ite
Using the lower equation
and the values for the
heats of combustion of
CO and C, we can
calculate the unknown
heat in the cycle
+ O2
? Hf(C O2 )
CO + 1/ 2O 2
? Hc omb ustio n(CO)
CO 2
? Hf(CO2) = ? Hf(CO) + ? Hcombus tion(CO)
? Hf(CO) = ? Hf(CO2)?- ? Hcombus tion(CO)
? Hf (CO2 ) = - 393.5 kJ ? Hcombustion(CO) = - 283.0 kJ
? Hf (CO2 ) = (- 393.5) – (- 283.0) = -110.5 kJ
24
Thermochemistry
Chemistry 120
Standard enthalpies of formation and reaction
Just as we cannot determine the absolute value for
the internal energy of a system and so concentrate
on the change in internal energy, so we cannot fix
an absolute zero-point for reaction and formation
enthalpies.
We chose the Standard state of a material as that at
1 bar pressure (1 bar = 1 x 105 Pa) and the
temperature of interest.
Thermochemistry
Chemistry 120
Standard enthalpies of formation and reaction
The standard enthalpy of formation of an element in
the standard state is defined as zero.
Using these two facts, we can calculate the heats of
formation and, through Hess’ cycles, the heats of
reaction for all substances.
Thermochemistry
Chemistry 120
Standard enthalpies of formation and reaction
When we combine different reactions, we must take
account of the stoichiometry of the reaction.
Remember that ? H can be thought of as a product
of reaction and must be combine with the correct
stoichiometry.
25
Thermochemistry
Chemistry 120
Standard enthalpies of formation and reaction
For the reaction
? Hdimerization(NO2)
2NO2
N2O4
We can construct a Hess’ cycle:
Thermochemistry
Chemistry 120
Standard enthalpies of formation and reaction
For the reaction
? Hdimerization(NO2)
2NO2
N2O4
?H dim erization(NO 2)
We can construct a
Hess’ cycle:
2NO 2
? H f(NO 2)
1
N 2O4
1
/2? Hf (NO 2)
/2N2+ O2
Thermochemistry
Chemistry 120
Standard enthalpies of formation and reaction
For the reaction
? Hdimerization(NO2)
2NO2
N2O4
?H dim erization(NO 2)
We can construct a
Hess’ cycle.
Note that we must
include
the
stoichiometry in the
calculation.
2NO 2
? H f(NO 2)
1
N 2O4
1
/2? Hf (NO 2)
/2N2+ O2
26
Atomic Structure
Chemistry 120
Introduction to Quantum Mechanics
Quantum mechanics is the most important scientific
and philosphical development in the last 100 years,
possibly since Galileo and Newton.
If you are not confused by Quantum Physics then you
haven't really understood it.
Niels Bohr
Atomic Structure
Chemistry 120
Introduction to Quantum Mechanics
Web sources:
http://phys.educ.ksu.edu/
http://newton.ex.ac.uk/people/jenkins/mbody/mbody2.html
http://www.chembio.uoguelph.ca/educmat/chm386/rudiment/tourquan/t
ourquan.htm
http://www.upscale.utoronto.ca/GeneralInterest/QM.html
http://www.upscale.utoronto.ca/GeneralInterest/Key/genPHY100.html#
THE COURSE CONTENT
Atomic Structure
Chemistry 120
Introduction to Quantum Mechanics
The Players
Planck
Sommerfeld
Pauli
Heisenberg
Dirac
Schrödinger
Bohr
27
Chemistry 120
Some forms of matter I
Matter comes in many
different forms........
Chemistry 120
Some forms of matter II
Matter comes in many
different forms........
Chemistry 120
Some forms of matter III
Impurities in the surface of copper metal ?
?
