Oxidation Numbers, Electronegativity, Formal Charges, Molecular Polarities, Climate Change, pH, the Checking of Calculation Results and the Correcting of Errors.

Steve Murov, Professor Emeritus of Chemistry, murovs@yosemite.edu

            This is the second of two web sites intended to provide insight into chemical concepts.  The first site entitled ATOMIC MASS and ISOTOPES:  INTERPRETING THE NUMBERS [1] focused on atomic mass and the information that can be gleaned from its value.  This utilitarian knowledge is not commonly discussed in texts but provides useful insight into the isotopes of each element and is worthy of students’ attention.  This paper continues on with the theme that students can often gain valuable insight into chemistry concepts by thinking beyond the box or reading between the lines.  Applications to oxidation numbers, formal charges, molecular polarities, climate change, pH, the checking of calculation results and the correcting of errors are presented. John Packer, et. al. [2] and David DeWit [3] have previously presented examples on some of these topics. 

     Oxidation numbers.  Oxidation numbers are useful for several reasons.  First, the oxidation number is needed to determine the name of compounds like FeCl3 and Sn(NO3)2.  Oxidation numbers are also used for determining if a reaction is a redox reaction and if so, what is oxidized and what is reduced. The oxidation number method assumes that bonds are 100% ionic and assigns all the electrons in bonds to the more electronegative partner. For covalent bonds, oxidation numbers give a very distorted view of the charges in the molecule.  For a compound like LIF, the oxidation number method gives a reasonable model for the bonding with a +1 on the lithium and -1 on the fluorine.  For HCl, the oxidation number method assigns a +1 to the hydrogen and -1 to the chlorine.  This model reflects the partial charges but is not an accurate model as the electrons are shared and not completely transferred.  Oxidation numbers yield a good model for the compound when the bonding is ionic but nothing more than a bookkeeping method for covalent bonds.
For pertinent exercises, please visit:  http://exercises.murov.info/ex4-2.htm 

     Electronegativity. The determination of bond character, that is, whether a bond is ionic or covalent, is not straightforward.  Probably the most common method relies on the use of a comparison of the electronegativity values of the bonding partners.  The use of electronegativity to determine the percent ionic character results in substantial uncertainty for several reasons.  First, there are several different electronegativity scales with significant differences in values.  As a result, the percent ionic character determined from the scales can vary substantially.  The primary complication is that few bonds are either 100% ionic or 100% covalent.  Several formulas have been developed that estimate the % of ionic character from the electronegativity difference.  The formulas and the resulting % ionic character for several DEN values are included below. 

% ionic equation DEN = 0.5 1 1.7 2 3
[1 - e-(DEN/2)2] x 100 % ionic 6 22.1 51 63 90
16(DEN)  +  3.5(DEN) 9 19.5 37 46 80
18(DEN)1.4 7 18 38 47 84
29.4(DEN) 15 29.4 50 59 88
(ENhigher - ENlower)/ENhigher            

      The last equation depends not only on DEN but also on values of EN so values cannot be caluculated with only DEN values.

Use of the graph below provides a visual method for determining the % ionic character but demonstrates that there is substantial uncertainty about the value.  Many sources claim that an electronegativity difference >1.7 can be interpreted to mean that the bond is ionic.  Between 0.5 to 1.7 the bond is supposedly polar covalent and <0.5 the bond is non-polar covalent.  Note, however, that CsI, LiCl and HF have similar electronegativity values but the reported % ionic character varies from about 45 to 74%.


     The formulas above were developed for use with the Pauling electronegativity scale.  However, three other scales have been found to correlate better with bond properties. [4]  For the purposes of this web site, when EN values are needed, the Allen scale will be used.  Problems still occur as carbon-sulfur and carbon-iodine bonds behave as if they are polar covalent with a partial positive charge on the carbon but these experimental observations are contradictory to DEN values. Unlike the Pauling scale, the Allen scale does appropriately have the electronegativity of nitrogen higher than for chlorine.    This is consistent with the observation that nitrogen participates in hydrogen bonding but chlorine does not.  Electronegativity is not the only parameter that needs to be considered when determining the % ionic character.  Size of the ions and other variables are also important and not necessarily taken into account by the EN value. 

