1. science
2. physics
3. thermodynamics

TECHNOLOGICAL EDUCATIONAL
INSTITUTE (T.E.I.) OF CRETE
DEPARTMENT OF ELECTRICAL
ENGINEERING ENGINEERING
PHYSICAL CHEMISTRY
LABORATORY
LABORATORY MANUAL
2014
Heraklion, Crete
TABLE OF CONTENTS
OCCUPATIONAL HEALTH AND SAFETY………………………………….
LABORATORY RULES AND REGULATIONS……………………………...
GENERAL FIRE ORDERS…………………………………………………......
ACKNOWLEDGEMENT FORM………………………………………………
3
3
5
5
EXPERIMENTAL SECTION
EXPERIMENT 1…………………………………………………………………
7
Thermodynamics of Galvanic Cells
EXPERIMENT 2…………………………………………………………………
16
Potentiometric Determination of the Dissociation Constant of a Weak Acid
EXPERIMENT 3…………………………………………………………………
20
Determination of the Adsorption Isotherm of Acetic Acid on Activated Carbon
EXPERIMENT 4…………………………………………………………………
23
Partial Molar Properties of Solutions
EXPERIMENT 5…………………………………………………………………
25
Kinetics of Dissolution of Solid Substances
EXPERIMENT 6…………………………………………………………………
29
Determination of Molar Mass From Freezing Point Depression
EXPERIMENT 7…………………………………………………………………
36
Enthalpy of Mixing of Acetone and Water
EXPERIMENT 8…………………………………………………………………
40
Dissociation Constant of an Indicator by Spectrophotometry
REFERENCES…………………………………………………………………… 45
OCCUPATIONAL HEALTH AND SAFETY
The present manual was written in order to assist you right and safe laboratory techniques.
You are required to read the following set of Laboratory Rules and Regulations, as well as to
consent that you have read and understood them. Additionally, in the laboratory
manuals/practical books and/or pre-practical lectures your attention will be drawn to the
correct and safe handling of specific chemicals/reagents/solvents and to the correct/safe
manner in which specified laboratory operations must be carried out. These specific
instructions and/or warnings must never be ignored.
WARNING: All substances handled and all operations performed in a laboratory can be
hazardous or potentially hazardous. All substances must be handled with care and disposed of
according to laid down procedures. All operations and manipulations must be carried out in
an organized and attentive manner.
LABORATORY RULES AND REGULATIONS
1. Students must be present about ten minutes before the start of each scheduled
laboratory session. Latecomers may be refused entry to the laboratory.
2. No student will be permitted to work in the laboratory outside of laboratory hours
except by express permission of the staff member(s) responsible for the session.
Never work in a laboratory on your own.
3. Smoking is strictly prohibited in all laboratories and instrument rooms.
4. Do not put anything into your mouth while working in the laboratory. NEVER taste a
chemical or solution. Eating is totally PROHIBITED in all laboratories.
5. All students are required to wear a laboratory coat and no student will be permitted to
work in the laboratory without one.
6. All students who do not wear conventional spectacles must wear eye protection.
Safety glasses must be worn throughout all practical sessions. Students who wear
conventional spectacles must have them on at all times when in the laboratory.
7. All students must wear closed shoes in the laboratory, unless permission has
been obtained to wear sandals for some medical reason.
8. Apparatus and chemicals are NOT to be removed from the laboratory.
9. Students will find the laboratory benches clean on arrival in the laboratory. The bench
at which you work must be left clean when you leave the laboratory at the end of the
practical session. Bench tops must be wiped clean. Glassware and other apparatus
should be left clean and dry, unless otherwise indicated or instructed.
10. Work areas must at all times be kept clean, and free from chemicals and apparatus
which are not required. All glassware and equipment must be returned to its proper
place, clean and dry, and in working condition, unless otherwise indicated or
instructed.
11. All solids must be discarded into the bins provided in the laboratory. Never throw
matches, paper, or any insoluble chemicals into the sinks. Solutions and liquids that
are emptied into the sinks must be washed down with water to avoid corrosion of the
plumbing. Waste solvents must be placed into the special waste solvent bottles where
provided.
12. Before leaving the laboratory at the end of a practical session make sure that all
electrical equipment is switched off, and that all gas and water taps are shut off.
13. Students who break or lose equipment allocated to them will be required to pay for
replacements. All breakages or losses must be reported to the teaching assistant in
charge.
14. Do NOT heat graduated cylinders or bottles because they will break easily.
15. Any apparatus or glassware which has to be heated must be heated gently at first,
increasing the amount of heat gradually thereafter.
16. Balances, spectrophotometers and other expensive equipment must be treated with
care and kept clean and tidy at all times.
17. Fumehoods must be used when handling toxic and fuming chemicals. Other
operations, such as ignitions, are also carried out in fumehoods. The only parts of the
human body which should ever be in fumehood are the hands - never put your head
inside the fumehood.
18. Never leave a laboratory experiment unattended without first consulting the
Laboratory Technical Assistant (TA) in charge.
19. Reagent bottles must be re-stoppered immediately after use. It is absolutely forbidden
to introduce anything into reagent bottles, not even droppers. Solutions and reagents
taken from bottles must NEVER be returned to the bottles. Do not place the stopper
of a reagent bottle onto an unprotected bench top.
20. Laboratory reagents and chemicals must be returned to their correct places
immediately after use. Spillage must be cleaned off bottles/containers. Labels must
face the front.
21. The use of reagent bottle caps as weighing receptacles is forbidden.
22. Liquids-whether corrosive or not-must be handled with care and spilling on the bench
or floor should be avoided. Any spillage must be cleaned up at once-if the liquid is
corrosive (acids or bases) call your TA or professor. Never hold a container above
eye level when pouring a liquid.
23. When carrying out a reaction or boiling a liquid in a test tube, point the mouth of the
test tube away from yourself and others in the laboratory.
24. Beware of hot glass and metal. Never handle any item which has been in a flame, a
hot oven or a furnace without taking precautions. Use leather/asbestos gloves or
tongs, or ask for advice on what to use.
25. Report all accidents, cuts burns, etc., however minor, to your TA or the professor.
Eye-wash stations are located in various places in the corridors. Ensure that you know
where the nearest one to your bench is located.
26. A chemical laboratory is not a place for horse-play. Do not attempt any unauthorized
experiments. Do not play practical jokes on your classmates. Such things are
dangerous and can cause serious injury. Any student found indulging in such
activities will be banned from the laboratory.
GENERAL FIRE ORDERS
Firefighting instructions are exhibited in individual laboratories. However, the following
orders must always be obeyed.
In the event of a fire
Attack it at once with the appropriate firefighting equipment and shout for help.
On hearing a fire evacuation alarm
1. Stop normal work immediately.
2. Make safe any apparatus, and material in use, shutting off as necessary any local gas
taps/valves, electricity and other potentially dangerous services under your control.
3. Immediately leave the building.
4. Go to the Fire Evacuation Area which for this CHEMISTRY BUILDING is outside to the
south west entrance to the building, on the grassed area between the Hall of
residence and Science Building 2 (which is the building you are presently).
TECHNOLOGICAL EDUCATIONAL INSTITUTE OF
CRETE
DEPARTMENT OF XXXXXXXX
ACKNOWLEDGEMENT FORM
I, the undersigned (please print full name)
..........................................................................
Student ID No. ........................................
do hereby acknowledge having read and understood the documents headed "Occupational
Health and Safety" and "Laboratory Rules and Regulations". Furthermore, I accept that
contravention(s) of these rules and regulations will lead to my expulsion from the laboratory.
I agree to abide by any additional laboratory regulations or safety rules presented in writing in
the practical manuals/books or issued verbally by the INSTRUCTOR-in-charge or his/her
responsible member of staff.
SIGNED........................................... DATE.......................
Department of Electrical Engineering, Heraklion, Crete, Greece
Editor: Dr. Minas M. Stylianakis
Contributors: Dr. Minas M. Stylianakis, Dr. Konstantinos Petridis, xxxxxxxxxxx
Laboratory manual for physical chemistry, 1st edition
Copyright ©2014 by Dept of xxxxxx, Technological Educational Institute (T.E.I.) of Crete,
Heraklion, Greece
EXPERIMENT 1
Thermodynamics of Galvanic Cells
Theory
The exchange of electrons during a redox process makes this type of reaction potentially
useful in a variety of ways. One of the more familiar applications of redox chemistry is the
galvanic or voltaic cell in the form of a dry-cell battery (a group of galvanic cells in series).
At the simplest level, a galvanic cell acts as a kind of electron "pump" which causes electron
flow from one point to another through the difference in electric potential created by the
redox reaction inside. This flow of electrons can be harnessed for a variety of practical tasks
and is related to the free energy expended by the chemical system in the cell as the reaction
proceeds to equilibrium.
A single galvanic cell consists of an oxidizing agent and reducing agent which are physically
separated by one or more electrolytes. In a dry-cell battery, the electrolyte is usually in the
form of a moist paste but it can also be liquid (as in an automobile battery). If the agents are
allowed to come in direct contact then no electrical work is done and the energy of the
reaction is released solely as heat. For this reason cells generally contain some kind of porous
barrier which permits ion movement within the cell but retards general mixing of the agents.