Defects on the surface of copper metal
28
Chemical Basics
Chemistry 120
Distance to the Horizon
10 26 m
Distance to M31
10 22 m
Distance to the center of the galaxy
10 20 m
Distance to the Nearest Star
10 17 m
Distance of Earth to Sun
10 11 m
Radius of Sun
10 8 m
Radius of Earth
10 6 m
Chemical Basics
Chemistry 120
Radius of Knoxville TN
10 4 m
A small cow
10 0 m
Unraveled human DNA strand
10 -3 m
Typical size of dust
10 -4 m
Typical size of a cell
10
(1
-6
m
micron,
1? m)
Chemistry 120
Chemical Basics
The Planck Length
10 -35 m
Radius of the proton:
10 -18 m
Radius of Electron "orbit"
about an atomic nucleus
10 -15 m
Wavelength of 1 MeV gamma-ray :
10 -12 m
Spacing of atoms in solid copper :
10 -10 m
(1 Ångstrom, 1Å)
?
29
Atomic Structure
Chemistry 120
Introduction to Quantum Mechanics
Classical Mechanics:
All objects move and interact through two forces
Electromagnetic force
Gravity
and the forces obey Newton’s laws of motion.
Electromagnetism obeys Clark Maxwell’s equations
Atomic Structure
Chemistry 120
Introduction to Quantum Mechanics
Classical Mechanics:
Objects have definite trajectories in space.
We understand the position of the object and it’s
velocity or momentum.
Energies are continuous and unrestricted.
These objects are large and are in our common
experience
Atomic Structure
Chemistry 120
Introduction to Quantum Mechanics
In order to observe a physical event, we must make a
measurement of some description
For large objects, this is not a problem but.........
30
Atomic Structure
Chemistry 120
Introduction to Quantum Mechanics
What happens when how we measure a property of a
microscopic object affects the object and changes it?
We can define a large object in an absolute sense as
one which is perceptibly unaffected by the
measurement.
A small object is one where the measurement chages
the object that we measure.
Elephants are large – atoms are small.
Atomic Structure
Chemistry 120
Introduction to Quantum Mechanics
In general, Newton’s laws of motion are applicable to
large objects whereas molecules and atoms and
objects smaller than these are not.
This fact, combined with the inherent nature of matter
and energy on the microscopic scale, that make the
quantum world very different from the world of our
common experience.
Atomic Structure
Chemistry 120
Introduction to Quantum Mechanics
Continuum energy states are those where there is no
restriction on values for the energy of a body.
The color of light is related to the wavelength and
therefore the energy – in a continuous spectrum all
energies are present
31
Atomic Structure
Chemistry 120
Introduction to Quantum Mechanics
When atoms are excited, the classically expected
continuum spectrum does not appear
Atomic Structure
Chemistry 120
Introduction to Quantum Mechanics
Atomic Structure
Chemistry 120
Introduction to Quantum Mechanics
When a magnetic field or electric field is applied to
the gas, the lines split into two, three or more
components.
In a magnetic field, this splitting is known as the
Zeeman effect
32
Atomic Structure
Chemistry 120
Introduction to Quantum Mechanics
In an electric field, this
splitting is known as
the Stark effect
Increasing
electric
field
Atomic Structure
Chemistry 120
Introduction to Quantum Mechanics
These effects and the discontinuous nature of the
spectra are entirely inexplicable using classical
mechanics.
A new dynamical and structural description of matter
and the interaction of matter with energy was
required.
The first model was the Bohr model
Atomic Structure
Chemistry 120
Introduction to Quantum Mechanics
These effects and the discontinuous nature of the
spectra are entirely inexplicable using classical
mechanics.
A new dynamical and structural description of matter
and the interaction of matter with energy was
required.
The first model was the Bohr model
33
Atomic Structure
Chemistry 120
Quantum Mechanics: The Bohr Model
The Bohr model is incorrect but is still shown as the
model of the atom today.
It is the model in which electrons orbit the nucleus in
a similar way that planets orbit the sun.
The strong central and radial force is provided by the
electric force between the nucleus and the electron
Atomic Structure
Chemistry 120
Quantum Mechanics: The Bohr Model
It is the model in
which electrons orbit
the nucleus in a
similar way that
planets orbit the sun.
Atomic Structure
Chemistry 120
Quantum Mechanics: The Schrödinger Atom
Erwin Schrödinger improved on the Bohr
description and succeeded in explaining the internal
dynamics of the atom, revealed by the Stark and
Zeeman effects.
