• Blog Stats

    • 89,097 hits
  • Archives

  • Enter your email address to subscribe to this blog and receive notifications of new posts by email.

    Join 168 other followers

  • Copyright notice

    This blog entry and all other text on this blog is copyrighted, you are free to read it, discuss it with friends, co-workers and anyone else who will pay attention.

    If you want to cite this blog article or quote from it in a not for profit website or blog then please feel free to do so as long as you provide a link back to this blog article.

    If as a school teacher or university teacher you wish to use content from my blog for the education of students then you may do so as long as the teaching materials produced from my blogged writings are not distributed for profit to others. Also at University level I ask that you provide a link to my blog to the students.

    If you want to quote from this blog in an academic paper published in an academic journal then please contact me before you submit your paper to enable us to discuss the matter.

    If you wish to reuse my text in a way where you will be making a profit (however small) please contact me before you do so, and we can discuss the licensing of the content.

    If you want to contact me then please do so by e-mailing me at Chalmers University of Technology, I am quite easy to find there as I am the only person with the surname “foreman” working at Chalmers. An alternative method of contacting me is to leave a comment on a blog article. If you do not know which one to comment on then just pick one at random, please include your email in the comment so I can contact you.

  • Advertisements

Resistor polyhedra

Dear Reader,

Those of you who want to work out your brains might be interested in the resistor polyhedra contest article which I wrote for RadCom. This has been designed to be a challenge which will both tax the minds of very bright people with years of experience in physics / electronics and also offer the new commer some easier problems to allow them to get their feet wet.

I have made a lot of funny networks out of 1000 ohm metal film resistors, my trusty 25 W Antex iron has been very handy for this task. I tend to like to use a iron jacketed 25 W Antex iron for most soldering work. I bought the Antex back in 1992 and it is still going strong. I used to use a 25 W Weller (from the late 1980s) with a copper tip but I found that that the tips were dissolving in the solder too much for my liking. I have to confess that I worked a lot with the Weller, the Weller had coated tips but they did slowly age and dissolve. So what I used to do with that iron was to use 1970s solid copper tips from another older iron I used to own as a lad. I used to have to file the copper tips once in a while to get the shape right.

I have found that a 50 W temperture controlled Weller with a modern tip to be a nice iron. I think that it is a better iron for large items than the 25 W Antex. But I think if you want the best value for money the 25 W Antex is hard to beat. I used that in my youth to build quite a few things.

RadCom is the magazine of the RSGB (Radio Society of Great Britain). Sadly due to an error in the production process it did not publish a closing date. The closing date is 08:30 GMT on the 7th of Jan 2019. To have a chance an entry must have reached the RadCom office by that time / date.

The contest is in RadCom in the december issue at around page 40

The rules by which I will be judging the contest are

Rule 1.

If one person has calculated or measured correctly more networks than any other person, then this person shall be the winner. Any person who gets within 2 % of the correct value will be judged to have got it correct. The networks made by Mark Foreman are to be used to referee what the correct values of the networks are. If the RadCom office or other RSGB workers were to create their own versions of the networks then the average of the values measured from the networks will be used.

Rule 2.

If under rule 1 no single winner can be identified, then Mark Foreman will judge the method used to determine the values of the networks. Mark Foreman normally favers methods which use the bare minimum of advanced mathematics. Thus if the solution requires exotic things like Laplace transformations, matrix operations and the like he will disfavour. Mark Foreman reserves the right to consult other people when judging methods which use advanced maths.

Rule 3.

If under rules 1 and 2 no single winner can be identified, then the first most correct and elegant answer to arrive at the radcom office will be the winner.

Rule 4.

If under rules 1, 2 and 3 no single winner can be identified, then the winner will be randomly selected. The possible winners will be assigned numbers such as 1, 2, 3 and 4. Then Mark will use a measurement of the background radiation in his office or lab as a random number generator. The least significant digit in the total count numbers (number of events detected) will be used to decide the winner.


Bridge in Genoa (Italy)

Dear Reader,

I strongly suspect that some of you will be aware that a bridge in Italy has fallen down resulting in a considerable loss of human life. Now some of you might be wondering what caused it to happen.

At this time I do not know for sure exactly what caused the bridge to fall down, there are reports that a lightning bolt hit the bridge shortly before the bridge came crashing down. The bridge was a suspension bridge (cable stayed bridge) which had reinforced concrete elements which go from the tops of the towers to the part of the bridge which the people / cars travel over.

Now years ago in the senior common room at Reading it was explained to me that there are two types of suspension bridge. There is the true suspension bridge where a long cable which has a shape similar to a washing line exists between two towers. From this cable a series of vertical elements are connected. At the bottom end of the vertical elements are connected to the road way on which the people, cars etc travel over. The other design is a cable stayed bridge in which straight elements which are under tension go from the tower to the road.

For the suspension bridge it is impossible to change the main cable (the one with the washing line shape) but for the cable stayed bridge it is possible to replace a cable.

