Paper #1: Chemistry Origins

The question of when modern chemistry and medicine started is a curious one.  There could be a wide variety of dates associated with this, including the first vaccine, Newton's theories on motion, and the start of alchemy.  During the Renaissance great advances were made.  This is where many of today's techniques in chemistry and many of our principles have come from.  Why did these advances come about though?

In late medieval times, alchemy was introduced to Europe by way of the Arabs.  At this time, they were under the belief that everything was made up of four elements, earth, fire, wind, and air.  A basic problem that alchemy tried to solve was the making of gold.  Alchemists regarded gold as the purest medal.  All other medals were made up of gold with different impurities.

They believed that all metals wanted to be gold, but something was stopping them, one or more of the elements.  Thus, the stereotypical view of alchemy is the transmutation of lead into gold.  Due to this stereotype, alchemy was banned in many parts of Europe in the fourteenth century.  That does not mean that it was not practiced.  In fact, many kings had alchemists working for them to find this cheep gold. [1]^,[2],[3],[4]

In their studies, the alchemists were actually melting, purifying, and studying metals and other substances in hope to find the philosophers stone, a substance that would transmute lead to gold.  Some of these experiments included using feces of various animals, urine of a pure (prepubescent) boy, eggs, and just about anything else that was available.  In the end though, nothing worked.  They did change their theories though.  The four elements, or essences, were changed to be quicksilver (mercury), sulfur, salt, and spirit.  The metals were therefor contaminated with one of these, keeping it from being gold.^1,[5]

This study was not completely useless though.  It led to the learning of how to assay metals and the production of some of the most common acids used today.  This assaying becomes very important.  For the first time, the actual amount of gold or silver in a coin could be determined.  Thus, the monetary systems were in some way standardized.   It was also important because the people mining the minerals could now determine what they had, and in what purity.  Even better was that they could do that on the site.  They now could make decisions on whether to continue mining that vein or go elsewhere.[6]^,[7]

One of the greatest advances of medicine and chemistry though came about by way of improved glass working.  One advance was the invention of glasses in 1288.  As one can find through experience, as the body grows older, the eyes start to deteriorate leading to the need for glasses.  This is important because it now allows the intellectual life to continue into the later years of ones life by allowing them to be able to read, and write.[8]

Another result from the improvement of glass involves what is now a standard part of any basic chemistry lab, distillation.  Distillation is when you boil a mixture of liquids, such as alcohol and water, condense the vapor on a surface and then collect that liquid.  Today when we do a simple distillation we cool the vapor in a tube of glass that is cooled by cold water.  Distillation works because the liquids have different boiling points and will vaporize at different times.[9]

Before the improved glass came about, the alchemists were using small, thick walled cones of glass above a furnace as condensers.  This did not allow much separation because the cooling of the vapor was not quickly accomplished, leading to a poor separation.  For example, if they were to distill wine, they would get a solution with slightly higher concentration of alcohol in water than the wine had.  This was done relatively early though, 1170. 

When glass was improved, they started using a thinner walled and larger cone that was still air-cooled.  They then distilled liquids such as beer and they were able to get rather pure alcohol.  After some study, they started calling this the quintessence.  Alcohol was therefore believed to be the medicinal equivalent of the philosopher's stone, a cure all.[10]

Alcohol plays a big role in medicine after it started being used around 1200 by the Franciscans.  Before and during this time, disease was thought to be caused by spirits invading and living in the body.  The popular way of removing these was by bloodletting, the intentional bleeding of a person quite often leading to infection or death.  Today it is known that this usually caused more harm than good.  Another method was to perform surgery.  This usually resulted in infection and death.  In short, infection was the usual result of medicine.

Alcohol is important because it is an antiseptic.  It could be poured over a wound and kill all the infectious material in it.  Alcohol was also prescribed as medicine.  This made the patient intoxicated.  This allowed the body to be relaxed and calmed.  It also made the patient happy, something that was lacking in all the previous treatments.  When the Franciscans started doing this, they started to be known as healers.  At about this point, medical alchemy started to be looked upon as a respectable occupation.[11]^{,[12],[13],[14]}

By 1267, the Franciscan monk Roger Bacon was studying medical alchemy as a way of saving bodies in addition to souls.  Medical alchemy, unlike esoteric alchemy and transmutation, was becoming respectable.  Bacon declared that the true purpose of alchemy was not to make gold for financial gain, but to make distilled medicines that would overcome the corruption that caused illness.[15]

About fifty years after Bacon, John of Rupescissa, another Franciscan, held the belief that disease was the result a corruption of some kind.  The then held that there was a fifth essence, a quintessence, that can be used to cure the disease.  He, and later followers, therefor started mixing almost anything that he could get his hands on.  Then he would boil, burn, treat with acid or base, or distill them hoping to find this quintessence.  During this process, many unknown substances were found, including many salts. 