The Schrödinger description is based on the wave
properties of matter, detailed by Louis de Broglie
34
Atomic Structure
Chemistry 120
The de Broglie relationship
Louis de Broglie formulated that
a particle of momentum p has an
associated wavelength
? =h
p
Where p = mv
Atomic Structure
Chemistry 120
The modern quantum atom
By considering the electron in an atom as a wave,
the energy of the electron becomes quantized and
gives the correct energy relation that Bohr
described empirically by
E= -B
n2
and we term n as the principle quantum number
Atomic Structure
Chemistry 120
The modern quantum atom
Classically a particle on a sphere can also move
over the surface and this motion is circular. In a
similar way, the electron in an atom has properties
that we can associate with circular or angular
motion.
Electrons in an atom have angular momentum – the
momentum that is associated with angular motion
35
Atomic Structure
Chemistry 120
The modern quantum atom
The angular motion is described by two quantum
numbers – l and ml termed the angular quantum
number and the magnetic quantum number
respectively.
The electron also has its own angular momentum,
called spin s and these four quantum numbers, n, l,
ml and s define the properties of the electron in an
atom. They all follow from the wave description of
the electron in an atom
Atomic Structure
Chemistry 120
The modern quantum atom
The principle quantum number defines the energy
of the electron.
The angular quantum numbers define the shape of
the region of space in which the electron is
confined – these are termed the orbitals of the atom
and they have definite shapes:
Atomic Structure
Chemistry 120
Quantum Mechanics: The Details
The solutions of the Schrödinger wave equations are
called wavefunctions and have discrete energies. The
solutions are complicated – the Schrödinger equation
is
36
Atomic Structure
Chemistry 120
Quantum Mechanics: The Details
The solutions of the Schrödinger wave equations are
called wavefunctions and have discrete energies. The
solutions are complicated – the Schrödinger equation
is
H? = E?
Atomic Structure
Chemistry 120
Quantum Mechanics: The Details
The solutions of the Schrödinger wave equations are
called wavefunctions and have discrete energies. The
solutions are complicated – the Schrödinger equation
is
H? = E?
-h 2 ?2 + ?2 + ?2 + V(x, y, z) ? = E?
2m ?x2 ?y2 ?z2
{
Atomic Structure
}
Chemistry 120
Quantum Mechanics: The Details
The solutions of the Schrödinger wave equations are
called wavefunctions and have discrete energies.
The equations are only soluble for the hydrogen
atom and give the shapes of the orbitals – the space
in which the electron can be found as well as the
energies.
37
Atomic Structure
Chemistry 120
Quantum Mechanics: The Details
The wavefunctions are characterized and labeled by