This barrier can take many forms including a glass tube filled with an electrolyte solution or
gel, a strip of filter paper soaked in an electrolyte, or unglazed porcelain separating the cell
electrolytes. A typical laboratory cell is diagrammed below:
Figure 1. The oxidation of zinc metal occurs spontaneously at the zinc electrode [anode] when the two
pieces of metal are connected by a wire. This oxidation releases electrons which flow through the wire
to the copper electrode [cathode] to enable the reduction of copper ions there. The direction of electron
flow in a cell is determined partly by the relative ease of oxidation of the electrode materials. Because
zinc is a more active metal than copper, a greater electric potential accumulates on the zinc strip when
it is placed in the zinc solution, i.e., some of the zinc atoms from the metal enter the zinc solution
spontaneously, resulting in a small surplus of electrons in the metal piece.
This process can be thought of as an equilibrium:
Zn(s) à Zn2+(aq) + 2 e-
The equilibrium constant for this process is very small (or the zinc would simply dissolve). A
similar equilibrium exists at the copper strip prior to connection:
Cu(s) à Cu2+(aq) + 2 eBut since copper is a much less active metal than zinc the equilibrium constant for this
process is even smaller than that for the zinc. We say the two metals have different potentials
in this cell, comparing the tendency to release electrons. Thus, when the two strips are
connected with a wire, electrons will flow spontaneously from the zinc strip to the copper
until the potential for electron release is the same at both strips. At that point equilibrium
exists and there is no net flow of electrons between the metals. In common terms we describe
such a cell as "dead". Thermodynamically speaking, its ability to do work is exhausted (i.e.,
ΔG = 0).
The two half-reactions in this and other similar cells are kept physically separate but ion
migration is permitted through the porous barrier. The movement of ions within the cell is
part of the charge circulation which is needed to engender electron flow. If ions cannot move
from one half of the cell to the other, there is a build-up of charge around each electrode. For
example, as zinc atoms are spontaneously oxidized, zinc ions enter the solution at the
electrode surface. This creates a greater concentration of these ions at that location and will
cause the equilibrium at the electrode to shift even more to the left (i.e., zinc metal). Ion
migration helps prevent this electrode polarization as well as moving charge through the
internal part of the cell.
The potential for electrons to flow spontaneously in cells like this is measured as voltage.
Each half-reaction has associated with it a standard potential which has been measured
relative to the reduction of hydrogen ions in 1 M acid solution at standard thermodynamic
conditions. The standard potentials are known as Eo values and represent electrical work that
may be done by the half-reaction in combination with another. In the copper-zinc example
presented earlier, the overall Eo value may be determined as:
Eo
Zn(s) à Zn2+(aq) + 2 e-
+0.76 V
Cu2+(aq) + 2 e- à Cu(s)
+0.34 V
---------------------------------------------------------------Zn(s) + Cu2+(aq) à Zn2+(aq) + Cu(s)
+1.10 V
Eo values in tables are typically given as reduction potentials. In the example above the zinc
half reaction has been written as an oxidation since zinc has a greater tendency to lose
electrons than copper. Therefore, the original table value of -0.76 V for the Eo of this process
has been changed to +0.76 V.
The maximum free energy available from a galvanic cell can be calculated from standard
thermodynamic values but because of the transfer of electrons through an external circuit (and
therefore through devices) with the potential to do work, the free energy is also obtainable
from the standard electric potential value for the cell.
The relationship is:
ΔGo= -nFEo
where n represents the moles of electrons transferred as seen in the overall balanced chemical
equation and F is a constant called the faraday, 96500 coulombs/mole e- [a coulomb(C) is a
unit of electric charge equivalent to 1 joule/volt].
This expression can be extended to great analytical advantage by recalling that there is also a
relationship between the maximum free energy change for a reaction and the equilibrium
constant, Kc:
ΔGo= -RT ln Kc
Since reactions seldom begin with substances at standard states, an amended relationship
allows the calculation of the free energy available at a given point in a reaction:
ΔG = ΔGo+ RT ln Qc
where Qc is the reaction quotient with the same form as Kc, but initial or current
concentrations rather than equilibrium concentrations. When Qc= Kc, ΔG = 0, i.e., the system
is at equilibrium.
Combining the relationship between the standard free energy and the standard cell potential
with that between the standard free energy and the equilibrium constant we have:
-nFEo = ΔGo = -RT ln Kc
This gives a relationship between the standard cell potential and the equilibrium constant for
the reaction. An even more useful relationship can be derived following the substitution
process shown earlier which relates the actual cell potential, E, with the ambient
concentrations:
-nFE = -nFEo + RT ln Qc
This is the basic relationship that is today known as the Nernst Equation and is generally
given as:
E= Eo –
𝑹𝑻
𝒏𝑭
ln Qc
In practice this relationship can only be used accurately at 298 K because of the presence of
the standard potential value. Other temperatures require an estimation of "Eo" for those
conditions (this can be done experimentally or by calculating an approximate "ΔGo" from the
Gibbs-Helmholtz equation using a nonstandard value for T). Because of the restricted nature
of the relationship, the constants (including T as 298 K) are traditionally combined along with
a conversion from the natural log to log10 and the expression is often written as:
E= Eo –
𝟎.𝟎𝟓𝟗𝟐
𝒏
log Qc
The power hidden in this expression may not be immediately evident on casual inspection. At
face value it appears useful for determining the voltage output of a galvanic cell at nonstandard concentrations. However, its real utility lies in doing just the opposite: determining
an unknown concentration based on a measured voltage.
In the laboratory, many reactions involve ions which are part of standard galvanic cell
combinations. The Nernst equation thus provides a tool for determining the concentration of
these ions in equilibrium systems.
For example, the complexation of copper (II) by ammonia is a reaction you have seen in the
lab:
Cu2+(aq) + 4 NH3(aq) à Cu(NH3)42+(aq)
We know that this process, while strongly favoring the formation of tetraamminecopper (II)
ion, is an equilibrium process. The Kf value for the formation of the complex ion can be found
in many references. If a known amount of excess ammonia is added to the copper half of the
Cu-Zn galvanic cell used as an example earlier:
Zn(s) + Cu2+(aq) à Zn2+(aq) + Cu(s)
Eo = +1.10 V
the concentration of Cu2+(aq) will drop dramatically. The measured cell voltage, E, will change
from the standard value, Eo, based on this decrease. The new equilibrium [Cu2+] will thus be
the only unknown left in the following expression (assuming original standard conditions):
E = Eo –
𝟎.𝟎𝟓𝟗𝟐
𝒏
log
𝐙𝐧𝟐!
𝐂𝐮𝟐!
If the equilibrium [Cu2+] can be found in this way and the initial [NH3] is also known, it is
possible to calculate Kf for the complexation process. The same technique can often be
applied to solubility product constants.
It is even possible to determine the concentration of an ion in one half of a cell with the same
anode and cathode! The measured E for a standard cell of that description should be 0.00 V
(since Qc= 1). But such "concentration cells" can generate small potentials based on the
slightly different equilibria that exist at each electrode by virtue of the fact that there are more
or fewer ions present in the electrolyte around one of the electrodes. An important application
of this behavior is found in every chemistry laboratory around the world in the form of a pH
electrode.
In addition to their analytical uses in the laboratory, galvanic cells are good systems for
examining relationships among thermodynamic quantities. The determination of standard free
energy values for reactions is generally an indirect process. If the equilibrium constant for
such reactions can be determined then ΔGo can be calculated from that value. We have seen in
the previous discussion that there is also a relationship between the standard potential for a
cell reaction and the standard free energy change:
ΔGo = -nFEo
Moreover, we know that standard free energy changes can be calculated from standard
enthalpy and standard entropy changes:
ΔGo = ΔHo - TΔSo
Combining these expressions we might write:
-nFEo = C – TΔSo
or
Eo =
𝜟𝑺𝒐
𝒏𝑭
T–
𝜟𝑯𝒐
𝒏𝑭
This expression, of course, is in the form of the equation of a straight line and suggests that
careful measurements of the cell voltage over a range of temperatures can yield a much more
difficult quantity to determine: the standard entropy change for the reaction, ΔSo. This
expression, like the Nernst equation, suffers from an important limitation: it is strictly correct
only at 298 K. However, the values of ΔS and ΔH typically change only a little over a small
temperature range and careful measurements in the vicinity of room temperature can give
results which agree well with other methods.
Experimental
There are three parts to this experiment:
• determine the apparent Eo value for the following cell:
Cu|Cu2+(1.0 M)|| Ag+(1.0 M)|Ag
• determine the following ion concentrations:
1. Cu2+(aq) in an unknown solution [reference half-cell: Cu|Cu2+ (1.0 M)]
2. Ag+(aq) in a saturated AgCl solution [reference half-cell: Cu|Cu2+ (1.0 M)]
3. Cu2+(aq) in excess NO2-(aq) solution [reference half-cell: Ag|Ag+ (1.0 M)]
• determine the temperature dependence of the voltage for the cell:
Cu|Cu2+ (1.0 M)||Ag+ (1.0 M)|Ag
The following non-locker materials will be provided:
• Solutions of 1.0 M Cu(NO3)2, 1.0 M AgNO3, 1.0 M NaNO2, 1.0 M KCl,
"x" M Cu(NO3)2, 0.10 M Cu(NO3)2
• Metal electrodes: Cu, Ag
• Glass tubing, cotton string and septum stopper (see Technique section)
• CBL thermometer probe
• CBL voltage probe (0 to +5 V)
• forceps
• beral pipets
• micropipettor and tips
• multimeter and leads
Chemicals
Copper (II) nitrate is the source of the Cu2+ ion in this experiment. Commonly available in
several hydrates, the blue-green solid is deliquescent and very soluble in water.