As soon as a new material was found, it was tested as a medicine.  This was like playing Russian roulette.  Sometimes it worked, other times it killed the patient.  Amazingly many effective drugs came out of these processes.  Ammonia distilled from urine became a standard medicine.  Antimony sulfide, a yellow gold compound, was also found very effective.  This is the potable gold that is talked about in Chinese literature suggesting that the alchemist of the time had some idea of what was happening in China.

John was still looking for his version of potable gold.  He firmly believed that alcohol either was the quintessence or made up of quintessence.  His version of potable gold was then made as follows.  Dip gold into a hot bath of alcohol, then drink the liquid.  This in reality did nothing unusual since alcohol does not react with gold.  He was in essence giving the patient warm alcohol.[16]

With this study of medical alchemy, salts of different types were discovered which were used eventually in medicine.  Salt in this context is used to mean a metallic center with other, usually harmless, compounds attached to it.  The salt is therefore usually somewhat soluble in water or acid, which is what you have to dissolve materials in your stomach.  They would not all have the same solubility.  The more soluble the compound, the more dangerous it was to use it, since these salts are poisonous.

Of the salts that were purified from this research, many were based on arsenic, antimony and bismuth.  These salts were often found together and had similar properties.  The solubility problem comes in to play here though.  If the patient was given equal doses of each salt the arsenic would kill them.  The arsenic is much more soluble and would therefor kill the person.  On the other hand, the other salts would often cure the problem.  If they all had the same solubility though, they would all probably kill the patient because they are all poisonous.[17]

By the sixteenth century, the medical alchemist had advanced greatly from the days of Aristotle.  They started to make observations and form ideas that are still valid today.  One discovery they had was that after a reaction was over, there quite often was some of the starting material left over, thus proving the Greek idea that matter could combine in any proportion.  This is the start of equation writing, and is a big part of any basic chemistry course today.

The medical alchemists also found that the properties of pure chemicals did not change much.  This started the trend to move away from the essences and into the current idea of atoms and molecules.  Another advance was the use of pure chemicals in reactions.  This does not seem like an advance, but it was.  The use of pure chemicals means that the final product of the reaction is going to be of a somewhat pure state.  There would be less side reactions with materials that the alchemist put in by accident.[18]

Probably the best way to understand why these changes were made in medicine is to look at some of the writings of the people making them.  Probably one of the first people to start using the purified salts as medicine was Paracelsus (1493-1541). 

The fundamental idea of Paracelsus seems to have been that life is essentially a chemical process.  If, then, man is a chemical compound (as the theories of the day would seem to demand) of mercury, sulfur, and salt, then good health must be the sign that the elements are mingled in the correct proportions, but illness shows that one or more of these elements is deficient.  The logical treatment, therefore, is to dose the patient with that which he lacks in some form suitable for assimilation.[19]

Because of this idea, Paracelsus started treating patients less with herbs, and more with salts and other similar compounds, usually with mercury as the metallic center.  A result of this was that he started encouraging alchemists to stop looking for gold but instead remedies and for physicians to start learning chemistry.

Paracelsus also advanced chemistry and medicine in an indirect way.  His emphasis on laboratory work and experimentation was of great influence to many of the following chemists.  His concentration on one-drug remedies and strict doses had effect on medicine forever.  This is probably one of the original times where there was an idea of what the lethal dose of a drug was, and kept the dosage below it, but still high enough to be effective.[20]^,[21],[22]

Another advancement in medicine was the discovery of a method to prepare ether.  This was done by Valerius Cordus (1515-1544).  He was the first person to describe the production of ether by using alcohol and sulfuric acid.  Ether is important at that time and until modern times because it can be used as an anesthetic.  Ether has since stopped being used for that, but is still a widely used solvent in current chemistry.[23]

In 1597, Alchymia, the first book that can be considered a textbook of chemistry, was written by Andreas Libavius (c. 1540-1616).  This book was a survey of all the chemical knowledge of the time.  It included descriptions of how a lab should be set up, where and how chemicals should be stored, and the general chemical knowledge.  He also wrote other books describing some of the analytical techniques.[24]

Around 1500, books for miners also started appearing.  Ein Nutzliches Bergbuchlein ("A Useful Little Book on Mining") printed in 1505, probably by Ruhlein von Kalbe (d. 1523) was the first printed book on mining and geology.  Probierbuchlein ("Little Book of Assaying") was another book of that time gave very clear and accurate instructions.