three quantum numbers,
n
the principal quantum number
l
the orbital quantum number
ml
the magnetic quantum number
The electron also has a quantum number to define its
behavior – s the spin quantum number
Atomic Structure
Chemistry 120
Quantum Mechanics: The Details
The three atomic quantum numbers are connected in
terms to the values they can take:
n
any integer, except 0
In quantum number n
l is confined to |n –1|
e.g n = 3, l = -2, -1, 0, 1, 2,
There are (2l +1) values for ml
e.g l = 3, ml = -3, -2, -1, 0, 1, 2, 3
Atomic Structure
Chemistry 120
Quantum Mechanics: The Details
These rules give a maximum number of electrons
that can take a value of n
n=1
2 electrons
2 in l = 0
n=2
8 electrons
2 in l = 0, 6 in l = 1
n=3
18 electrons
2 in l = 0, 6 in l = 1
10 in l = 2
n=3
32 electrons
2 in l = 0, 6 in l = 1
10 in l = 2, 14 in l = 3
38
Atomic Structure
Chemistry 120
Quantum Mechanics: The Details
The orbitals for the hydrogen atom can be calculated
explicitly and analytically
n = 1, l = 0
Atomic Structure
Chemistry 120
Quantum Mechanics: The Details
The orbitals for the hydrogen atom can be calculated
explicitly and analytically
n = 2, l = 0
Atomic Structure
Chemistry 120
Quantum Mechanics: The Details
The orbitals for the hydrogen atom can be calculated
explicitly and analytically
n = 2, l = 1
39
Atomic Structure
Chemistry 120
Quantum Mechanics: The Details
The orbitals for the hydrogen atom can be calculated
explicitly and analytically
n = 3, l = 0
Atomic Structure
Chemistry 120
Quantum Mechanics: The Details
The orbitals for the hydrogen atom can be calculated
explicitly and analytically
n = 3, l = 1
Atomic Structure
Chemistry 120
Quantum Mechanics: The Details
n = 3, l = 2
40
Atomic Structure
Chemistry 120
Quantum Mechanics: The Details
n = 4, l = 0
Atomic Structure
Chemistry 120
Quantum Mechanics: The Details
n = 4, l = 1
Atomic Structure
Chemistry 120
Quantum Mechanics: The Details
n = 4, l = 2
41
Atomic Structure
n = 4, l = 3
Chemistry 120
Chemistry 120
Atoms, Molecules and Ions
The S block
s block
1
H
1
2
Li
3
Na
11
Be
4
Mg
12
K
19
Rb
37
Cs
55
Fr
86
Ca
20
Sr
38
Ba
56
Ra
88
3
4
5
6
7
p block
He
2
d block
Sc
21
Y
39
Lu
71
Lr
103
Ti
22
Zr
40
Hf
72
Rf
104
V
23
Nb
41
Ta
73
Db
105
Cr Mn
24 25
Mo Tc
42 43
W Re
74 75
Sg Bh
106 107
Fe
26
Ru
44
Os
76
Hs
108
Co
27
Rh
45
Ir
77
Mt
109
Ni
28
Pd
46
Pt
78
110
Cu
29
Ag
47
Au
79
111
Zn
30
Cd
48
Hg
80
112
B
5
Al
13
Ga
31
In
49
Tl
81
C
6
Si
14
Ge
32
Sn
50
Pb
82
N
7
P
15
As
33
Sb
51
Bi
83
O
8
S
16
Se
34
Te
52
Po
84
F
9
Cl
17
Br
35
I
53
At
85
Ne
10
Ar
18
Kr
36
Xe
54
Rn
86
f block
La
57
Ac
89
Ce
58
Th
90
Pr
59
Pa
91
Nd Pm
60 61
U Np
92 93
Sm
62
Pu
94
Eu
63
Am
95
Gd
64
Cm
96
Tb
65
Bk
97
Dy
66
Cf
98
Ho
67
Es
99
Er
68
Fm
100
The S block and P block
s block
H
1
2
Li
3
Na
11
Be
4
Mg
12
K
19
Rb
37
Cs
55
Fr
86
Ca
20
Sr
38
Ba
56