      Generally, it is not necessary to consult an electronegativity table and it is sufficient to conclude that ionic bonding predominates for metals to non-metals. Bonding between identical non-metals and carbon to hydrogen bonds are non-polar covalent. Polar covalent bonding predominates for non-identical non-metals to non-metals. 

For problems on bonding types, please see:  http://exercises.murov.info/ex6-3.htm

     Oxidation Number Calculations.  Determination of oxidation numbers in a compound requires an assumption of the value of the oxidation number of one of the partners of the bond.  A set of rules determines the priority for the assumptions.  For a compound like NaCl, the sodium has the higher priority.  Since IA elements in compounds have a (except for H) +1 oxidation number, the chlorine by calculation has to have an oxidation number of -1.  As rule 2 states, the sum of the oxidation numbers in a neutral compound must be zero, 1 +  x  =  0 and x = -1.  A later rule is that VIIA elements in binary compounds have an oxidation number of -1.  For this case, the calculation is consistent with both rules.  For a compound like H2O2, the prioritization of the rules becomes necessary but also is consistent with logic.  When hydrogen is bonded to an element more electronegative than itself, it behaves like the other IA elements and has a +1 oxidation number.  This results in a -1 oxidation number for oxygen [2(+1) + 2x = 0].  If the prioritization had been ignored and it was assumed that oxygen is -2, then hydrogen would come out +2.  This is an impossible conclusion.

The rules should be used in this order - the higher the rule, the higher its priority.
 1. The oxidation number for an element in its elemental form is zero.(e.g. I2, carbon in diamond and graphite).
 2. The sum of the oxidation states of all the atoms or ions in a neutral compound is zero.
 3. The sum of the oxidation states of all the atoms in an ion is equal to the charge on the ion.
 4.  Fluorine has an oxidation number of -1 in compounds (other than F2).
 5. The O.N. of group IA elements is +1.
 6. The O.N. of group IIA elements is +2
 7. The O.N. of oxygen is -2, except peroxides where it is -1.
 8. The O.N. of halogens is usually -1.
 9. The O.N. of hydrogen is +1 when bonded to non-metals and -1 when bonded to metals.
10.  The oxidation numbers of polyatomic ions must be learned (e.g. nitrate in NO3-)

In summary, the least electronegative element is assigned a positive oxidation state. The more electronegative element in a substance is assigned a negative oxidation state. Remember that electronegativity is greatest at the top-right of the periodic table and decreases faster going down than going to the left. Fluorine is the most electronegative element with an oxidation state -1 except in F2.


AlCl3     x + 3(-1) = 0    x (O.N. for Al) = 3

Ti(NO3)It needs to be recognized that nitrate has a charge of -1.  For the titanium x + 4(-1) =0 with x or the oxidation number of titanium = 4.  Thus the name would be titanium(IV) nitrate.  For the nitrogen, see the next example.

NO3Application of the rules results in O = -2.  For the nitrogen, x + 3(-2) = -1 and x = 5.

For more examples, see:  http://exercises.murov.info/ex13-1.htm

The periodic table below give very approximate values of the oxidation numbers for the elements.

     Information from oxidation numbers. 

Q1.  Calculate the oxidation states of the central atom in polyatomic ions permanganate, chromate, chlorate, perchlorate.  To jump to answer click on Q1.

It should be pointed out to students that the resulting large and perhaps unexpected oxidation numbers should have led to the expectation of strong oxidizing ability. [5]  The high oxidation state and/or positive oxidation states for electronegative elements does not guarantee that the ion will be a good oxidizing agent but just the suspicion that it could be gives the student potentially valuable information and a better feel for chemistry.  Exceptions such as perchlorate can be used to explore thermodynamic vs kinetic reasons for the apparent lack of oxidizing ability. [6] 

      Hydrogen peroxide, hydrides and Fe3O4 are further examples in which unusual oxidation numbers are indicators of extraordinary behavior.  The discussion earlier demonstrated that oxygen has an oxidation number of -1 in H2O2.  This result should immediately raise a red flag as we recognize that oxygen in compounds almost always has an oxidation number of -2.  This should lead to the consideration that H2O2 could have unusual behavior and be very reactive.  In fact, hydrogen peroxide can function as an oxidizing agent or a reducing agent.  Left alone, H2O2 slowly undergoes disproportionation (undergoes oxidation and reduction with itself).