One big problem is tension, now it is important to understand that concrete is very weak in tension but strong in compression. This is why reinforced concrete is so good a material. The strength of a concrete object can be sometimes increased further by stressing the structure by putting the concrete under additional compression. This can be done by having a hole going through the concrete, the concrete is poured and allowed to set. Afterwards a steel rope in the hole is then put under tension, this then subjects the concrete to compression. One way of doing this would be to have a long bolt passing through the hole with large washers on both ends. By putting a nut on this bolt and tightening it up then the bolt will be under tension and the concrete under compression.

post stressed concrete

Another method would be to use prestressing where the rebar is put under tension before the concrete is poured. It is important to note that when carbon steel is placed in concrete made from ordinary portland cement (OPC) that the pore water in the cement is slightly alkaline. This is good for the steel, under these conditions the steel does not corrode quickly. The steel is in a chemical environment in which the corrosion is very slow.

Corrosion or rusting of rebar is a very big problem, the volume occupied by the rust is greater than that of the steel rebar. As a result if rusting occurs then not only does the rebar lose its strength but also it tends to cause concrete to spall off from the structure. This expansion from within tends to make more holes in it.

However there are two main problems, if the concrete becomes contaminated with chloride salts from sea spray or deicing salts used on the road then the rebar can start to corrode more quickly. Also if as a result of cracking carbon dioxide from the air can enter the concrete then the pore water will become less alkaline. The steel will then be exposed to a new chemical environment in which it will corrode more quickly. All concretes will slowly be carbonated by the air, but in the ideal world only the very outer layer will be carbonated.

If the concrete becomes cracked due to vandalism, a changing mechanical load or even due to corrosion then the rate of carbonation tends to increase. This is due to the fact that the air has greater access to the inner part of the concrete object.

The last main thing which we should be aware of is that some corrosion modes such as stress corrosion cracking are worse when the object is placed under tension such as in the cable of the suspension or cable stayed bridge.

What I think that one of the things the investigators should be doing is to check the chemistry of the concrete used in the reinforced concrete cables used to connect the towers to the deck of the bridge. There are two simple chemical tests which can be used.

The first one is to drill a hole into the concrete and apply a solution of phenolphthalein to the surface. This is an acid/base indicator. When it is acidic it is colourless but when it is alkaline it is intense pink. What you then do is to measure how far the colourless reagion extends into the concrete object. This will give an indication of how bad the carbonation effect was at the point where the hole was drilled. As the bridge has fallen down this test can be used without having to worry so much about plugging up the holes made in the test if you were to examine the fallen lumps of concrete.

Another simple test is to grind up a sample of concrete, then to make this into a paste with a known amount of water. If this paste is then examined by either ion chromatography or a chloride test strip (based on the reaction of silver nitrate with sodium chloride to form insoluble silver chloride) then it is possible to determine how much chloride contamination was present in the concrete.

It would be interesting to know if the people responsible for the bridge were using these tests and some other corrosion tests before the bridge fell down. Now I think that the wreckage from the bridge should be subject to these tests and some other tests to try to work out what has happened. I will try to write more about the bridge and steel corrosion when I get the chance.

About the chemistry of the nerve gas attack in Japan

About 20 years ago when I was a PhD student, Stuart the medical student (He is now an anaesthetist) emailed me to tell me of a scary case in Japan. I then looked at the news and discovered what had happened.

To remind you what happened was that a series of cult members split open plastic bags containing sarin inside subway trains in Tokyo. The fumes of this substance then seriously injured a large number of people and killed more than ten people.

Now as well as having a chemists point of view on this matter, I have a little knowledge of the type of religion which the cult can be classified within. Now some religions maintain that some religious figure is going to appear or return, then right a series of wrongs and punish the ungodly. Some others maintain that some dramatic event will occur which will change the world as we know it, a common theme is that the members of the faith will survive and thrive while those outside the cult are absymally corrupt and evil people who are destined for suffering and destruction.

One example would be Elizabeth Clare Prophet and the Church Universal and Triumphant they were getting ready for nuclear war and expecting an end to society as we know it. Their leader and prophet predicted the date of a nuclear war, this day came and went without incident.

Now do not get me wrong, some faiths which are morally perfectly OK have this feature, for example the “Open Brethren”, the Church of England and the Roman Catholic Church hold the view that one day there will be the day of judgement when Christ will appear on earth. They hold the view that he will come to “judge the living and the dead”, those who are believers will assend into heaven (where everything will be fine and rosey for ever and ever) while those ungodly people will be seporated from God for the rest of eternity.

There are some faiths which seem to lack this feature (millenarianism). One thing which I think is important about millenarianism is the degree to which is infulances the thoughts and actions of the faithful. Others have written about this topic.

In conventional christainity while it is a matter of belief that “Christ will come again”. I have taken the text of the Nicene creed and I have marked in bold the parts which relate to millenarianism.