It is used in light-sensitive reproductive papers and as a colorant in ceramics. The compound
is also an ingredient in a solution for producing an antique black finish on copper. It is
employed in a variety of electroplating baths. The solid material is irritating to the skin.
Silver nitrate (the source of Ag+ in this experiment) forms colorless, transparent crystals. It is
stable and not darkened by light in pure air but darkens in the presence of organic matter and
H2S. It decomposes at low red heat into metallic silver. It is used in photography and the
manufacture of mirrors, silver plating, indelible inks, hair dyes, etching ivory and as an
important reagent in analytical chemistry. It has been used as a topical antiseptic in a 0.1 to
10% solution. However, it is caustic and irritating to skin. Silver nitrate stains skin and
clothing. These stains will wear off skin in a few days to a week but clothing is generally
ruined. Swallowing silver nitrate can cause severe gastroenteritis that may end fatally.
Potassium chloride is a white, crystalline solid or powder. One gram will dissolve in as little
as 2.8 mL of water. The compound occurs in nature as the mineral sylvine. It is used in
photography, buffer solutions and electrodes. Large doses by mouth can cause gastrointestinal
irritation, purging and circulatory disturbances. In this experiment it is the source of Cl- used
to saturate a solution with AgCl.
Silver is one of the few metals that can be found native and is also found associated with
copper, gold, or lead. It constitutes 1 x 10-5 % of the earth's crust. It is more malleable and
ductile than any metal except gold and when pure is perhaps the best electrical conductor. It is
insoluble in acids except nitric or hot concentrated sulfuric. Most silver salts are light
sensitive (they darken on exposure to light) and this property makes them useful in the
manufacture of photographic film. Small crystals of silver chloride are used in some
photochromic eye glasses. Absorption of light causes the AgCl to dissociate into Ag and Cl.
The finely dispersed silver atoms tint the glass gray. The reverse reaction occurs in subdued
light.
Copper makes up about 0.01% of the earth's crust. It is one of the earliest known metals and is
known for its unique reddish color when pure. However it becomes dull when exposed to air,
forming oxides of copper, and in moist air becomes coated with green copper carbonate (this
is part of the patina that appears on old copper or copper alloy exposed to the elements--like
the Statue of Liberty). It is very slowly attacked by dilute hydrochloric acid and sulfuric acid,
while nitric acid can readily dissolve it. It also slowly dissolves in aqueous ammonia.
Copper is used in the manufacture of bronzes (copper + tin) and brasses (copper + zinc), and
is used extensively in electrical conductors (wires, printed circuits, etc.). Of course copper
also makes up a percentage of nearly all U.S. coins minted today.
Copper itself probably has little or no toxicity, but some of its compounds can be quite
hazardous.
Technique Discussion
Electrode preparation is always very important for good results in electrochemical
experiments. Electrodes should be cleaned with an abrasive pad of some kind, then wiped
clean. Contamination of the electrode solutions can also contribute to inaccurate results. For
this reason, only the solutions within the two standard half-cells should be reused. The
standard copper and silver half-cells used in the first part of the experiment may be retained
for later parts, but all other solutions must be discarded at the end of each measurement and
new, clean test tubes should be used for each solution.
The standard half-cells are constructed from pieces of glass tubing. A short length of cotton
string, thoroughly soaked with 1 M NaNO3, is inserted into one end of the tubing and is held
in place by firmly inserting a rubber septum stopper. When the collar of the septum stopper is
folded over there should be a small length of the string exposed (and a small length visible in
the tube as well):
The cotton string acts as a salt bridge but prevents solution from dripping out (or diffusing in)
at an observable rate. Two half-cells should be made in this way. One holds a copper
electrode in 1.0 M Cu(NO3)2, the other has a silver electrode in 1.0 M AgNO3. The half-cells
only need to be filled about ½ to ⅔ of the way with solution. During the experiment the halfcells are inserted into (clean) locker test tubes which are used for the other half of the cell. In
these test tubes the electrolyte is filled to about the same level as the solution in the tube and a
second electrode is inserted. Both electrode strips can be folded over gently to keep them
from falling into the tubes and to aid in connecting to electrical leads.
Because the standard half-cells will be used in several parts of the experiment it is important
to rinse the outside of the cell thoroughly with distilled water between parts, paying special
attention to the protruding cotton string. The outside of the tube should then be dried before
reuse. Care should be exercised with the silver half-cell as some silver nitrate will have
diffused into the string. Gloves may be helpful.
The multimeters have several scales for displaying small voltages. In general more significant
digits are better. Two digits are the absolute minimum and you should always try to adjust the
meter to display three by using the millivolt settings. It is important to note the polarity of the
cell (i.e., which electrode is the anode and which the cathode is). This will enable you to
establish the spontaneous direction of the reaction. When a positive reading is displayed on
the multimeter, the electrode connected to the black lead (marked COM on the meter) is the
anode.
For the initial measurement of the standard cell voltage, 1.0 M solutions of Cu2+ and Ag+ are
used. For ease of clean-up and conservation of expensive silver solution it is best to use the
silver half-cell as the inner tube.
In the second part of the experiment the solution volumes in the outer half-cell (in the test
tube) are critical only in the determination of [Cu2+] for the Cu2+ - NO2- mixture. To ensure
that the maximum amount of complex is formed, a 0.10 M Cu(NO3)2 solution should be used
with excess 1.0 M ligand solution (suggested volume ratio: 300:2700 µL).
For the determination of [Ag+] in a saturated AgCl solution, only one drop of 1.0 M silver ion
should be added to the 1.0 M KCl to sustain a visible precipitate. Be sure to mix thoroughly.
Be sure to bring your calculator to lab and have the Origin 9.0 in your PC memory.
A 250 mL beaker can be used as a stirred water bath for temperature control in part 3. The
silver/copper cell should be clamped so that all of the solution is below the water bath level.
A second test tube filled with room temperature water should also be clamped in place and a
thermometer probe suspended in it. This should give a better indication of the temperature in
the actual galvanic cell.
Care should be exercised in heating the water bath so that there is time for temperature
equilibration. The hotplate setting of "2" seems to work well. The CBL should be set up for
two probes, voltage (0 to +5) on channel 1 and temperature on channel 2. Record data every 5
minutes (300 s) for 60 minutes. A temperature range of 5 oC to about 60 oC should be
sufficient. Pre-chilled water will be available.
Scientific Report
Your initial calculations should include:
1. The half-cell potential of Cu2+|Cu, taking the reduction half-cell potential of the silver
system to be +0.80 V [relative error]
2. The Ksp of AgCl based on the concentration of Ag+(aq) after precipitation with 1.0 M
KCl [relative error]
3. The concentration of the unknown Cu2+(aq) solution
4. The Kf for [Cu(H2O)3NO2]+ based on the equilibrium concentration of free Cu2+(aq)
remaining after addition of 1.0 M NaNO2
5. A graph of E vs. T for the Cu-Ag cell
6. Estimates of ΔGo, ΔSo, ΔHo, and Eo for the Cu-Ag cell [relative error]
You should include a comparison of your calculated half-cell potentials and constants with
literature values as well as a discussion of possible sources of error if your values do not agree
well. Can you suggest experimental conditions under which you might obtain better results?
Why is the silver half-cell chosen in this experiment as the "standard" (i.e., it's potential is
assumed to be +0.80 v)?
In a previous experiment you ranked the nitrite ligand among several others for its ability to
displace the others from a copper (II) complex ion. Does the Kf determined in this experiment
agree with your ranking? If not, attempt to account for the discrepancy.
Finally, the entropy change in the Cu-Ag cell is negative. For the cell Pb|Pb2+(1.0 M)||Cu2+
(1.0 M|Cu the entropy change is found to be positive. What effect would this have on the
temperature dependence of E for this cell? Attempt to account for the different signs of the
entropy changes.
EXPERIMENT 2
Potentiometric Determination of the Dissociation Constant of a Weak Acid
Theory
Dissociation of a week acid represents one of the proton exchange reactions, they are also
called the acid-base reactions. The Bronsted-Lowry classification defines an acid as a proton
donor (protogenic substance) and a base as a proton acceptor (protofilic substance). The acid
HA generates the following equilibria in the water:
HA + H2O ß à H3O+ + A-
Ka =
𝒂 𝑯! 𝒂 𝑨!
𝒂 𝑯𝑨
(1)
We have assumed that the activity of the water is constant and have absorbed it into the
definition of the acid dissociation constant Ka. The species A- (anions of the week acid) acts
as a proton acceptor in the equilibrium. Therefore it is a base according to the BronstedLowry definition, and it is called the conjugate base of the acid HA. The hydrated hydrogen
ions H3O+ are written as H+ in mathematical formulae, for brevity.