Ra
88
3
4
5
6
7
Yb
70
No
102
Chemistry 120
Atoms, Molecules and Ions
1
Tm
69
Md
101
p block
He
2
d block
Sc
21
Y
39
Lu
71
Lr
103
Ti
22
Zr
40
Hf
72
Rf
104
V
23
Nb
41
Ta
73
Db
105
Cr Mn
24 25
Mo Tc
42 43
W Re
74 75
Sg Bh
106 107
Fe
26
Ru
44
Os
76
Hs
108
Co
27
Rh
45
Ir
77
Mt
109
Ni
28
Pd
46
Pt
78
110
Cu
29
Ag
47
Au
79
111
Zn
30
Cd
48
Hg
80
112
B
5
Al
13
Ga
31
In
49
Tl
81
C
6
Si
14
Ge
32
Sn
50
Pb
82
N
7
P
15
As
33
Sb
51
Bi
83
O
8
S
16
Se
34
Te
52
Po
84
F
9
Cl
17
Br
35
I
53
At
85
Ne
10
Ar
18
Kr
36
Xe
54
Rn
86
f block
La
57
Ac
89
Ce
58
Th
90
Pr
59
Pa
91
Nd Pm
60 61
U Np
92 93
Sm
62
Pu
94
Eu
63
Am
95
Gd
64
Cm
96
Tb
65
Bk
97
Dy
66
Cf
98
Ho
67
Es
99
Er
68
Fm
100
Tm
69
Md
101
Yb
70
No
102
42
Chemistry 120
Atoms, Molecules and Ions
The S block , P block
s block
1
H
1
2
Li
3
Na
11
Be
4
Mg
12
K
19
Rb
37
Cs
55
Fr
86
Ca
20
Sr
38
Ba
56
Ra
88
3
4
5
6
7
p block
He
2
and D block
d block
Sc
21
Y
39
Lu
71
Lr
103
Ti
22
Zr
40
Hf
72
Rf
104
V
23
Nb
41
Ta
73
Db
105
Cr Mn
24 25
Mo Tc
42 43
W Re
74 75
Sg Bh
106 107
Fe
26
Ru
44
Os
76
Hs
108
Co
27
Rh
45
Ir
77
Mt
109
Ni
28
Pd
46
Pt
78
110
Cu
29
Ag
47
Au
79
111
Zn
30
Cd
48
Hg
80
112
B
5
Al
13
Ga
31
In
49
Tl
81
C
6
Si
14
Ge
32
Sn
50
Pb
82
N
7
P
15
As
33
Sb
51
Bi
83
O
8
S
16
Se
34
Te
52
Po
84
F
9
Cl
17
Br
35
I
53
At
85
Ne
10
Ar
18
Kr
36
Xe
54
Rn
86
f block
La
57
Ac
89
Ce
58
Th
90
Pr
59
Pa
91
Nd Pm
60 61
U Np
92 93
Sm
62
Pu
94
Eu
63
Am
95
Gd
64
Cm
96
Tb
65
Bk
97
Dy
66
Cf
98
Ho
67
Es
99
Er
68
Fm
100
The S block , P block ,
s block
H
1
2
Li
3
Na
11
Be
4
Mg
12
K
19
Rb
37
Cs
55
Fr
86
Ca
20
Sr
38
Ba
56
Ra
88
3
4
5
6
7
p block
He
2
D block and F block
d block
Sc
21
Y
39
Lu
71
Lr
103
Ti
22
Zr
40
Hf
72
Rf
104
V
23
Nb
41
Ta
73
Db
105
Cr Mn
24 25
Mo Tc
42 43
W Re
74 75
Sg Bh
106 107
Fe
26
Ru
44
Os
76
Hs
108
Co
27
Rh
45
Ir
77
Mt
109
Yb
70
No
102
Chemistry 120
Atoms, Molecules and Ions
1
Tm
69
Md
101
Ni
28
Pd
46
Pt
78
110
Cu
29
Ag
47
Au
79
111
Zn
30
Cd
48
Hg
80
112
B
5
Al
13
Ga
31
In
49
Tl
81
C
6
Si
14
Ge
32
Sn
50
Pb
82
N
7
P
15
As
33
Sb
51
Bi
83
O
8
S
16
Se
34
Te
52
Po
84
F
9
Cl
17
Br
35
I
53
At
85
Ne
10
Ar
18
Kr
36
Xe
54
Rn
86
f block
La
57
Ac
89
Ce
58
Th
90
Pr
59
Pa
91
Nd Pm
60 61
U Np
92 93
Sm
62
Pu
94
Eu
63
Am
95
Gd
64
Cm
96
Tb
65
Bk
97
Dy
66
Cf
98
Atomic Structure
Ho
67
Es
99
Er
68
Fm
100
Tm
69
Md
101
Yb
70
No
102
Chemistry 120
The Aufbau Principle and the Periodic Table
The quantum mechanical rules the relate n, l and ml
dictate the structure of the periodic table through the
aufbau prinicple, when used in conjunction with the
Exclusion principle
The rules are that, given n,
l = n – 1 and ml = +/- l including 0
43
Atomic Structure
Chemistry 120
The Aufbau Principle and the Periodic Table
For each value of n, l ml there are two possibilities
for s the spin of the electron - + ½ and - ½.
Each orbital can therefore accommodate two and
only two electrons.
