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Physical Chemistry
Sixth Form Practicals - 2016
Porter Laboratory
INTRODUCTION
Physical chemistry is a quantitative science. Skill in practical work is as important as a
knowledge of theory. Many important discoveries have resulted from observations of small
inconsistencies in repeated measurements or minor discrepancies between theory and
experiment. Well known examples are the discovery of the noble gases from the precise
measurement of relative molar masses; the development of the idea of electron and nuclear
spin from observations on the fine splitting of spectral lines; the discovery radioactivity from
the fogging of photographic plates left in the proximity of uranium salts. These developments
would not have taken place without the acute observation of the researchers and an
appreciation of the reliability and significance of their measurements.
The main objective of physical chemistry laboratory work is to provide training and practice
in the collection and critical evaluation of experimental data and in the preparation of reports.
The emphasis in the practical work is in making measurements and assessing the errors in
the measurements and final results. There is also the opportunity to use a computer for
tabulating data, calculating results and plotting graphs.
Two programs are available:
Microsoft Excel – most students will have used this package previously.
OriginPro - A graph drawing package with spreadsheet facilities. It will plot straight line
graphs and calculate the gradient and intercept with error limits. Very easy to use!
Each student will be able to perform two experiments.
1.
The Ionisation Energy of the Hydrogen Atom
2.
Kinetics of a first order reaction (hydrolysis of t-butyl chloride) by measurements of
conductivity.
EXPERIMENT 1
The Ionisation Energy of the Hydrogen Atom
The OBJECTIVES of this experiment are:
1. To measure the wavelengths of the first three lines of the Balmer series in the emission
spectrum of the H atom using a spectrometer.
2. To calculate the Rydberg constant and the ionisation energy of the H atom.
BACKGROUND
Spectra refer to patterns of emission and absorption of light from atoms. The observation of
spectra was a important step in the development of atomic theory and led to the Bohr model
of atoms. In this model, electrons orbiting the nucleus can exist only in discrete orbits and at
specific energies.
Absorption spectrum - Shows atoms changing states on absorption of electromagnectic
radiation. Atomic states are defined by the arrangement of electrons in atomic orbitals. An
electron in one orbital i.e. the ground state, may be excited to a more energetic orbital by
absorbing one photon of energy. Absorption spectra can be used to identify elements present
in liquids and gases.
Emission spectrum - a molecule undergoes a transition from higher energy level to a lower
energy level, usually the ground state. It gives out energy of a particular wavelength showing
the discrete lines of an emission spectrum. The spectra can be used to determine the
Energy
composition of a material, i.e. composition of stars.
Absorption
Emission
E2
E1
Frequency, wavelength, wavenumber and energy
Electromagnetic radiation is characterised by its frequency  and its wavelength . These are
related to the speed of propagation c by the equation c = . The energy  possessed by one
quantum of radiation (a photon) of frequency  is given by the Planck equation
 = h ,
where h is Planck’s constant and has the value 6.62607  10-34 J s.
The frequency of a photon is expressed in the SI unit reciprocal seconds (s1). The energy of
one mole of photons is given by E = NAh, where NA is the Avogadro’s constant and has the
value 6.02214  1023 mol1. This equation yields energy in J mol1.
Spectroscopists usually characterise radiation by its wavenumber,   1/  . In SI units the
wavenumber would be m1 but invariably the unit used is cm1 (1 cm1 = 100 m1).
Hydrogen Spectrum
This figure illustrates the energy levels of the hydrogen atom and the possible transitions
occurring in the emission spectrum.
To the far left is the Paschen series which was
discovered by Friedrich Paschen in 1908 and is in the Infra-red region of the electromagnetic
spectrum.
The middle series was discovered by Theodore Lyman in 1906 and is in the far Ultraviolet
region. On the right is the Balmer series and the part of most interest for this experiment.
In 1885, the Swiss Physicist Johann Balmer, observed the emission spectrum of hydrogen in
the visible region of the electromagnetic spectrum. He deduced that the frequency of each
line was given by a formula. This formula related the energy levels that the electron in
question left, (n2) and decayed to, (n1). and included a constant. The formula was later refined
by Johannes Ryberg, for whom the constant was named.
 1
1
1
   RH  2  2 

 n1 n2 
(1)
RH is the Rydberg constant for the H atom,  is wavenumber and n1 and n2 are positive
integers (n1 < n2)
In this experiment, the different energy levels accessible to the electron in a hydrogen atom
are examined using a spectrometer. The wavelengths of the emission lines from a hydrogen
discharge lamp will be measured. From these, the values of the electronic energy levels can
be calculated, and by extrapolation, the ionisation energy of the hydrogen atom can be
determined. Modern spectrometers are made up of a fibre optic cable into a box with the
output to a computer.