In 1912, Herbert Hoover, a famous mining engineer who later became president of the United States, wrote that with the exception of references to atoms, twentieth century works on dry assaying were very much the same as the fifteenth century Probierbuchlein.[25]

One thing that made the book useful though was that it was written in the vernacular, German.  Another was the detail that it used in describing the processes used.

To separate silver from gold, take one part of silver which contains gold, and one part of Spiessflas, one part copper, one part lead, and fuse together in a crucible.  When melted, pour into a crucible containing powdered sulfur and as soon as poured in, cover it with a soft clay so that the vapor cannot escape.  Then, let it cool and you will find your gold in a regulus.  Place this on a dish and submit it to the blast.[26]

A very similar process is used today.  In the above, Spiessflas refers to Antimony sulfide.  A regulus is a mass of metal.  To submit something to the blast meant that you heated it in a stream of air.

For the art world, Bernard Palissy (c. 1499-1589) made some great discoveries with enamels.  He was able to prove the process of enamels drying was not one of the solidification of certain liquids, or the transmutation of water.  It was actually the separation of  substances which were present in the water.  This was of importance because he was now putting alchemy to work for the common man outside of the world of medicine.[27]

Another book that was published in 1544 was De La Pirotechnia ("Of Pyrotechnology"), by Vanoccio Biringuccio (1480-1538).  This book contained information on metallurgy, the casting of metals.  It also contains information on pyrotechnics, such as fireworks and gunpowder.  This book was written for the worker, and not the scholar making it a unique book.  Again, it was in the vernacular.

This book was also of importance because it held descriptions of how to make alum and other useful salts, and acids such as sulfuric acid.  The was also discussion on how to reprocess waste ore at mines.  Interestingly though, Biringuccio did not believe in alchemy and that there were never any transmutations.  He even described an experiment where he heated lead with a flame, and it actually gained weight (it picked up oxygen).  Flame was thought to consume material, not add any.  The question of what happened remained for years. [28]

From the end of the twelfth century to the start of the seventeenth century, the sciences known today as chemistry and medicine made great advances.  The foundation was set for the discovery of the many advances made in the seventeenth century.  At the end of this age of discovery, many text were written, most of them for the practicing alchemist, doctor, or miner.  The majority of these works though, were just compilations of what was known.

Around the turn of the seventeenth century, alchemy basically died out.  The main focus of it turned from the search for the philosopher's stone and elixir of life, to scientific studies.  As I was doing research on this subject, I was amazed at how similar the processes the alchemist used are to the ones used today.  I was even more surprised at how they were able to separate and identify the materials that they had, with so little equipment.  The modern chemist would have a tough time accomplishing what they did without the use of modern equipment, and even with it, we would have a long and tedious task to be anywhere near as good as they were.

Paper 2: The effects of substituents on the phenyl rings of zinc a,b,g,d-tetraphenylporphyrins.

Robert M. Lewis

Abstract:               The equilibrium study of substituted zinc a,b,g,d tetraphenylporphyrin with imidazole can give results dealing with how strong a Lewis acid the porphyrin.  This is directly related to how electron withdrawing the substituents are on the phenyl rings in the porphyrin.  The more withdrawing a group is, the higher the value for the equilibrium constant for the reaction A+BàAB where A is the porphyrin, B is imidazole, and AB is the complex they form.  The substituents on the phenyl ring studied are 3-methyl, 3-bromo, 4-triflouromethly, and hydrogen.  The equilibrium constants, and standard potentials gave the following ranking to the acidity of the porphyrin:  3-CH₃<H<3-Br<4-CF₃.

Introduction:

The study of metallic porphyrins and their equilibrium with imidazole can lead to conclusions about how strong an acid is the porphyrin.  As will be shown how strong a Lewis acid is the porphyrin is determined by what substituents there are on the phenyl rings of the tetraphenylporphyrin, Figure 1.