We can therefore write the electronic configurations
of the atoms in terms of the occupations of each
orbital.
Atomic Structure
Chemistry 120
The Aufbau Principle and the Periodic Table
For hydrogen,
n = 1, l = n – 1= 0 and ml = 0.
The only possibilities are therefore ± ½ and we write
that H has a configuration of 1s 2 , showing the
prinicipal quantum number, the l quantum number
and the number of electrons.
Atomic Structure
Chemistry 120
The Aufbau Principle and the Periodic Table
All the orbitals that we can calculate from the
Schrödinger equation are hydrogenic as we can only
solve the Schrödinger equation for a two particle
system.
In hydrogen all the orbitals with the same n with
non-zero l and ml have the same energies, the only
energy differences between orbitals being n. Such
orbitals are termed degenerate.
44
Atomic Structure
Chemistry 120
The Aufbau Principle and the Periodic Table
In atoms heavier than hydrogen, the l quantum
number does effect the energy slightly and the
orbitals are no longer degenerate. This becomes
more important for heavier atoms and effects the
order of filling in the periodic table.
Atomic Structure
Chemistry 120
The Aufbau Principle and the Periodic Table
A second and highly important factor is the
distribution of the electrons with in the atom.
Any orbital with non-zero l has an angular node that
runs through the nucleus – the density of the
electrons at the nucleus is zero for these orbitals .
s orbitals have density at the nucleus and the force
on these from the nucleus is higher, so they are more
strongly bound
Atomic Structure
Chemistry 120
The Aufbau Principle and the Periodic Table
In general, the higher l the less penetrating the
orbitals are and the order of filling is
s before p before d before f
Anomalies appear at the 3d sub-shell. After Ar (3p 6 ),
the 4s shell fills first, before the 3d. A similar feature
occurs before the filling of the 4f shell.
45
Atomic Structure
Chemistry 120
The Aufbau Principle and the Periodic Table
Hund’s rule is the final rule for the configuration of
the atom.
Orbitals are filled such that all spins are parallel and
all orbitals are singly filled first, before doubling
filling the orbitals with paired spins.
Spin-parallel electrons cannot occupy the same
space and so the repulsion between electrons is
reduced. Spin-paired electrons can occupy the same
region of space and the repulsion is higher.
Chemistry 120
Atoms, Molecules and Ions
s block
1
Building the Periodic Table
p block
H
1
He
2
Chemistry 120
Atoms, Molecules and Ions
s block
1
H
1
2
Li
3
Building the Periodic Table
p block
He
2
Be
4
B
5
C
6
N
7
O
8
F
9
Ne
10
46
Chemistry 120
Atoms, Molecules and Ions
Building the Periodic Table
s block
1
H
1
2
Li
3
Na
11
3
p block
He
2
Be
4
Mg
12
B
5
Al
13
The Periodic Table
s block
H
1
2
Li
3
Na
11
Be
4
Mg
12
K
19
Ca
20
3
4
d block
Sc
21
Ti
22
V