Water can play the role of both acid and base. Therefore even in pure water the autoprotolysis
equilibrium occurs:
H2O + H2O ßà H3O+ + OHwith the equilibrium constant
Kw =a(H+) a(OH-)
(2)
in which both water activities have been absorbed into the Kw. At 25oC, Kw=1.008x10-14, and
this very small value indicates that only very few water molecules are dissociated. Both in
pure water and in the diluted aqueous solutions the activities (concentrations) of H3O+ and
OH- ions are mutually interdependent by the equation for Kw. The strength of an acid is
measured by its dissociation constant. Strong acids are strong proton donors, and then the Ka
is then large. Week acids have low values of Ka because the proton equilibrium lies in favour
of HA (at room temperature acetic acid has Ka=1.8x10-5).
The concentration of protons plays an important role in many applications of chemistry and it
can vary over many orders of magnitude. The pH scale is a convenient measure of proton
activity and is defined as:
pH = -log a(H+)
(3)
In a similar way, the value of pKa = -logKa is usually introduced. Transformation of the
definition equation of the dissociation constant of the week acid HA gives:
𝑯𝑨
pKa = pH + log 𝑨!
(4)
where the pKa value is alternative measure of the acid strength (acids with pKa>2 are labeled
as week acids) - terms in the brackets represent the equilibrium concentrations.
The measurement of the pH of a solution is the key to the determination of the strengths of
acids and bases. The neutralization plot of week acid shows the dependence pH of the
solution on the percentage of the neutralized acid. The pKa can be estimated from the plot at
p=50% (halfway of neutralization), which corresponds to equal concentrations [HA]=[A-] and
so at this point it holds pH=pKa.
Consider the neutralization reaction of week acid HA by a strong hydroxide MeOH (e.g.
KOH, NaOH, LiOH ...). The letter is a strong electrolyte, completely dissociated into the Me+
and OH- ions in diluted aqueous solutions. The OH- anions are regarded as a strong base and
they react with the acid HA:
HA + OH- ßà H2O + ATherefore we can write the following mass balance equations for each step of the
titration from 10% to 90% of neutralization between the initial point and the end
point:
[HA] = c(HA) - c(MeOH)
[A-] = c(MeOH)
(5)
(6)
where c(x) denotes the analytical concentration of the component x (acid and the
hydroxide).
Figure 2. Neutralization plot of week acid
Experimental
Determination of the dissociation constant of acetic acid and statistical comparison of the
experimental and table values. The procedure is based on the pH measurement of the set of
prepared acetic acid solutions partially neutralized with NaOH at constant ionic strength.
Equipment and chemicals
Precision pH-meter, combination glass electrode (or glass and calomel reference electrodes),
standard buffer solutions, 10 ml and 20 ml pipette, 9 graduated flasks (50 ml), 2 beakers,
commercially purchased solutions of CH3COOH (0.1M), NaOH (0.1M), NaCl (0.2M)
Preparation of solutions
Pipette 20 ml of 0.1 M CH3COOH to the clean and labeled 50 ml flasks. Add solution of 0.1
M NaOH in following amounts:
2ml (No.1), 4 ml (No.2), 18 ml (No.9) and 0.2 M solution of NaCl 12 ml (No.1), 11.5 ml
(No.2), 8 ml (No.9). Complete the samples with water to the total volume of 50 ml. Stir the
flasks to homogenize the solutions.
Table 1. Pipetting scheme of the sample solutions
Sample
Solution
CH3COOH
NaOH
NaCl
H 2O
Total volume
1
2
20
2
12
16
20
4
11.5
14.5
3
4
5
6
7
Pipetted volume of solutions in mL
20
20
20
20
20
6
8
10
12
14
11
10.5
10
9.5
9
13
11.5
10
8.5
7
50 mL
8
9
20
16
8.5
5.5
20
18
8
4
Potentiometric determination of pH
Connect the electrode(s) to the precision pH-meter (combination electrode should be
connected to the G-terminal; in case of using the glass electrode-calomel electrode system
connect the glass electrode to the G-terminal and the other one to the R-terminal. Calibrate
the electrode using the standard solution if is it necessary. Carefully clean and dry the
electrode(s). Dip it into the measured sample. Wait 2-3 minutes and record the displayed pH.
Repeat the outlined procedure for each sample (1-9).
Processing of the measured data
Calculate the analytical concentration of acetic acid (it should be equal in each sample) and
the analytical concentration of NaOH in the samples using equation:
c(x) =
𝒗 𝒙 𝒄 𝒙 𝒑𝒓𝒆𝒄
𝑽𝒕𝒐𝒕𝒂𝒍
(7)
where cprec(x) is the precise concentration of the stock solutions of CH3COOH or NaOH given
as a following product: cnominal.factor), v(x) is the pipetted volume and Vtotal is the total volume
of the sample (50 ml).
Determine the equilibrium concentrations of the acid and the base ([CH3COOH], [CH3COO-])
using the following equations:
[CH3COOH]= c(CH3COOH) - c(NaOH)
(8)
[CH3COO-] = c(NaOH)
(9)
c(CH3COOH) > c(NaOH)
(10)
The final equation of acetic acid's pKa is given:
pKa = pH + log
𝑪𝑯𝟑𝑪𝑶𝑶𝑯
(11)
𝑪𝑯𝟑𝑪𝑶𝑶!
Calculate the pKa for each sample and from the Kas determine the mean <Ka>. Using the
mean <Ka> recalculate the mean <pKa> as following:
<Ka> =
𝑵
!𝒑𝑲𝒂 𝒊
𝒊 𝟏𝟎
(12)
𝑵
(!)
If N is the number of the samples and 𝐾! defines the i-th dissociation constant then finally
we get:
<pK> = -log <K>
(13)
Read the table value of the acetic acid's pKa (for the nearest temperature) and calculate the
relative error of your measurement.
(14)
Plot the neutralization diagram (pH versus percentual amount of the neutralized acid - p).
Read the pH function value for p=50%. (Transform the added volume (x axis) to p%).
𝒄 𝑵𝒂𝑶𝑯
p = 100% 𝒄 𝑪𝑯𝟑𝑪𝑶𝑶𝑯
(15)
The protocol should include the points:
Ø
Ø
Ø
Ø
Definition of the dissociation constant and related terms
Experimental procedure, calculations
Tables of the results, neutralization diagram
Statistics of the results
Table 2. Calculated and measured quantities
No.
1
c(NaOH)
mol/ml
c(CH3COOH)
mol/ml
log([HA]/[A-])
p%
pH
pKa
Ka
EXPERIMENT 3
Determination of the Adsorption Isotherm of Acetic Acid
on Activated Carbon
Theory
When a gas or vapor is brought into contact with a solid, part of it is taken up by the solid.
The molecules that disappear from the gas either enter the inside of the solid, or remain on the
outside attached to the surface. The former phenomenon is termed absorption (or dissolution)
and the latter adsorption. When the phenomena occur simultaneously, the process is termed
sorption. Molecules can attach to surfaces in two ways.
Physisorption is based on the Van der Waals interactions between the adsorbate and the
substrate and also between the adsorbed molecules. It is completely nonspecific, i.e. almost
all gases can be physisorbed under the correct conditions to almost all surfaces. The
geometrical structure and electronic characteristics of the adsorbed molecule or atom and also
of the surface are essentially preserved. At the most a slight deformation takes place. A
physisorbed molecule can spontaneously leave the surface after a certain time. The energy
necessary in order to desorb a physisorbed molecule has the same order of magnitude as the
condensation enthalpy (typically ~20 kJ mol-1). Physisorption is therefore observed mostly at
low temperatures. At room temperature, retention times are around 10-8s, at 100 K on the
order of seconds. Physisorption can occur as a preliminary state to chemisorption.
Chemisorption occurs when there is the formation of a chemical (often covalent) linkage
between adsorbate and substrate. In this case, the enthalpy is around an order of magnitude
higher (~200 kJ mol-1) than with physisorption. Often with chemisorption a dissociation of the
adsorbate is observed at the same time. This effect is very important in catalysis, where
chemisorption can represent a low-activation-energy dissociation route. Chemisorption is
almost always exothermic. It is a spontaneous process and therefore requires a negative
change in the free enthalpy ΔG. Since the adsorbate, when adsorbed, loses freedom of
movement, the entropy change ΔS is likewise negative.
Since ΔG = ΔH- TΔS, ΔH is also usually negative, meaning that the process is exothermic.
An exception of this rule is H2-Adsorption on glass. Hydrogen dissociates when adsorbing
and hydrogen atoms have a very high mobility on the glass surface. With this process, ΔS is
strongly positive. Thus, a negative ΔG can be achieved (spontaneous process) despite the
positive ΔH (endothermic reaction). Often one finds chemisorption as a successor step to
physisorption. As the following diagram (Figure 3) shows, this transition can be activated.
Chemisorption can also take place slowly due to this activation barrier.
Figure 3. The profiles of the potential energy for the dissociative chemisorption of an A-A-molecule.
Δp, AdH is the enthalpy of the non-dissociative physisorption, Δc, AdH the enthalpy of the chemisorption
(with T=0). According to the position of the intersection of the two curves, chemisorption can occur
without activation (left) or with activation (right).
Experimental
Determinate the course of adsorption isotherm of acetic acid using activated carbon.
Activated was found to “decolorize” solutions by a surface adsorption mechanism.