It was demonstrated that the more electron withdrawing the substituents are, the higher the equilibrium constant and the larger the standard potential.  The reaction of A+Bà AB was also shown to be exothermic for the 3-methyl compound.  Finally a ranking of how withdrawing a group is was determined.

Experimental:

Materials:

            3-methyl-benzaldehyde                                  Aldrich

            3-bromo-benzaldehyde                                   Aldrich

            Pyrrole                                                             Aldrich

            Propionic Acid                                                Fisher

            Methanol                                                         Fisher

            DMF                                                               Baker

            Zn acetate                                                       Aldrich

            DDQ                                                               Aldrich

            Alumna Absorbtion                                        Fisher

            Toluene                                                           Fisher

            Methylene Chloride                                        Fisher

            Acetonitrile                                                     Fisher

            TBAP                                                              GFS

            ZnT(4CF₃)PP                                                  J. Belli

            ZnTPP                                                             G. Vogel

Synthesis:

Making TXPP:

The tetra(X)phenylporphrins, TXPP, where X is the substituent 3-methyl, 3-bromo, 4-trifluromethyl, or hydrogen, used in these experiments was made using the following procedure.  To a flask of refluxing propionic acid, equal amounts of freshly distilled pyrrole and substituted benzaldehyde were added.  The solution was refluxed for thirty minutes and then allowed to cool to room temperature.  This left a dark purple solution with purple crystals.  This mixture was then suction filtered using a buchner funnel and washed with small quantities of methanol and water.[1]

Adding Zinc:

Inserting a Zn(II) ion into the ring was done as followed.  To a quantity of refluxing N,N’-dimethylformamide, (DMF) the TXPP was dissolved.  To follow the reaction, a visible spectrum of the solution was taken using a Shimadzu UV-Vis 2101PC scanning UV-Vis Spectrophotometer.  An equal quantity of zinc acetate was added.  After stirring for ten minutes, the visible spectrum was taken again.  The total disappearance of a peak confirms that all the TXPP had been converted to Zn TXPP.  The solution was removed from heat and allowed to cool to room temperature, followed by insertion into an ice bath for 20 minutes.  Ice cold water was then added to help the crystals crash out.  The mixture was then suction filtered and washed with water.[2]

Removing Chlorin:

In the process of making TXPP, some tetraphenylchlorin, TXPC, was inadvertently made.  The following was done to remove the TXPC.  The Zn TXPP was dissolved in methylene chloride and heated to reflux.  An amount of 2,3-dichloro-5,6-dicyanobenzoquinone (DDQ) was then added and the solution was left to reflux for one hour.  The solution was then filtered through alumna abosrbtion.  The liquid was then roto-evaporated to dryness.[3]

Thermodynamics:

To find the equilibrium constant, K, for the addition of one imidazole to the complex was done using UV-Vis spectra in methylene chloride.  First a Beer-Lambert plot had to be made to ensure that the Beer-Lambert Law was followed in the concentration range we used.  A stock solution of the metallic porphrin was made so that when diluted 2:10, the absorbance would be at least 1, and less than 2.  A fixed quantity of the stock solution was added to a volumetric flask, followed by a varying quantity of imidazole.  The change in absorbance was then measured to determine the equilibrium constant.

Standard Potentials:

The ionization energies for the complexes was determined through cyclic voltammetry.  A saturated solution of the porphrin was made with a 0.1 molar solution of tetrabutal ammonium perchlorate (TBAP) in acetonitrile.  The TBAP is used as an electrolyte, allowing current to run through the system.  The solution then had the three electrodes, reference, auxillary, and working, inserted into it and then scanned from –1.5 to +1.5 volts using a CV-27.  To get the second peak in some complexes, the scan had to be run to –1.9 volts.  At this point the solvent started to break down.[4]

Results:

The synthesis of a tetraphenylporphrin is demonstrated in the following acid catalyzed reaction.¹

4 Benzaldehyde + 4 Pyrrole +3/2 O₂ à TPP + 7 H₂O                                         (1)

In this study, the benxaldehydes were either 3-methylbenzaldehyde or 3-bromobenzaldehyde.  The quantities of materials used and the resulting yields are given in Table 1.