2 H2O2  =   2 H2O  +  O2

For hydrides such as NaH or LiAlH4, the calculated oxidation number of the hydrogen is -1.  Recognizing that hydrogen in compounds is usually +1, the -1 result again raises a flag.  As expected, hydrides are strong and very useful reducing agents as energetically, hydride does not mind giving up electrons.  A calculation of the oxidation number of iron in Fe3O4 results in the value of 8/3.  This is best explained by concluding that two of the irons are +3 and the remaining one +2.  This unusual state of affairs could be expected to result in unusual properties.  Fe3O4 is called ferrosoferric oxide and also magnetite.  Most ferromagnetic materials are metals but the compound Fe3O4 is distinguished by its ferromagnetism.  It also has an unusually high electrical conductivity that is about 1 million times greater than the value for Fe2O3.

     Formal charges.  Formal charges are also useful for anticipating unusual behavior.  The formal charge method assumes that the bonds are 100% covalent with bonded electrons equally shared by the two partners.  In general, everything else being equal (e.g., octet rule is satisfied), the structure with the minimum number of formal charges will be favored. The formal charge is calculated from the following formula:

formal charge = valence electrons - bonds - nonbonded electrons

Many texts suggest the use of formal charges to prioritize resonance structures and to choose between different isomeric structures. [7] In thiocyanate, the use of formal charges leads to the conclusion that the first isomeric structure should be more stable than the other two because it has the minimum number of formal charges. 

Formal Charges and Resonance | Chemistry for Majors

Q2.  For laughing gas (N2O), use Lewis structures and a consideration of formal charges to predict if the sequence of bonding should be NNO or NON.  One of the guidelines for Lewis structures is that symmetrical structures are usually favored over asymmetrical structures.  Is this one of the exceptions?

Q3.  In hypochlorous acid, would the H be expected to be bonded to the O or the Cl?

For the resonance structures of the enolate ion, the resonance structure with the negative formal charge on the more electronegative oxygen would be expected to be more important than the one with the charge on the carbon. 

 DeWit points out that formal charges can be used to predict that carbon monoxide should be more reactive than nitrogen. [3]  The formal charges for CO on the left are contrary to electronegativity values and the middle structure lacks an octet on the carbon.  The structure on the right does not satisfy the octet rule and has formal charges.  The choice for the best model is between the 1st and 2nd and bond lengths and energies indicate a triple bond is present.  The  very small dipole moment for CO is also consistent with two competing factors.  The formal charges indicate the dipole should be from oxygen to carbon whereas the electronegativity values favor the dipole going from carbon to oxygen.  These two factors come close to canceling.  There is some debate about the direction of the very small dipole but it is probably from oxygen to carbon.

What is the oxidation number of carbon monoxide? | Socratic

9.4: Polar Covalence - Chemistry LibreTexts

Ozone resonance structure: differing opinions - Chemistry Stack Exchange

The formal charge of +1 on the central oxygen of ozone in the identical resonance structures of ozone also leads to expectations of high reactivity.  These expectations are realized as ozone is dangerously reactive and a severe health hazard.  Ozone is also environmentally destructive as it attacks double bonds including those in rubber tires.



See the source image

Free radicals.  Students are often alerted to the probability of high reactivity of compounds with unpaired electrons (free radicals).  Probably the most common example of a free radical is the diradical oxygen.  See the source imageThis incorrect model is one of the few failings of the Lewis structure method as liquid oxygen when poured through a magnetic field bends towards one of the magnetic poles.  This means that O2 is paramagnetic and that it has at least one unpaired electron.  A decent and correct Lewis structure of oxygen cannot really be drawn.  A molecular orbital model does correctly depict oxygen as a diradical with two unpaired electrons.  The structure on the left below does depict a diradical but also shows only a single bond. Diatomic oxygen behaves as though it has a double bond.  The structure on the right goes beyond normal Lewis structure guidelines and is difficult to interpret.

See the source imageSee the source image

     The very hazardous pollutant, nitrogen dioxide, is a reactive free radical.  Despite the common in depth discussion in texts of the dimerization of of the free radical, NO2, the reasons for this reaction not going virtually to completion are not usually presented.  Packer, et. al., explain that the two adjacent +1 formal charges on the nitrogens of N2O4 make this observation understandable. [2] The image on the right below shows the orange color of NO2.  The middle image shows that the orange color of smog is consistent with hazardous concentrations of NO2.
Traffic density, wind and air stratification influence concentrations of air  pollutant nitrogen dioxideWhat is the colour of NO2? - Quora


Q4.  Now many unpaired electrons does each of the following have:  NO, SO2, Fe, Nd, N2 ?