Equipment and chemicals
Six 250 ml round-bottom flasks, six 250 ml Erlenmayers's flasks, six funnels, stand for
funnels, two 50 ml burettes, stand for burettes, titrimetric flask, pipettes (50, 25, 10, 5 ml),
filtering paper, glazed paper for weighting, spoon, rubber stoppers, activated carbon, solution
of acetic acid (0.4 mol/l), solution of NaOH (0.1 mol/l) and phenolphthalein.
Preparation of solutions
Prepare aqueous solutions of acetic acid into numbered flasks according to the following
table:
Table 3. Pipetting table for acetic acid dilutions
Solution / ml
0.4M CH3COOH
Distilled water
Total volume
1
2
105
0
105
55
55
110
0.400
0.200
3
Flask number
4
5
30
15
10
90
105
150
120
120
160
Approximate concentration (mol/l)
0.100
0.050
0.025
6
5
155
160
0.012
Titrate the prepared solutions using aqueous solution of NaOH 0.1M and phenolphthalein to
determine their real concentration. Take off the following amounts of solution (V) from each
flask for titration:
Table 4. Amounts of solution taken for titration
Flask number
V in ml
1
5
2
10
3
20
4
20
5
50
6
50
Calculate the real concentration of above solutions of acetic acid inserting volume (V) from
the table 4 Pipetting scheme for acetic acid dilutions and consumption of NaOH at titrations
(n) into equation 1:
Cacetic acid = 𝒏
𝑪𝑵𝒂𝑶𝑯
𝑽
(1)
where cNaOH is real concentration of aqueous solution of NaOH. Take 10 ml from the fifth and
sixth flask to obtain the same amount of solution in all six flasks (100 ml).
Thereafter, weight 2g of activated carbon six times, using glazed paper and then add it
portion-wise into each solution of the acetic acid in the flasks. Secure the flasks with the
rubber stoppers and shake approximately for 10 minutes. Then, filter these solutions into
clean and dry flasks. The first drops (approximately 10 ml) of the filtered liquor must be
removed in order to avoid the disturbing effect of the adsorption of acetic acid on the filtering
paper. After ending the filtration, mix the flask volume and titrate again with 5, 10, 20, 20, 50,
50 ml of the filtered liquor as before the adsorption. Calculate the amount of adsorbed acetic
acid from the change of its concentration before and after the activated carbon addition and
table the results.
Processing of the measured data
Calculate the initial concentration of the acetic acid (C0) and the equilibrium concentration
(C) after the adsorption using the equation (1), and the adsorbed amount of acetic acid per 1 g
of activated carbon according to the equation below:
m=
𝑽𝒓 𝑪𝟎 – 𝑪
𝒃
(2)
where Vr is the volume of the aqueous solution of acetic acid (100 ml) and b means the mass
of the activated carbon (2 g).
The plot of 1/m against 1/C should be a straight line of slope 1/Amax and intercept 1/(k.Amax),
where k is the adsorption coefficient and Amax is the adsorbed amount of acetic acid
corresponding to the complete surface coverage. Evaluate Amax and k from the straight line
above, using the least-squares method.
The report must include the points:
Ø
Ø
Ø
Ø
Theoretical principles of the determination
Equipment and chemicals
Working procedure and measurements
Tables of results, calculations and diagrams
EXPERIMENT 4
Partial Molar Properties of Solutions
Theory
Any extensive property X of a solution can be represented by partial molar properties XA, XB
of the constituent substances A and B, respectively. These molar properties are functions of
the temperature, pressure and concentration of that solution. Here we will take A as being the
solvent while B is the solute. Concerning the volume of a solution, the total volume, V, is
given through the partial molar volume by equation (1).
V = nAVA + nBVB (T, p constant)
(1)
where nA and nB are mole fractions.
The partial molar volume can be calculated by measuring the density of the solution.
Apparent molar volume, øVB is defined by equation (2)
ø
VB = (V - nAVA*)/ nB (T, p constant)
(2)
where VA* is the molar volume for pure A.
From equation (2),
V = nB øVB + nAVA* (T, p constant)
(3)
𝐕𝐁 = (𝛛𝐕/𝛛𝐧𝐁 )nA , T, p = ø𝐕B + nB(𝛛ø𝐕B/𝛛𝐧𝐁 ) nA , T, p
(4)
VA = (V - nBVB)/nA = [nAVA*- nB2(𝛛ø𝐕B/𝛛𝐧𝐁 ) nA , T, p]/nA
(5)
and therefore
and,
From the density ρ measured from the experiment and the molar mass of both components
ø
MA, MB, VB is given as:
ø
VB = [nAMA + nBMB)/ρ – nAVA*]/nB
(6)
The molality of the solute is defined by:
mB = nB/(nAMA)
(7)
Substituting nB into equation (6),
ø
VB = (ρA- ρ)/(mBρΑρ) + ΜΒ/ρ
(8)
where ρA is the density of the pure solvent.
Equation (8) is used to calculate the values of the apparent molar volume from the density
measurements.
Therefore partial molar volumes can be obtained by using equations (4) and (5). You should
ø
ø
plot VB versus nB, but sometimes it is more useful if you plot VB versus mB½.
(𝛛ø𝐕B/ 𝛛𝒏B)nA , T, p = (𝛛ø𝐕B/ 𝛛𝐦B½)nA , T, p (𝛛𝐦B½/ 𝛛𝒏B) nA , T, p
(9)
By using equation (7), equation (9) becomes,
(𝛛ø𝐕B/ 𝛛𝒏B)nA , T, p = (𝛛ø𝐕B/ 𝛛𝐦B½)nA , T, p/ (2 𝐦B½nAMA)
(10)
Therefore
VB = ø𝐕B + ½𝐦B½(𝛛ø𝐕B/ 𝛛𝐦B½)nA , T, p
(11)
And
VA = VA* - ½𝐦B3/2𝐌A½( 𝛛ø𝐕B/ 𝛛𝐦B½)nA , T, p
(12)
Experimental
Prepare accurately five aqueous solutions containing about 2, 4, 8, 12 and 16% (w/w) sodium
chloride. For this experiment the total volume required for each solution is 75 ml. First
determine the volume of the pycnometer by using pure water. Ask the demonstrator about
how to use the pycnometer. Fill the pycnometer with the prepared solutions and determine
their weight. From these measurements determine the respective densities. For each solution
carry out the density determination three times.
Results and Calculation
All weightings must be corrected for air buoyancy (ask the demonstrator). Calculate the
molality of each solution and determine the apparent molar volume øVB for each molality. Plot
ø
VB against mB½ and use equations (11) and (12) in order to obtain the values of the partial
molar volumes.
Important Note
i) Prepare all solutions by accurately weighing the amount of salt and water used
ii) To make corrections for air buoyancy on all the weights, use the formula below:
Wv = Wa + Wa du (1/dm – 1/dw)
Wv = true weight (in vacuum)
Wa = value read from the balance
du = density of air (assumed to be 0.0012 g cm3)
dw = 8.0 g cm3 (steel density)
dm = density of the weighted object
EXPERIMENT 5
Kinetics of Dissolution of Solid Substances
Theory
Dissolution of a solid substance is one of the heterogeneous processes occurring on the
boundary between two phases, which is called the phase interface. Obviously one of the
phases is solid, so it is the reaction on the solid surface and it can be divided into following
steps:
Ø
Ø
Ø
Ø
Ø
diffusion of interacting substances to the surface
adsorption on the surface
reaction on the surface
desorption from the surface
diffusion of products from the surface.
The total reaction rate of heterogeneous processes is controlled by the rate of the slowest step
and in the case of solid/liquid systems the rate determining stage are subprocesses involving
diffusion.
The pharmaceutical importance of dissolution of solid substances can be demonstrated on
biological accessibility of weekly soluble (or retarded) active compounds in solid peroral
formulations. In biological systems, water represents the most frequent liquid environment solvent. In the process of dissolution of crystalline solid compounds into aqueous solution, the
above steps are supplemented with hydration of the surface, and the products of dissolution.
Dissolution of the solid substance is controlled by the slowest reaction stage, which is the
diffusion of dissolved and hydrated compound from the solid surface. The diffusion transports
the dissolved substance across a thin diffusion layer δ, where the concentration of dissolved
substance continuously decreases from the concentration of saturated solution (cs) at the solid
surface to the concentration level (c) in the bulk solution. The driving force of diffusion is the
spatial concentration gradient according to First Fick's Law:
dn
dt
𝒅𝒄
= - DS 𝒅𝒙
(1)
where: dn [mol] is the amount of the dissolved substance within time interval dt [s]
D [m.s-1] is the diffusion coefficient
S [m2] represents the total surface (phase interface) of the dissolved solid substance
dc/dx is the mentioned concentration gradient
When the mixing is efficient, the diffusion layer is very thin (0.02-0.05 nm) and the
concentration gradient may be replaced by a single linear approximation
𝒅𝒄
𝒅𝒙
=
𝒄 – 𝒄s
𝜹
For the amount of dissolved substance we can then write dn = Vdc
(2)
where V is the total volume of the solution
dc is the concentration increment
The final shape of the Nernst equation is:
𝒅𝒄
-𝒅𝒙 =
or
!"
!"
𝒄s!𝒄
𝜹
(3)
= k(cs – c), where k represents the rate constant of dissolution.