The zinc was then added to the ring by the following reaction under reflux in DMF.  The quantities of materials used and the resulting yields is also given in table 1.^2,[5]

TXPP + Zn(CH₃CO₂)₂ à ZnTXPP + 2 CH₃CO₂H                                             (2)

The resulting products of the syntheses so far were actually a mixture.  This was  shown by there being a peak in the visible spectra around 630 nm.  This peak is known as the chlorin peak since it is due to a by-product of the reaction to synthesize TXPP, tetraphenylchlorin (TXPC).  The spectrum for TXPC looks similar to the spectrum for TXPP with the relative size of the peaks being reversed.[6]^,[7],[8]  Figure 2

With the disappearance of the peak around 630 nm, the one furthest to the right in figure 1, signifies that the TXPC is removed.  To remove the ZnTXPC, the ring needed to be oxidized.  This was done using DDQ in refluxing methylene chloride.^3,[9]

ZnTXPC + DDQ à ZnTXPP + 2,3dichloro-5,6dicyano-1,4dihydroxy-benzene     (3)

The solution was then passed through alumna to remove all charged particles, including the dihydroxy-benzene.  The resulting solution was then roto-evaporated to dryness.  The quantities of materials used, and the resulting yields are in table 1.

A Beer-Lambert plot was then prepared in order to do the thermodynamic study.  It was found that the law is followed in a concentration range of 10^-6 M to 10^-5 M, and the extinction coefficients were found from the plot.  The extinction coefficients for the ZnTXPP and ZnT(4-CF₃)PP were given when the compounds were received, Table 2.  Since the Beer-Lambert is obeyed, equilibrium studies using visible spectroscopy can be used to measure the extent of the reaction.

The study of the equilibrium A + B à AB where A is the ZnTXPP, B is imidazole, and AB is the ZnTXPP-imidazole complex, was done using visible spectroscopy.  This was possible because the Beer-Lambert law was followed.  Since the spectra of ZnTXPP and ZnTXPP-imidazole overlap, there is no point where the abosrbance of one is zero where the other is much larger, and hence the determination of the concentration of AB becomes harder to obtain.  The equilibrium constant is the concentration of the products divided by the concentration of the reactants, all raised to their given power:[10]

                                                             (4)

Where [A] is the final concentration of A, [B] is the final concentration of B, [AB] is the final concentration of AB, [A]_o is the initial concentration of A, and [B]_o is the initial concentration of B.  Since this is a one to one adduct with imidazole not absorbing in the region, the final concentration of A is the initial concentration of A minus the final concentration of AB.  Using the following derivation, [AB] can be found:

a = eLC                                                                                                                 (5a)

C_t = C_A+ C_AB = [A]+[AB] = [A]_o                                                                         (5b)

a_t=a_A+ a_AB                                                                                                                                                  (5c)

L=1                                                                                                                                                               (5d)

a_A=e_A [A]                                                                                                                                                   (5e)

a_AB=e_AB [AB]                                                                                                                                          (5f)

a_t= e_AB[AB] + e_A[A]                                                                                             (5g)

a_o=e_A[A]_o                                                                                                                                                   (5h)

                                                                                                  (5i)

Where a_t is total absorbance, a_o is the absorbance of A before the reaction, e_AB is the extinction coefficient of AB, and e_A is the extinction coefficient of A.  This can be condensed into the Rose-Drago equation:[11]^,[12]

                                               (6)

When it a solution of fully complexed A, i.e. all AB, this equation must be used because there is no way of finding the extinction coefficient of AB.  If guesses are made for e_AB - e_A and then plotted vs. 1/K, you get a straight line.  Plotting more than one of these lines for different starting concentrations of B, you get an array of lines that cross at one point.  This point is 1/K, e_AB - e_A, and can be used to calculate e_AB.  For real data though, this will lie over a small area, Figure 3.

Since it was possible to convert all ZnTXPP to ZnTXPP-imidazole, e_AB- e_A was able to be determined, henceforth both methods were attempted to determine the K for the system.  The  Rose-Drago method did not work very well when there was a small change in absorbance.  This resulted in some lines not crossing, or crossing elsewhere than the majority of the lines.  This is most likely due to error in pipeting  the solutions causing small differences in the starting concentrations.¹¹

A useful tool to predict the constants is the Hammett plot.  This plot takes the log of K vs. 4 s where s is a constant dependant on the substituent and the number of substituents and are given in Table 3.  The slope of the line, r, indicates relatively how much of an effect the substituents have on the K.  The larger the r, the more effect.[13]  For the ZnTXPP studied, the r was 4.23 indicating that the equilibrium is very dependent on the substituents, Figure 4.