      Molecular polarity.  Understanding the polarity of molecules can go a long way towards understanding and predicting solubility and the outcomes of organic reactions.  Even trends in boiling points can be predicted when molecular polarity is considered.  The polarities of iodine and CO2 can be determined from Lewis structures. 

      glass of sparkling water  

     Because the structures show that both molecules should be non-polar, both should have low solubility in very polar water.  The mass percent solubility in water of I2 and CO2 are 0.03% and 0.17% at room temperature respectively.  Solubility is often arbitrarily defined as above 1%.  The solubility values are consistent with the prediction of low solubility of these substances in water.  The iodine solubility can be observed in a glass bottle containing a saturated iodine solution.  Because the solution is dark amber, some people conclude that contradictory to predictions, iodine is soluble in water.  However, a small amount of iodine produces substantial color despite its low solubility. 

      The relatively low solubility of carbon dioxide in water is demonstrated when a bottle of a carbonated soda is opened.  Using high pressure, the CO2 was forced into the water.  Given the opportunity, when the container is opened, most of the CO2 escapes by bubbling out of the solution.  It should be noted that polarity is not the only factor that determines solubility.  Many ionic compounds despite their polar character are not soluble in water.


    solvent formula b.p.


in water
    1 cyclohexane C6H12 80.7 6.6 0.779 0.006 0.005 0 2
    2 hexane C6H14 69 -95 0.655 0.009 0.0014 0 1.9
    3 toluene C7H8  110.6 -93 0.867 0.099 0.05 0.36 2.4
    4 ether C4H10O 34.6 -116.3 0.713 0.117 7.5 1.25 4.3
    5 ethyl acetate C4H8O2 77 -83.6 0.894 0.228 8.7 1.78 6.0
    6 acetone C3H6O 56.2 -94.3 0.786 0.355 M 2.85 21
    7 1-octanol C8H18O 194.4 -15 0.827 0.537 0.096 1.68 10.3
    8 1-hetanol C7H16O 176.4 -35 0.819 0.549 0.17 1.6 12
    9 1-hexanol C6H14O 158 -46.7 0.814 0.559 0.59 1.60 12.5
  10 1-pentanol C5H12O 138.0 -78.2 0.814 0.568 2.2 1.7 14
  11 1-butanol C4H10O 117.6 -89.5 0.81 0.586 8.5 1.7 17.5
  12 1-propanol C3H8O 97 -126 0.803 0.617 M 1.68 22
  13 acetic acid C2H4O2 118 16.6 1.049 0.648 M 1.68 6.2
  14 ethanol C2H6O 78.5 -114.1 0.789 0.654 M 1.7 24
  15 methanol CH4O 64.6 -98 0.791 0.762 M 1.6 33
  16 water, heavy D2O 101.3 4 1.107 0.991 M 1.84 78.3
  17 water H2O 100.00 0.00 0.998 1.000 M 1.85 78.3

M =  miscible

       For more complete tables of solvent properties, please see:  http://murov.info/orgsolvents.htm  http://murov.info/orgsolvsort.htm

      As noted, the solvent table has been arranged according to increasing relative polarity using a solvent spectral shift measurement.  Solvent polarity much like electronegativity is not a well defined property.  In addition to the relative polarity values used above, dipole moments and dielectric constants are also used to rank polarities.  The table shows that there is a correlation of the solvent shift polarities with dipole moments and dielectric constants with some notable exceptions. 

     The best predictor of solubility is probably "like dissolves like."  Because many variables affect solubility, the best way by far to determine solubility is to refer to the literature or experimentally determine it.  There are some trends that are predictable.  For the series 1-octanol, 1-heptanol, 1-hexanol, 1-pentanol, 1-butanol, 1-propanol, ethanol and methanol, the table shows a consistent trend towards increasing solubility in water as the number of carbons decreases.  One way to view these molecules is to consider them to be composed of two parts, a non-polar carbon chain and a very polar OH group.  When the carbon chain is long, the non-polar properties dominate and the compound has low solubilty in water.  As the carbon chain shortens, the polar hydroxy group becomes the dominating part of the molecule.  The three alcohols with three carbons or less are all miscible with water.