23
Cr
24
Mn
25
Fe
26
Co
27
Ni
28
Cu
29
Zn
30
B
5
Al
13
Ga
31
H
1
2
Li
3
Na
11
Be
4
Mg
12
K
19
Rb
37
Ca
20
Sr
38
C
6
Si
14
Ge
32
Ne
10
Ar
18
N
7
P
15
As
33
O
8
S
16
Se
34
F
9
Cl
17
Br
35
Ne
10
Ar
18
Kr
36
Chemistry 120
The Periodic Table
s block
5
F
9
Cl
17
He
2
1
4
O
8
S
16
p block
Atoms, Molecules and Ions
3
N
7
P
15
Chemistry 120
Atoms, Molecules and Ions
1
C
6
Si
14
p block
He
2
d block
Sc
21
Y
39
Ti
22
Zr
40
V
23
Nb
41
Cr Mn
24 25
Mo Tc
42 43
Fe
26
Ru
44
Co
27
Rh
45
Ni
28
Pd
46
Cu
29
Ag
47
Zn
30
Cd
48
B
5
Al
13
Ga
31
In
49
C
6
Si
14
Ge
32
Sn
50
N
7
P
15
As
33
Sb
51
O
8
S
16
Se
34
Te
52
F
9
Cl
17
Br
35
I
53
Ne
10
Ar
18
Kr
36
Xe
54
47
Chemistry 120
Atoms, Molecules and Ions
The Periodic Table
s block
1
H
1
2
Li
3
Na
11
Be
4
Mg
12
K
19
Rb
37
Cs
55
Ca
20
Sr
38
Ba
56
3
4
5
6
p block
He
2
d block
Sc
21
Y
39
Lu
71
Ti
22
Zr
40
Hf
72
V
23
Nb
41
Ta
73
Cr Mn
24 25
Mo Tc
42 43
W Re
74 75
Fe
26
Ru
44
Os
76
Co
27
Rh
45
Ir
77
Ni
28
Pd
46
Pt
78
Cu
29
Ag
47
Au
79
Zn
30
Cd
48
Hg
80
B
5
Al
13
Ga
31
In
49
Tl
81
C
6
Si
14
Ge
32
Sn
50
Pb
82
N
7
P
15
As
33
Sb
51
Bi
83
O
8
S
16
Se
34
Te
52
Po
84
F
9
Cl
17
Br
35
I
53
At
85
Ne
10
Ar
18
Kr
36
Xe
54
Rn
86
f block
La
57
Ce
58
Pr
59
Nd Pm
60 61
Sm
62
Eu
63
Gd
64
Tb
65
Dy
66
Ho
67
Er
68
The Periodic Table
s block
H
1
2
Li
3
Na
11
Be
4
Mg
12
K
19
Rb
37
Cs
55
Fr
86
Ca
20
Sr
38
Ba
56
Ra
88
3
4
5
6
7
Yb
70
Chemistry 120
Atoms, Molecules and Ions
1
Tm
69
p block
He
2
d block
Sc
21
Y
39
Lu
71
Lr
103
Ti
22
Zr
40
Hf
72
Rf
104
V
23
Nb
41
Ta
73
Db
105
Cr Mn
24 25
Mo Tc
42 43
W Re
74 75
Sg Bh
106 107
Fe
26
Ru
44
Os
76
Hs
108
Co
27
Rh
45
Ir
77
Mt
109
Ni
28
Pd
46
Pt
78
110
Cu
29
Ag
47
Au
79
111
Zn
30
Cd
48
Hg
80
112
B
5
Al
13
Ga
31
In
49
Tl
81
C
6
Si
14
Ge
32
Sn
50
Pb
82
N
7
P
15
As
33
Sb
51
Bi
83
O
8
S
16
Se
34
Te
52
Po
84
F
9
Cl
17
Br
35
I
53
At
85
Ne
10
Ar
18
Kr
36
Xe
54
Rn
86
f block
La
57
Ac
89
Ce
58
Th
90
Pr
59
Pa
91
Nd Pm
60 61
U Np
92 93
Atomic Structure
Sm
62
Pu
94
Eu
63
Am
95
Gd
64
Cm
96
Tb
65
Bk
97
Dy
66
Cf
98
Ho
67
Es
99
Er
68
Fm
100
Tm
69
Md
101
Yb
70
No
102
Chemistry 120
Periodic Trends
As the number of electrons in an atom rises, the size
of the atom increases.
As the binding energy of the electrons rises, the size
of the atom decreases.
These two factors mean that the size of the atom
increases right to left and top to bottom in the
Periodic Table. Cs is the largest stable atom and F
the smallest.
48
Atomic Structure
Chemistry 120
Periodic Trends
Ionic radii also follow the same trends.
Cations are smaller than the neutral atoms and
anions are larger than the neutral atoms, though the
trend in ion sizes follow those of the atoms.
Atomic Structure
Chemistry 120
Periodic Trends
The energy required to remove electrons from the
atoms is termed the ionization energy.
In breaking a subshell there is a large jump in
ionization energy.
In breaking a shell, there is a huge jump in
ionization energy.
49