Experimental
The spectroscopic method involved in this experiment involves exciting electrons within the
hydrogen atoms by means of an electrical discharge. Electrons are promoted to excited
states and then emit a photon as they fall back to lower states. When large numbers of atoms
undergo such transitions, the emission is of sufficient intensity for spectral lines to be
observed by eye. The discharge method is not very discriminating and so a large number of
different excited states are produced in the gas which gives rise to several series of lines.
The wavelengths of the spectral lines are measured using a spectrometer.
Calibration of the spectrometer
 The first stage in a spectroscopic investigation typically involves an accurate calibration of
the spectrophotometer. Commercial instruments have a wavelength scale marked on
them, but it may not be sufficiently accurate for our purpose.
 The calibration is obtained by comparing the measured wavelength of a set of emission
lines for which the wavelength is already precisely known, see table on results page.
 The calibration for each instrument has previously been carried and you will be provided
with a value, , which describes the extent to which the spectrometer is inaccurate. This
has been calculated as the average of the difference between the observed wavelength
and true wavelength (    (true )   (obs ) ) of lines in the Cadmium and Krypton sprecta.
 To learn how to use the spectrometer and to check the calibration, measure the red line at
643.8 nm from the cadmium lamp - See instructions.
 Remember that each spectrometer will have a different value of .
 You will need to use the value of  for your spectrometer to correct the readings that
you take in the experiment.
Emission lines from the H atom (Balmer series)

Set up the hydrogen discharge tube with its capillary section horizontal and just in front of
the spectrometer slit, see picture below. Switch it on. Set the wavelength drum to 650 nm
and adjust the vertical position of the spectrometer until brightest image is obtained.
 The first and second Balmer lines are red and green; they are easily seen. The violet third
line is fainter and will be found at about 430 nm. Open the slit slightly if you have difficulty
in seeing the third line. Your eyes may need to be dark adapted for a few minutes. Take
two or three independent readings of the lines. You will not be able to see the fourth line,
which is at 410.2 nm.

Turn the hydrogen lamp off when finished.
Results - Write your results on the results page in this script.
 Use your correction value  to obtain the true wavelengths from your measured values
and then convert these to the corresponding wavenumbers.
Remember that wavelegth is in nanometers and wavenumber is in cm-1
 / cm-1  1 / 
1 nm = 1  10-9 m
 Identify the transitions. In each case, we know that the lower energy level has a principal
quantum number n1 = 2. The lines must therefore correspond to transitions from higher
levels, with n2 = 3, 4 etc. Look back at the diagram of the hydrogen spectrum.
 To help with the assignment, consider the following questions:
which transition in the Balmer series has the lowest energy change?
which of the observed lines corresponds to the lowest energy?
 In this way, assign the principal quantum number n2 of the excited state to each of the
observed lines and enter the value of 1/ n22 in the final column in each case.
 Plot a graph of  against 1/ n22 using the computer and obtain the gradient and intercept
Gradient =
±
Intercept =
±
 Equation 1 can be written in a straight line form;
 1
1
1
   RH  2  2  multiplying out gives

 n1 n2 
  RH
1
1
 RH 2
2
n1
n2
y=
c
m  x
RH =
±
cm-1
from the intercept: RH =
±
cm-1
Mean value:
±
cm-1
from the gradient:
RH =
Compare your result with the literature value:
RH = 1.09677  105 cm-1
The Ionisation energy for a hydrogen atom is the energy required to remove the electron from
the ground state where n1 = 1 to the state corresponding to complete removal of the electron,
i.e. n = 
 Using your value of RH estimate the ionisation energy for the hydrogen atom from the
equation
E = RH  c  h  N A
Speed of light
=
2.998 108 m s-1
h =
Planck’s constant
=
6.62607  10-34 J s
NA =
Avogadro’s constant
=
6.02214  1023 mol1
where c =
Ionisation energy of the H atom =
Compare your result with the literature value:
±
E = 1312 kJ mol-1
kJ mol1
RESULTS SHEET
CALIBRATION
 The true wavelengths for the calibration lines are given in the table:
/nm
Cadmium
/nm
Krypton
red
643.8
yellow
587.0
green
508.6
green
557.0
blue
480.0
blue
467.8
violet
441.5
Average correction factor:  =
nm
HYDROGEN ATOM (Balmer series)
Colour
 (observed) /nm
Mean  (observed) /nm
RED
GREEN/BLUE
VIOLET
 (true) /nm
RED
GREEN/BLUE
VIOLET
VIOLET
410.2
 / cm -1
n2
1
n 22
EXPERIMENT 2
Kinetics Of Hydrolysis Of Halogenoalkanes
The OBJECTIVES of this experiment are:
1.