After separation of variables and integration we obtain the following equation:
c = cs(1 - 𝒆!𝒌𝒕 )
(4)
which is formally equivalent to the equation for the first order reaction kinetics.
Some remarks on chemical kinetics
Chemical kinetics can be defined as a quantitative study on concentration (or pressure)
changes with time brought about by chemical reaction. In other words, the chemical kinetics
investigates velocities of various chemical reactions. Reaction rate is the decrease of the
concentration per unit time of one of the reactants. The rate constant is a measure of the rate
of a given chemical reaction under specified conditions (pressure, temperature). It may be
defined in words as the rate of change in concentration of reactant or product with time for a
reaction in which all the reactants are at unit concentration. The order of reaction is usually a
small integer, but in special cases it may have a fractional value or be zero. It is formally
defined as the sum of the powers of the concentration terms that occur in the differential form
of the rate law. If the chemical reaction proceeds in a series of sequential stages, then the rate
of the reaction is limited by the slowest stage. This stage is referred to as the rate determining
(controlling) stage. Molecularity is the number of molecules or ions from which the transition
state is formed. The time taken for 50% reaction to occur is called the half-life.
Method
Kinetic measurements are usually performed for determination of reaction rate (or rate
constant) or reaction order at a given conditions. Dissolution process of ionic substances can
be observed by measuring the conductivity changes with time:
G(t) = Gs(1 - 𝒆!𝒌𝒕 )
(5)
assuming the surface changes of the dissolved substance are negligible. In the case of less
stable organic compounds, precise determination of the conductivity of saturated solution is
impossible because of side reactions (e.g. acetylsalicylic acid hydrolyzes to acetic and
salicylic acid). Thus, the saturated conductivity GS is handled as unknown quantity and must
be determined, too.
The Guggenheim's method of evaluation of the rate constant will be used, because the final
concentration is unknown. The essence of the method may be characterized as follows: there
are some measurement series done within the experiment, where the time between the series
remains constant. The concentration data are recorded at time "t" and t + t´ (t´ is the
appropriate time shift). Using the Guggenheim's method the mentioned kinetic equation for
the conductivity dependence may be rewritten as:
ln[G(t + t´) – G(t)] = A – kt
(6)
A=ln[Gs(1-𝒆!𝒌𝒕 )]
'
where
(7)
The series are not to be taken from the start and the end of the measured process, because the
experimental errors are bigger at these points.
Device and materials
Apparatus for experiment includes (see Figure 4):
1.
2.
3.
4.
5.
6.
7.
8.
9.
beaker 400 ml
perforated test tube
acetylsalicylic acid tablets 4 pcs
commercial conductometer with
electrode
stirring element
electromagnetic stirrer
laboratory holder
stop-watch
rinsing bottle
Figure 4. Apparatus for measurement of tablet
dissolution
Experimental
Place the beaker with 200 ml of redistilled water on the electromagnetic stirrer. Using the
laboratory stand fix the perforated test tube and the conductivity cell as it is shown on the
Figure 4. Set the mixing rate on 800 rpm, which is constant for the time of the experiment
(note that no heating is needed). Determine the conductivity of the pure redistilled water (it
must be less than 2µS). Now carefully put the tablet into the test tube and start the stop-watch.
Write down the conductivity data every minute and from the 5-th minute every 5 minutes.
Repeat the described conductivity determinations for 85 minutes. All measured values of
conductance (Gt) write down to the Table 1. After finishing the measurements switch off the
stirring and conductometer and rinse the conductivity cell with distilled water.
Table 5. Measured and calculated values
t
G(t)
t + t´
G(t + t´)
[min]
[µS]
[min]
[µS]
1
2
3
4
5
34.2
45
152
10
50
15
35
40
90
Note: the values in t = 5 is an example
G(t + t´) – G(t)
[µS]
ln[G(t + t´) – G(t)]
117.8
4.769
Processing of the measured data
1. Plot the function Gt = f(t) to characterize the overall development of the dissolution in
time.
2. Select two series from the measured conductivity data, which differ in reaction time by a
constant time shift (t ´ = 40 min). Calculate the appropriate quantity: G(t + t´) – G(t) and
ln[G(t + t´) – G(t)] (See Table 5).
3. The first data set is given by conductivities at reaction time: t = 5, 10, 15, 20, 25, 30, 35
min. The second data set is defined likewise: t + t´ = 45, 50, 55, 60, 65, 70, 75 min.
4. Using Origin Lab plot the dependence ln[G(t + t´) – G(t)] = f (t). Fit the experimental
points with a linear function and write down its equation. Compare the equation of
straight line with the Equation (6), and determine the dissolution rate constant.
The report must include the points:
Ø
Ø
Ø
Ø
Ø
Theory (dissolution, Fick’s law, Guggenheim’s method, etc.)
Equipment and chemicals
Working procedure and measurements
Tables of results, calculations and graphs – Gt = f(t), ln[G(t + t´) – G(t)] = f(t)
Conclusions with the dissolution rate constant of acetylsalicylic acid tablets.
EXPERIMENT 6
Determination of Molar Mass From Freezing Point Depression
Theory
Homogeneous mixtures, or solutions, have properties that are dependent on the concentration
of the solute; such properties are known as colligative properties. Freezing point depression,
ΔTf, is an example of a colligative property. In order to understand this concept, consider the
following. Even though sucrose and ethylene glycol are two completely different compounds
with different physical properties, a solution of 1.5 molal sucrose has the same freezing point
depression as a solution of 1.5 molal ethylene glycol because ΔTf is a concentration
dependent property.
Freezing point depression can be defined as the difference between the freezing point (Tf) of
the solution and the Tf of the pure solvent.
ΔTf = |Tf solution – Tf solvent|
(1)
When a non-volatile solute is dissolved in a solvent, the vapor pressure of the solvent is
lowered; this results in depression of the solvent freezing point. Thus, the freezing point of the
solution is always lower than the freezing point of the pure solvent. The amount by which the
solvent freezing point is lowered depends on the concentration of the solute, as shown below.
ΔTf = Kf m
(2)
where
m = molal concentration
Kf = freezing point depression constant
The freezing point depression constant is a value associated with the solvent; it is a numerical
constant that can be found in a reference text. Note that the greater the molal concentration of
the solute, the greater the freezing point depression will be. It follows that a solution that is
5.0 molal sucrose will have a lower freezing point than a solution that is 1.0 molal sucrose.
Determination of Molar Mass using ΔTf
Colligative properties can be used to determine the molar mass of a compound. Freezing point
depression is particularly useful for molar mass determination because the freezing point of a
solution is comparatively easy to find experimentally. The experiment involves measuring the
freezing point of the pure solvent and the freezing point of a solution of the compound in the
solvent. The freezing point depression is the difference between the two temperatures. The
molar mass is found through a series of calculations. Consider a general example in which
5.00 grams of compound X are mixed with 25.00 grams of solvent, and the freezing
temperatures of the pure solvent and the solution are measured. The calculations for finding
molar mass are as the following steps:
Step one: find the freezing point depression.
ΔTf = |Tfsolution – Tfsolvent|
Step two: use freezing point depression to determine the molal concentration of the
solution
m=
ΔTf
Kf
Step three: find the moles of compound X using solution molality and mass of solvent.
mol X = (molal concentration of solution) x (kg of solvent)
Step four: calculate the molar mass of X from calculated moles and measured mass.
Molar mass =
grams X
mol X
Experimental
The objective of this experiment is to determine the molar mass of an unknown alcohol Z.
Preparation of Ice-Salt Bath
Into a large beaker (1000 ml) place a stir bar, about 10 ml of water, and approximately 100 ml
of crushed ice combined with 30 g of rock salt. Place an alcohol thermometer mounted with a
clamp attached to a ring stand in the cup. Mix the contents and monitor the temperature of the
ice salt mixture. Within a few minutes the temperature of the mixture should approach -7 ºC
to -10 ºC (See Figure 5).
Add an additional 100 ml of crushed ice or enough to fill the beaker to an inch of the rim and
additional small amounts of rock salt with mixing to achieve a temperature that remains stable
near -10 ºC ± ca. 1 ºC. Depending on the size beaker, the ratio of ice and salt can be adjusted
to maintain the -10 ºC target temperature. Begin stirring the bar at a moderate speed to agitate
solid rock salt settling to the bottom.
Figure 5. Apparatus for freezing point determination
NOTE 1: During the experiment a large amount of ice may melt. When this happens, the salt
mixture may become difficult to keep cold due to the amount of liquid. Use a bottle adapted
with rubber tubing to siphon off melted ice and mix in fresh ice with a spatula. There should
still be enough solid ice at the bottom of the bath to restore the -10 ºC temperature.
Measuring the Freezing Point of Pure Water (two trials)
Into a clean dry large test tube add 25 mL of distilled water dispensed from either a pipet or
burette. Set the test tube into the ice-salt bath so that the test tube is about ½ inch above the
stir bar. Place a clean wire mixing loop and a clean digital thermometer in the test tube.
Immediately, while the 25 mL sample of water is still near room temperature begin taking an
initial temperature and time measurements at time zero (t0) and repeat this each 30 seconds
until about 5 consecutive steady readings are reached at or around 0ºC when ice crystals begin
forming within the test tube. It will take about 5 consecutive constant temperature readings at
or near 0 ºC for the water in the test tube to solidify completely. The run is complete at this
point and you should prepare for a duplicate trial by cleaning and drying the test tube, then
adding a new 25 mL aliquot of distilled water and repeating the steps.