Q5.  Should the first compound listed be more soluble in the first solvent or the second?

a.  NaCl in water or toluene
b.  KOH in water or toluene
c.  HCl in water or toluene

d.  wax in water or toluene

Q6.  Using solubility differences only, suggest a method for distinguishing between:
a.  PbCl2 and BaCl2
b.  BaSO4 and ZnSO4
c.  acetone and hexane

a.  The molecular mass values for hexane and 1-pentanol are similar.  Suggest a reason that the b.p. of 1-pentanol is higher than the b.p. of hexane.
b.  The boiling points of methane, water and hydrogen iodide are -162oC, 100oC, and -35oC respectively.  Suggest an explanation for the values.

     In addition to the use of molecular polarity for the prediction of solubility, polarity is a very useful property for the determination of the course of organic reactions.  Many reactions are initiated by the attack of a nucleophile or and electrophile.  Where should we expect a nucleophile to attack but on a site that has a partial positive charge.  Common examples are carbons bonded to a leaving group such as a halide or protonated alcohol or to an sp2 hybridized carbon that has a double bond to an oxygen such as a carbonyl or carboxyl group.  Electrophiles or species with positive or partially positive charges should be expected to attack regions of high electron density such as an aromatic ring.  Examples of attack by nucleophiles on carbons with partial positive charges are below.

Reactions initiated by nucleophiles:

Reactions initiated by electrophiles:

     Climate change and pH. Climate change is one of the most daunting challenges currently confronting all life on earth.  The first step in the effort to overcome the challenge is to significantly increase climate change science literacy.  Thinking about the magnitudes of concentrations can provide valuable insight.  Most people including those with strong opinions on both sides of the global climate debate cannot name the three most abundant gases in dry air.

Q8.  Name the 3 most abundant gases in dry air.

      Many name carbon dioxide among the top three.  It is difficult to understand how people can be so opinionated on global climate change if they do not even know that carbon dioxide ranks number 4 but far down in concentration value from the top three.  Because carbon dioxide is a minor constituent of the air, combustion of fossil fuels by humans has produced sufficient CO2 to increase its concentration from 280 ppm to over 410 ppm. [8] 

Q9.  Convert the values of 280 ppm to 410 ppm to mass percentages.

     Even if people notice the units of ppm, most do not realize that these values translate to very low concentrations.  While the consequences of the 46% increase in CO2 atmospheric concentration on the global climate are difficult to predict with high certainty, understanding that human activity has changed the content of the atmosphere does help when trying to explain the reason for concern.  Unfortunately, scientific studies of the effects of increasing CO2 and other Greenhouse gases are consistent with an alarming increase in global air and water temperatures with severe consequences for life everywhere.  For a Powerpoint presentation on climate change, please visit reference [8c]

     pH is another measurement that does not receive sufficient attention with regard to interpretation of its values.  When it is stated that neutral aqueous solutions have a pH of 7, how many think about how low the acid and base concentrations are in neutral water. 

Q10.  What is the pH of a solution prepared by the addition of 1 drop (0.05 mL) of 1 M acid to 1 L of pure water. 

Q11.  How much sodium chloride is needed to prepare 1 L of 1x10-7 M NaCl and is it possible to weigh the resulting quantity. 

Q12.  Why does the pH of freshly distilled water drop below a pH of 7 after sitting for a few hours open to the atmosphere?

Ocean Chemistry & Acidification – Time Scavengers

      Strongly related to this concept is the observation that the pH of the oceans has decreased about 0.1 pH unit as a result of the atmospheric carbon dioxide increase and is threatening ocean life and the sustainability of coral reefs. [8]  Thus it is possible to argue that because of ocean threats, air and water pollution, wars etc., even without consideration of climate change consequences, fossil fuels need to be phased out.

     It is also important for students to think about the high end of practical concentrations.  Most students have a real problem when asked to calculate the concentration of pure water (about 5M) and most will not have thought about the reason why acids generally do not and cannot exceed about 20 M.

Q13.  What is the molarity of pure water (assume the density of water is 1 g/mL)?