To follow the rate of hydrolysis of t-butyl chloride (2-chloro-2-methylpropane) using
conductivity measurements.
2.
To determine the value of the rate constant for this reaction.
3.
To determine the activation energy EA for this reaction.
BACKGROUND
Determination of the rates of reactions provides vital clues as to how a process is taking place
on molecular scale i.e. the reaction mechanism.
A classic illustration of how kinetics can provide evidence for a reaction
mechanism is given by the work of Sir Christopher Ingold, a Professor of
Organic Chemistry at Leeds between 1924 –1930. He suggested that
there were two possible mechanisms of nucleophilic substitution.
So, for example, primary haloalkanes react directly with the nucleophile
Y¯ (an SN2 process):
CH3CH2CH2X + Y¯
CH3CH2CH2Y + X¯
whereas tertiary haloalkanes form water-stabilised carbocations in a rate-determining step (an
SN1 process):
slow
(CH3)3CX
(CH3)3C+ + Y¯
(CH3)3C+ + X¯
(CH3)3CY
Hence the rate of an SN1 reaction is independent of the nucleophile concentration.
In this experiment, you will follow the rate of hydrolysis of tertiary butyl chloride (t-BuCl) to give
an alcohol and hydrochloric acid:
 CH3 3 CCl  2H2O   CH3 3 COH  H3 O   Cl
As water plays the role of both nucleophile and solvent in this reaction, it is not possible to
distinguish between an SN1 and SN2 mechanism from changes in the nucleophile concentration.
However other evidence suggests that the reaction proceeds via two processes:
slow
  CH3 3 C  Cl
 CH3 3 CCl 
(2)
fast
  CH3 3 COH  H3O
 CH3 3 C  2H2O 
(3)
The reaction rate equation can be written as;

d [ t BuCl]
 k [ t BuCl]
dt
(4)
Integration of equation (4) to obtain the concentration [t-BuCl]t at any time t in terms of the initial
concentration [t-BuCl]0 and the rate coefficient k gives;
ln[t-BuCl]t = ln[t-BuCl]0 − kt
(5)
The reaction will be monitored by measuring the change in conductivity G (in S m-1), which
is proportional to the concentration of the ions H+ and Cl−, as the hydrolysis proceeds. The
concentration of t-BuCl in time is given by:
t  BuCl  G  Gt
(5)
G G 
where G∞ is the final conductivity. Thus a graph of ln   1t  versus time will give a straight
 S m 
line if the reaction is first order and the gradient will be -k.
The units of conductivity are included to make the log dimensionless.
Experimental
The reaction is carried out in a jacketed reaction vessel. The temperature is maintained by
water pumped through the jacket from a thermostatted water bath. The conductivity cell is a
pair of platinum black electrodes with electrical connections and an integrated thermometer.
Instructions for the use of the conductivity meters and computer data acquisition units are
provided with the apparatus.
 Each pair of students will follow the variation of conductivity with time at two different
temperatures (20C or 30C and 35C or 40C): The rate constant values from the other
temperatures can be obtained from another group of students.
Run
Number
1
Target
Temperature/°C
20
2
Time of Run / mins
Frequency of readings / s
20
20
30
10
10
3
35
5
1
4
40
5
1
If t-BuCl is added to water at room temperature, the reaction is too rapid to be followed by the
techniques available to us in this experiment. The reaction rate can be reduced by diluting the
water with a suitable organic solvent, 80/20 (v/v) water/acetone mixture is used in this
experiment.
Procedure
 Read the additional instructions with each set of apparatus before starting the run.
 Each run can be performed in any order.
 Measure 100 cm3 of the 80/20 water / acetone reaction solvent and pour this into the reaction
vessel. Make sure the magnetic stirrer bar is rotating.
 Note the temperature of the mixture. You should not begin your run until you are satisfied
that the temperature of the solvent has settled to a constant value.
 Record the actual temperature to 0.1°C of your solvent at least 3 times during the run.
 For runs 1 and 2, you will be using the data logger within the conductivity meter to record the
results.
 For runs 3 and 4, a network connection will allow you to save all your work in a directory
(Z:) which will be accessible on any networked PC. Get the computer ready.
 The reaction is started by introducing 1 cm3 of t-BuCl solution via the metered pipette into the
water/acetone solvent. Immediately start the data logger or acquisition unit.
 The conductivity of the reaction mixture will increase with time.
For run 1, readings of conductivity will be logged every 20 s.