NOTE 2: It is possible for the test tube temperature to reach a few steady readings at or near
0 ºC and then progressively decline to the temperature of the ice-salt bath itself. This is
unusable data because it merely represents the additional cooling of solidified water in the test
tube below its freezing point.
NOTE 3: When time and temperature readings begin do not remove the wire mixer or the
thermometer, because dripping can change the sample size. It is especially important that you
not use the same thermometer for the test tube and water-salt bath, since this would introduce
salt into the test tube and alter the results.
Measuring the Freezing Point of the Water/Alcohol Z solution (two trials)
Measure 25 mL of water and 5 mL of alcohol Z into a large test tube, and stir the sample.
Place a temperature probe with a clean digital readout into the solution. Record the solution
temperature. Place the test tube into the ice – rock salt bath and record the temperature every
30 seconds. Use the temperature probe to stir the sample. Continue to record the temperature
until one of the following conditions is met: 1) there are five consecutive temperature
readings that are the same; 2) the sample freezes; or 3) the temperature reaches -10 oC. Repeat
the procedure for a second trial.
Processing of the measured data
1.
Pure water
Prepare a graph of temperature versus time for each trial. The graphs should clearly indicate
the freezing temperature of the water. Each graph should look similar to the following
example:
2.
Alcohol solution
Prepare a graph of temperature versus time for each trial. Each graph should look similar to
the following example:
This graph clearly indicates the freezing temperature of the solution. However, in the case of
the solution, it is possible to obtain results that deviate from the expected graph shown above.
Occasionally, the digital thermometer reads the temperature of the bath rather than the
sample, and the temperature readings decrease to -10 oC, as shown below.
In this case, lines can be drawn from the graph as indicated below. The y value that
corresponds to the intersection of these lines is taken as the freezing point of the solution.
It is also possible to observe supercooling; a condition where the temperature dips below the
freezing point of the sample while the sample remains in liquid form. This occurs when the
sample is cooled too quickly for crystals to form the ordered structure of the crystal lattice.
Consider the following graph:
In this case, the freezing point is taken to be the temperature after stabilization.
Calculations
Take the average freezing point from the two water trials and the average freezing point from
the two solution trials to find ΔTf. {Recall, Z is the unknown alcohol.}
ΔTf = |Tfsolution – Tfwater|
Determine molar mass via the following calculations:
mass Z = (Z ml) x (0.785 g/ml)
𝜟𝑻f
molalitysolution = 𝟏.𝟖𝟓𝟖 o𝑪/𝒎
mol Z = (molalitysolution) x (kg water)
Molar mass =
𝐦𝐚𝐬𝐬 𝐙
𝐦𝐨𝐥 𝐙
Table models
1.
Freezing point pure DI water
Time
Temperature
Freezing point pure DI water
Time
Temperature
2.
Freezing point pure DI water + unknown
Time
Freezing point pure DI water + unknown
Temperature
Time
Temperature
1. Average Freezing point (pure water):________
2. Average Freezing point (solution):___________
3. Freezing point depression:
4. Molal concentration of the solution.
5. Mass of the unknown. (Note the density of the unknown is 0.785 g/ml)
6. Moles of unknown
7. Molar mass of the unknown.
EXPERIMENT 7
Enthalpy of Mixing of Acetone and Water
Theory
The molar enthalpy of mixing, ΔHmxg/(nA + nB) of two liquids A and B to form a liquid
mixture, can be defined as the enthalpy change accompanying the formation of 1mole of the
liquid mixture from the requisite amounts of the two pure liquid components at the same
temperature and pressure as the mixture.
In this experiment the molar enthalpies of mixing of various mixtures of acetone and water
will be determined.
Experimental Procedure
The procedure may be divided into two parts:
a) Determination of the heat of mixing, for each mixture
b) Determination of the heat capacity of the calorimeter plus the mixture, for each
mixture
Before proceeding further, ensure that the thermometer supplied (HANDLE WITH CARE!)
is set to read about 2.0 when placed in water at room temperature. If not, readjust (consult
demonstrator).
Now support the large boiling tube (the calorimeter vessel) on the magnetic stirrer. Place a
magnetic stirrer bar in the tube, add 200.00 ml acetone, and then assemble the stopper with
the thermometer and a small test tube passing through the two holes. Ensure that the
thermometer bulb is covered by the mixture. Place 4.20 ml water in the test tube and ensure
that the portion of the test tube containing the water is below the level of the acetone. Switch
on the magnetic stirrer, and set the stirring rate to about 300 r.p.m.
a) Determination of the enthalpy change on mixing
Read and record the temperature (the thermometer can be read to three decimal places) at the
end of each minute for 5 minutes. At the end of this period, smash the bottom of the test tube
by means of a sharp tap with the iron rod supplied. Ensure that thorough mixing takes place
by raising and lowering the broken test tube a few times. The temperature will either rise or
fall, depending upon whether the mixing process is exothermic or endothermic, respectively.
Continue reading and recording the temperature at the end of each minute for a further
5 minutes. On graph paper, plot the temperature as ordinate against the time in minutes as
abscissa. Join the plotted points. The figure 6 obtained may look more or less as follows - for
an exothermic mixing process:
Figure 6. The typical diagram of temperature (oC) vs. time (sec)
The rise in temperature ΔTm corresponding to mixture formation may be estimated by
extrapolating the lead and trail periods and drawing a vertical line through a point mid-way
up. Note that the mixing process takes place relatively rapidly after the test tube is broken.
b) Determination of the heat capacity of the calorimeter plus the mixture
This determination is carried out immediately after the measurements described in part (a) are
carried out - and makes use of the reaction mixture prepared in part (a). The calorimeter is left
as it was at the end of part (a), i.e. the broken test tube and glass fragments, etc., remain as
part of the calorimeter.
Read and record the temperature at the end of each minute for 5 minutes. At the end of this
period switch on the power to the heating element in the tube, so that a potential difference of
exactly 2.50 V and a current of approximately 2 ambers (A) are applied. Measure the current
by means of the digital multimeter provided. Simultaneously, switch on the stopclock/stopwatch provided. Read and record the potential difference and current on the meters
as accurately as possible. Continue reading and recording the temperature of the calorimeter
at the end of each minute. When the temperature has risen by approximately 1 oC, switch off
the heater, and also the stopclock/stopwatch. Note the period time over which the heater was
activated. Continue reading and recording the temperature as before for a further period of 5
minutes. On the graph paper, plot the temperature as ordinate against the time in minutes as
abscissa. Join the plotted points. The figure 7 obtained may look more or less as follows:
Figure 7.
Note that, in contrast to the situation encountered in the heat of mixing experiment described
in part (a), the electrical heating extends over an appreciable time interval. The rise in
temperature ΔTh resulting from the electrical heating may be estimated by extrapolation as
described in part (a) and shown in the figure above.
More sophisticated and accurate methods exist for correcting calorimetric data for heat
exchange with the surroundings. However, the extrapolation method described above is
sufficiently accurate for the purposes of this experiment.
Repeat the above procedures for the following mixtures:
i) Starting with the 200 ml acetone - 4.2 ml water mixture, add successively 7.9, 7 ml and
15.8 ml of water
ii) Starting with 200 ml water add successively 15 ml volumes of acetone until a total of 45
ml is reached.
Note that, particularly after a heat of mixing determination in which the mixture formation is
markedly exothermic, it may be necessary to cool the calorimeter vessel before the heat
capacity is determined. This may be done by wrapping tissue paper around the vessel and
moistening the paper with acetone. Evaporation of the acetone will result in the required
cooling effect.
Processing of the measured data
Calculations
a) Calculations of heat capacity
If the potential difference applied to the heater is denoted "V", the current "I", and the time
for which the heater was activated is denoted "t", then the heat capacity "Cp" of the
calorimeter plus contents is given by equation (1):
Vit
Cp = Δ
Th
(1)
b) Calculations of enthalpies of mixing
The enthalpy of mixing "ΔHi" for any particular mixing experiment is given by equation (2):
ΔHi = -CpΔTm
(The negative sign is introduced for reasons of sign convention.)
(2)
c) Calculations of molar enthalpies of mixing
The mixtures produced in this experiment are not all produced by mixing the pure
components together. Some of the mixtures are prepared by adding more of one of the pure
components to an existing mixture from a previous determination. It is therefore necessary to
accumulate enthalpies of mixing ΔHi as calculated in part (b) above in order to calculate the
cumulative enthalpy of mixing ΔHmxg corresponding to formation of any particular mixture
from the respective pure components.
Thus,
ΔHmxg =
i ΔHi
(3)
If the amounts (mol) of acetone and water in any particular mixture are denoted nac and nH O
respectively, then the molar enthalpy of mixing ∆Hmxg/nTOT is given by equation (4):
2
∆Hmxg
nTOT
=n
ΔHmxg
ac+nH2O
(4)
Finally, plot a graph of molar heat of mixing against mole fraction of water. Compare with
the figure given in Atkins and comment on the results.