     Checking and correcting calculations.  For the final topic, the importance of reflecting on the results of calculations, and learning from mistakes needs to be emphasized.  Too often, students obtain results and then move on without questioning the logic of the result and its implications.  As a carefully selected example, when students are asked to calculate the mass of an antimony atom, some will come out with a result of 7.3x1025 g because of the inverted use of Avogadro’s number.  Making this mistake is ok but it is not ok to not notice that the answer is unreasonable as this value is close to the mass of the moon.  Calculations should always be followed by the question:  Does the answer make sense?  For example, values of atomic and molecular mass have practical boundary values and answers out of the logical range should lead to rechecking of the problem.  The simple technique of using insight to determine if the result makes sense can frequently lead to a discovery of a calculation error.  Instructors are often too lax when it comes to encouraging students to learn from their mistakes.  Students need to be encouraged and perhaps required to correct missed problems on tests.  Students have a tendency to merely look at the score and not learn from their mistakes.  Probably more important than a tool for assessing progress in a course, tests should function as learning instruments.  Insight gained from missed problems can go a long way toward making a student more competent in chemistry.  When students realize they have acquired insight in the field of chemistry, they will become the positive learners and will enjoy learning.


Q1.  O.N. of permanganate MnO4-, chromate CrO42-, chlorate ClO3-, perchlorate ClO4- .       7, 6, 5, 7, 6    Return to Q1.


 For N2O, the use of formal charges favors the prediction that the bonding sequence is NNO rather than NON (note:  only 1 of 3 possible resonance structures for the sequence NNO are shown).   Return to Q2.

Q3.  H-O-Cl     H-Cl-O  The former does not have formal charges but the latter has a +1 on the chlorine and a -1 on the oxygen.  Minimal formal charges are usually preferred thus HOCl is preferred.  Return to Q3.

Q4.  NO - 1, SO2 - 0, Fe - 4, Nd - 3, N2 - 0   Return to Q4.

Q5.  Water, water, water, toluene.  The first three are polar and prefer the polar water.  Wax is non-polar and prefers the non-polar toluene.  Return to Q5.

a.  PbCl2 and BaCl2 .  The first is insoluble in water and the second is soluble.
b.  BaSO4 and ZnSO4   The first is insoluble in water and the second is soluble.
c.  acetone and hexane
    The first is soluble in water and the second is insoluble.   Return to Q6.

a.  Because 1-pentanol is polar (with potential H bonding), the intermolecular attractions are higher than in hexane.
b.  Everything else being equal, boiling points generally correlate with molecular mass due to greater V-D-W forces.  However, water is not just polar but also strongly hydrogen bonds to itself making its boiling point very high.  Compared to water, hydrogen iodide has a much higher molecular mass but polarity is a much larger factor.  The boiling point of HF is also higher than that of HI due to greater intermolecular attractions. 
Return to Q7.

Q8.  78% nitrogen, 21% oxygen, 1% argon.  See:  https://en.wikipedia.org/wiki/Atmosphere_of_Earth  Return to Q8.

Q9.  0.028% and 0.0410%.  Return to Q9.

Q10.  Approximately 4.3.  Return to Q10.

Q11.  About 5.8x10-6 grams.  Because of vibrations, air currents and other technical issues, the lowest limit of a balance is about 1x10-5 grams thus the amount needed cannot be directly weighed on a balance.  Return to Q11.

Q12.  Although CO2 is a minor constituent of air (0.041%) and it is not very soluble in water (0.17%), after exposure to air for several hours or days, sufficient carbon dioxide will dissolve in the water to lower the pH to 6 or lower. Return to Q12.

Q13.  Because of the low molecular mass of water, compared to most molarities, the molarity of pure water is very high and about 55 M.  Return to Q13.

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[2]  Packer, J. E.; Woodgate, S. D., J. Chem. Ed., 1991, 68, 456.

[3]  Dewit, D. G., J. Chem. Ed., 1994, 71, 750.

[4]    Gordon Sproul  https://pubs.acs.org/doi/10.1021/acsomega.0c00831   

[5]  Anderson , P., J. Chem. Ed., 1998, 75, 187.

[6]  Urbansky, E, T., Bioremediation Journal, Vol. 2, 2, 81-95. (1998)

[7]  Rayner-Canham, G. and Huelin, S., Chem 13 News, Sept., 2000, #286, 6, 7.