The equilibrium constants also follow the same pattern as the standard potentials determined through cyclic voltammetry.  The standard potentials were determined by taking the average of the potential for the peaks in the cyclic voltammagram,^4,[14] Table 4.  The reactions are shown in equations 7 a-d.

Ox₂… ZnP²⁺ + e^- à ZnP⁺                                                                              (7a)

Ox₁… ZnP¹⁺ + e^- à ZnP                                                                                (7b)

Red₁… ZnP + e^- à ZnP^-                                                                                (7c)

Red₂… ZnP^- + e^- à ZnP^2-                                                                              (7d)

Due to solubility problems with the ZnT(3-Br)PP, the potentials could not be measured.

Discussion:

The synthesis of the ZnT(3-Br)PP had some problems adding the zinc.  A possible reason for the trouble with inserting the zinc is due to the large amount of charge located near the binding site due to the bromine on the meta carbon of the benzene.  This high charge density may be enough to retard the zinc from inserting into the ring.  This resulted is very low yields of the compound.

This compound also had a solubility problem that led to problems with obtaining equilibrium constants.

The binding of the imidazole can be pictured as a nitrogen donating electrons to the metal to form a bond.  Since imidazole has 2 nitrogens, the question of which one binds is asked.  As described a lone pair of electrons formed the bond.  This then leaves the nitrogen without any hydrogen as the only one available to bond.  The next logical thing to ask is how many imidazole bond.  This can be seen through visible spectroscopy.  If two imidazole bond the coordination around the metal would be octahedral.  It has been shown that the extinction coefficients for octahedral complexes are usually in the range of 10^{^2}.  Since all of our coefficients are much larger, it indicates that only one imidazole bonds.

The Rose-Drago approach to determining the equilibrium constant had problems due to small variations in starting concentration of the porphyrin. This error can be seen in the spectrum taken.  When there are equilibrium spectrum that overlap and cross at a point, you have an isobestic point, Figure 5.  In the event that the reaction can be pushed to completion, and the concentration stays the same, at the point where the spectrum cross they have equal absorbance.  Since L, a, and C are the same, that means that e is also the same for both compounds at that point.  When the spectrum are taken they should all cross at that point, if the same starting concentration of ZnTXPP is used:[15]

a_t = a_A + a_AB = e_ABL [AB] + e_AL [A] = eLC_t                                                  (8)

Due to experimental error though, the point is in reality a small area.  This lead to the problems experienced using the Rose-Drago equation.  The first method, using equations 4 and 5i, gave consistent answers that are listed in Table 3.  The constants were determined using both the absorbance at the wavelength of the largest extinction coefficient in the starting material and the final product.  The extinction coefficients for each wavelength used are listed in Table 2.

Since there was one study of the equilibrium constant at a different temperature than 21^oC, some generalizations can be made about the reaction.  Since the K is larger at a lower temperature (15^oC) the reaction is exothermic.  This is understandable since there is a bond being formed, and the formation of bonds is usually exothermic.  The slope of the line obtained from plotting Log K vs –1/2.3RT is DH^o.  In the case for the two points obtained for ZnT(3-Me)PP, the slope is -1.19E+02 kJ/Mol.

From the Hammett plot, Figure 4, and the standard potentials some generalizations about the electron movement in the compound can be made.  A larger K indicates that the compound is a stronger Lewis acid.  To be a better Lewis acid, the metal needs to be a better electron acceptor.  This can be done by the metal loosing electrons to the surrounding ring.  The equilibrium constant then is a measure of how electron withdrawing the substituents are, the larger the K, the more withdrawing. 

This can also be shown with the potentials.  The more withdrawing the group, the harder it is to remove an electron from the metal.  This is seen by a higher potential.  Conversely, the easier it is to put on an electron, resulting in a potential closer to zero.

Conclusion:

The equilibrium study of substituted zinc tetraphenylporphyrins can lead to the ranking of substituents according to their ability to increase the ability of the metal as a Lewis acid.  Of the groups used in this study, the ranking from weakest Lewis acid to strongest Lewis acid is:

3-Me<H<3-Br<4-CF₃

This is also the ranking for how electron withdrawing the substituent is.  The more withdrawing the group is, the higher the standard potential, and the larger the K.  From the Hammett plot it is also shown that the equilibrium is very dependent on the substituents.  This is demonstrated by a large r.  More time needs to be devoted to the study of these substituted prophyrins to determine how the groups effect the enthalpy.