EXPERIMENT 8
Dissociation Constant of an Indicator by Spectrophotometry
Theory
An indicator is a weak acid or base whose conjugate forms have different colors. In this
experiment, the indicator, also used as a biological stain, is Neutral Red (3-amino-7dimethylamino-2-methylphenazine hydrochloride) (NR), which has the structure (protonated
form) and acid dissociation equilibrium shown below in figure 8.
Figure 8. The structure and acid dissociation of Neutral Red
(3-amino-7-dimethylamino-2-methylphenazine hydrochloride)
HNR+ + H2O = H3O+ + NR
The thermodynamic acid dissociation constant for HNR+ is given in terms of activities:
aH3O+ aNR
Ka = a
HNR+ a H2O
(1)
which reduces to:
Ka =
aH3O+ aNR
aHNR+
(2)
because the pure solvent is taken to be standard state (a = 1). The activity is a concept of
"effective concentration" which is evoked to correct for non-ideal solution behavior which is
expected in aqueous electrolytes. This non-ideality may be represented by an activity
coefficient, g, which is the ratio of the activity over the physical concentration.
ai = γi ci
(3)
where ci is the molar concentration of species i. The equation for Ka is, therefore,
γH3O+ γNR
Ka = γ
HNR+ γH2O
x
𝑯𝟑𝑶+ [𝑵𝑹]
[𝑯𝑵𝑹+]
(4)
The activity coefficient of a neutral molecule in a dilute solution may be taken as unity. The
activity coefficient of an ion is determined by the total ionic atmosphere of the solution,
called the ionic strength, µ.
µ=½
𝒊 cizi
2
(5)
where ci is the concentration of ion i, zi is its charge, and the sum is taken over all ions in
solution. Several equations can be used for calculation of activity coefficients, but a very
common one is the extended Debye-Huckel equation:
-­‐ Az2 µμ
log γ = 1+Βα
µμ
(6)
where z is the charge of the ion of interest, and a is the radius of the solvated ion (ion plus its
tightly bound sheath of water molecules; a = ca. 900 pm for H3O+; a = ca. 700 pm for a large
cation like HNR+. A and B are factors which depend on the density (A only) and dielectric
constant of the solvent and the temperature. Values of at 25 oC for various ionic strengths and
a's are conveniently obtained from the literature.
If the ionic strength is held constant for all measurements involving Kaµ, a "concentration"
dissociation constant, valid only at that ionic strength, may be used:
K΄a =
𝑯𝟑𝑶+ [𝑵𝑹]
[𝑯𝑵𝑹+]
(7)
In this experiment, the Kaµ=0.10 will be measured at a total ionic strength of 0.10M, maintained
by adding an inert salt, NaCl, to all solutions.
The [H3O+] will be controlled by a buffer of NH3OH+/NH2OH created by incremental
addition of standard 0.10M NaOH to a known number of moles of either NH3OH+ (Kaµ=0.10 for
NH3OH+ at 25oC and µ = 0.1M is 1.07 x 10-6). As described further below, the addition of
NaOH will increase the solution volume, necessitating a correction for dilution in the
calculation of all concentrations.
The [NR]/[HNR+] ratio will be determined spectrophotometrically. If a solution with
a total indicator concentration of cT is made very acidic, all of the indicator exists as
HNR+. The absorbance of the solution at a given wavelength of light, λ, is given by:
AHNR+ = εHNR+ b cT
(8)
where εHNR+ is the molar absorptivity of HNR+ at wavelength λ and b is the cell path
length. If, by making the solution very basic, the same concentration of indicator is
converted entirely to the NR form, the absorbance at the same wavelength is given by:
ANR = εNR b cT
(9)
where εNR is the molar absorptivity of NR. At an intermediate pH the absorbance is:
A = εHNR+ b cHNR+ + εNR b cNR
(10)
where the total concentration can be defined under any conditions as:
cHNR+ + cNR = cT
(11)
For a given cT, equations 8-11 can be combined to give:
[𝑵𝑹]
[𝑯𝑵𝑹+]
𝒄NR
=𝒄
HNR+
=
𝑨 ! 𝑨HNR+ 𝑨NR ! 𝑨
(12)
If possible, the ratio should be evaluated at multiple wavelengths, including one where HNR+
absorbs appreciably but NR does not, and one where NR is a much stronger absorber than
HNR+, and one where the two species absorb at approximately the same extinction (What is
this point called??). The pCH's (-log[H3O+]) of the solutions should be in the transition range
of the indicator, so that both HNR+ and NR exist in appreciable concentration. With a
spectrophotometer having a conventional sample holder (cuvette) a series of separate
solutions must be prepared. However, if the instrument is equipped with a fiberoptic probe,
the experimental procedure can be greatly simplified. A single solution containing the
indicator plus NH3OH+ is prepared and known increments of NaOH are added to convert the
respective acid to its conjugate base form. This addition changes the total volume and
decreases cT, but equation 12 can still be used if the absorbance values are corrected for the
dilution effect.
Referring to equation 7, Kaµ is numerically equal to [H3O+] when [NR]/[HNR+] is one. This
can be evaluated graphically by converting equation 7 to logarithmic form:
[𝑵𝑹]
log [𝑯NR+] = pcH – pK΄a
(13)
Thus, a plot of the logarithm of the [NR]/[HNR+] ratio versus pCH (-log [H3O+]) has an ideal
slope of unity. If this condition holds, the y-intercept gives the negative of pKa directly.
However, usually the experimental slope is not exactly 1.000. Extrapolation from the pCH's of
the measurements to pCH = zero (which is typically a factor of 106 in concentration for this
study) results in a very large error in pKaµ. On the other hand, data are obtained on both sides
of the x-intercept, which is determined with very little uncertainty. Therefore, better results
are obtained by solving the least-squares equation for the x-intercept (the value of the pCH
when [NR]/[HNR+] is one).
Experimental Procedure
Consult the demonstrator about the operation of the spectrophotometer.
You are provided with a stock solution of the indicator, methyl red (0.1 g per 250 ml).
Prepare, accurately, the following solutions:
a) 1 ml indicator made up to 50 ml with 0.01 mol/l HCl
b) 1 ml indicator made up to 50 ml with 0.01 mol/l NaOH
c) 1 ml indicator made up to 50 ml with pH 4.0 buffer
d) 1 ml indicator made up to 50 with pH 5.0 buffer.
Plot the absorption curves of these four solutions over the region 400 to 600 nm at 10 nm
intervals. The four curves should intersect at one point, the isobestic point. (Measure the pH
of all four solutions with the pH meter provided.)
Confirm the Beer-Lambert law by determining the absorbance of one of the solutions at a
fixed wavelength, at say four different concentrations (e.g. by diluting one of the above
solutions, listed in (a) − (d), successively 1:1 with 0.01 mol/l HCl, 0.01 mol/l NaOH or the
buffer solutions as appropriate).
Note:
i) Once a cell is filled with solution, it should be carefully wiped with tissue-paper to ensure
that the transparent sides of the cell are completely clean, i.e. free from any traces of liquid
or fingerprint marks. There should also be no air bubbles in the path of the light beam.
ii) At each change of wavelength, the instrument should be re-zeroed.
iii) The pH meter should be calibrated using the two standard buffer solutions provided.
Processing of the measured data
Calculation:
Absorption of light by a solution is governed by the Beer-Lambert law:
A = log
Io
I
= εcl
(14)
where ε is the molar absorptivity, c the concentration of the solution in mol/l, l the absorption
wavelength of the cell in cm, Io the intensity of the incident radiation and I the intensity of the
radiation after passing through the cell.
The absorbance, A, is given by
A = log (Io/I)
(15)
The dissociation of a weak acid of concentration c can be represented by
HA ßà H+ + AAssuming that the absorbance of the two forms of the indicator are additive we have
cεmix = cHAεHA + cA−εA−
(16)
also
c = cHA + cA−
From these two equations we get
(17)
cA-­‐
cHA
=
εHA -­‐ εmix
(18)
εmix -­‐ εA-­‐
also
cA-­‐
pH = pKa + log c
HA
(19)
i.e.
pH = pKa + log
𝜺HA ! 𝜺mix
𝜺mix ! 𝜺A-­‐
(20)
or
pH = pKa + log
𝑨HA ! 𝑨mix
Amix ! 𝑨A-­‐
(21)
Thus pKa can be calculated.
Hint: It can be assumed that at pH ∼2 all the indicator will be in the protonated form (HA),
and that at pH ∼12, all the indicator will be in the deprotonated form (A−).
Questions:
1. Why should all four spectra intersect at a single point, i.e. the isosbestic point? If they
do not all intersect at a common point, what would this indicate?
2. In the test of the Beer-Lambert law, would it have been correct to dilute the solutions
with water? If not, why not?
3. For calculating the pKa of the indicator, should use be made of absorbance data
obtained at wavelengths at, or close to, the isosbestic point? If not, why not?
REFERENCES
1. Atkins, Physical Chemistry, 2009, 9th Edition.
2. Physical Chemistry Laboratory Manual 2011, Department of Chemistry, Portland
State University.
3. Laboratory Manual for Physical Chemistry, 1996, 1st Edition, Faculty of Pharmacy,
Comenius University, Bratislava.
4. Laboratory Manual of Physical Chemistry, Year 2, Department of Chemistry,
University of Malaya.
5. Garland, Nibler and Shoemaker, Experiments in Physical Chemistry, McGraw-Hill,
2003, 7th Edition.