For run 2, readings of conductivity will be logged every 10 s.
For runs 3 and 4, the conductivity will be recorded at 1 second intervals and displayed via the
computer data acquisition unit.
When you have finished each run, raise the cell out of the vessel by pressing the clamp and
lifting. Wash the cell with deionised water. Carefully remove the reaction vessel from the
clamp and empty the waste into a plastic bowl. Rinse the vessel and stirrer bar with water,
clamp the reaction vessel in place so that it is clean and ready for the next user.
Dispose of the solvent into the waste solvent container under the fume cupboard.
RESULTS
Run __1__
Time
/s
0
Target temperature = 20°C
Conductivity
/ S m-1
Time
/s
240
Conductivity
/ S m-1
Actual temperature /°C =
Time
/s
480
Conductivity
/ S m-1
Time
/s
720
20
260
500
740
40
280
520
760
60
300
540
780
80
320
560
800
100
340
580
820
120
360
600
840
140
380
620
860
160
400
640
880
180
420
660
900
200
440
680
220
460
700
Run __2__
Time
/s
0
Target temperature = 30°C
Conductivity
/ S m-1
Time
/s
130
Conductivity
/ S m-1
G
Actual temperature /°C =
Time
/s
260
Conductivity
/ S m-1
Time
/s
390
10
140
270
400
20
150
280
410
30
160
290
420
40
170
300
430
50
180
310
440
60
190
320
450
70
200
330
460
80
210
340
470
90
220
350
480
100
230
360
490
110
240
370
500
120
250
380
G
Run __3__
Filename
Run __4__
Filename
Target temperature = 35°C
Actual temperature /°C =
_______________________________________
Target temperature = 40°C
Conductivity
/ S m-1
Actual temperature /°C =
_______________________________________
Conductivity
/ S m-1
 If you plot the raw data, i.e. conductivity against time, you should get graph 1.
Unfortunatly this does not give the rate of reaction so we need to do a little bit of maths on
the data. Conductivity values at time t = Gt.
Conductance at the end of the run = G.
Take the Gt values away from the G value and then take the natural logarithm of these
values. This gives ln(G- Gt) for all the values of time. Only process the results where the
conductance is changing significantly, i.e. before it starts to level off. In graph 1 this is
~150 seconds.
 For each of your runs, plot a graph of ln(G - Gt) versus time, see graph 2. This should give
a straight line if the reaction is first order and for which the gradient will be – k.
Graph 1
Graph 2
G value
Plot of ln(G - Gt) against Time/s
0
0.5
for run 2 at 30.1°C
-1
-1
Conductivity
/ mS m-1
Conductance / 
0.6
0.4
ln(G - G t)
-2
0.3
Gt values
0.2
0.1
Do not include
these points when
calculating gradient
-3
-4
Gradient = rate constant = -k / s
-1
0.0
0
100
200
300
400
500
600
700
800
900
1000
-5
0
Time / seconds
Time
/s
50
100
150
200
250
Time / seconds
 If your plots show any scatter at long times, see graph 2, replot your data using only the points
showing a linear relationship. This may give a slightly different result for the gradient and,
hence, the rate constant in each case.
Run
Actual Temperature/C
T/K
k/s-1
1 or 2
3 or 4
You should get to this point.
We can now show by looking at the values of k for the whole group that as the temperature
increases, the rate of reaction also increases.
The results can then be used in the next part to determine the activation energy of the reaction.
Your School can do this bit with you at a later date.
Activation Energy
The final part of the experiment involves determining the activation energy from the rate
constants. The activation energy, Ea - is the minimum kinetic energy required for a collision to
result in reaction.
The Arrhenius equation expresses how rates of chemical reaction vary with temperature.
k = A exp (-Ea/RT)
where Ea is the activation energy, A is the pre-exponential factor
R is the gas constant, T is temperature.
Transformation of the Arrhenius equation into a form that can be used to obtain Ea and A from
the gradient and intercept of a straight-line plot gives;
ln k = ln A - Ea / RT
Ea 1
R T
m  x
which is the same as ln k = ln A y=
c
 You have obtained values of the rate constant at two temperatures and should obtain values
at the other temperatures from another group of students.
 A graph of ln k versus 1/T (where T is in Kelvin) should be a straight line with
gradient = -Ea/R and intercept= ln A.
Complete the following table:
Run
T/K
k / s-1
T-1/K-1
From the plot, calculate the activation energy Ea.
where
R = Gas Constant
=
8.314 J K-1 mol-1
Ea / kJ mol-1
Compare your result with the literature value:
Ea = ≈ 80 kJ mol-1
ln(k / s-1)