I believe in one God the Father Almighty,
Maker of heaven and earth,
And of all things visible and invisible:
And in one Lord Jesus Christ, the only-begotten Son of God,
Begotten of his Father before all worlds,
God of God, Light of Light,
Very God of very God,
Begotten, not made,
Being of one substance with the Father,
By whom all things were made;
Who for us men, and for our salvation came down from heaven,
And was incarnate by the Holy Ghost of the Virgin Mary,
And was made man,
And was crucified also for us under Pontius Pilate.
He suffered and was buried,
And the third day he rose again according to the Scriptures,
And ascended into heaven,
And sitteth on the right hand of the Father.
And he shall come again with glory to judge both the quick and the dead:
Whose kingdom shall have no end.
And I believe in the Holy Ghost,
The Lord and giver of life,
Who proceedeth from the Father and the Son,
Who with the Father and the Son together is worshipped and glorified,
Who spake by the Prophets.
And I believe one Catholick and Apostolick Church.
I acknowledge one Baptism for the remission of sins.
And I look for the Resurrection of the dead,
And the life of the world to come.

While the typcial or average christain might believe in the second coming, they do not spend all their time and energy expecting the second coming to come in the next hour or day. As a boy it was explained to me by a presbitarian preacher that the christain lives their life in battlefield between God (and that which is right and proper) and the devil (and that which is morally wrong). The clergyman explained that the christain should believe in God and with the help of God live a good life (as free from sin as possible). The preacher was not concentrating on telling me to make sure that I am ready at a moment’s notice to greet Jesus as he returns to earth in the second comming.

Some parts of the church do appear to have a higher tendency towards millenarianism, what is more scary in some ways by far are some of the “Cargo Cults” and similar groups who hold the view that they by their actions can change the timescale of when the great event will occur. In the case of the Aum cult they appear to have believed that they could by their actions on earth accelerate the coming of the end time.

The cargo cults in the pacific thought that if they imitiated the actions of the american military (doing things like building their own air strip) that all manner of wounderful things would appear from the air. I think that the Aum cult of the 1990s should be classified as a religious movement with a very tendancy towards millenarianism. The Aum cult believed that there would be a war between the cult and the outside world, they held the view that with the aid of a serious of super weapons that they would win this war and usher in a wounderous “new age”. While we are here it is interesting to note that the neo-pagans and mystics who were known in the 1990s as the “New Agers” are also  millenarian. They thought that a wounderful new thing would come to pass and that humans would evolve into something new and glorious as a result of their mystic activities.

In terms of social harm I think we can ignore the effects of people praying to God for him to hurry up with the second comming, but in some cases some people may attempt to speed up the arrival of the end time. It is noteworthy that some non religious people have a tendancy towards millenarianism such as Charles Manson who wanted to incite some form of war. In the case of Manson he wanted to trigger a race war between blacks and whites. While Manson was not a “relgious” figure, he was attempting to create a “goldern age” in which he thought that in the post-race war world he would be able to dominate the black people and be some form of lord and master of many.

I suspect that the Aum cult thought that they could trigger a change on earth which would usher in their new transformed world in which they would be doing much better than others.

Nerve gas cult leader hanged

Dear Reader,

It has come to my attention that the leader (Shoko Asahara) of the horrible nerve gas cult in Japan (Aum Shinrikyo) has been hung in Japan. I first heard of this cult before the nerve gas attack which made it famous for all the wrong reasons (infamous). Some of the tales which were leaking out from this cult were perfectly horrifying, one author in a book on religious cults described some of the deeds of the cult as being like something from a Edgar Alan Poe story. But he did comment that it would be unlikely that Poe would have been able to imagine some of the atrocities which involve modern technology.

The Japanese have a death penalty for murder, I checked and a Law academic (Prof Norio Takahashi) wrote some time ago

In the “serial shooting murder case (Nagayama Incident) (Showa 58-7-8 Police Procedure 37-6 609 pages), the supreme court ruled that the death penalty may be imposed inevitably in consideration of the degree of criminal liability and balance of justice based on a nine-point set of criteria which includes;

  1. degree of viciousness of the crime,
  2. motive of the crime,
  3. how the crime was committed-especially the manner in which the victim was killed,
  4. outcome of the crime especially the number of murdered victims,
  5. sentiments of the victim’s bereaved family members,
  6. impact of the crime on society,
  7. defendant’s age,
  8. defendant’s previous criminal record,
  9. degree of remorse shown by the defendant.

Now if we look at Shoko Asahara we can point out that

  1. The murder weapon causes the victims to suffer greatly before death, this also touches point three.
  2. The motivation for the crime was an attempt to overthrow the state and inhibit the actions of the police.
  3. The crime does involve wanton cruelty.
  4. The attack caused multiple deaths (13) and causes injuries to many other people (1000s)
  5. I have no idea what the different families think about the death sentence, but Minoru Kariya whose father died in another of the cults crimes (the smaller scale nerve gas attack) supported the death sentence.
  6. The crime was intended to have a serious impact on society and the first nerve gas attack was an attempt to inhibit the legal system (it targeted judges involved in a case regarding the cult)
  7. The defendant was an adult at the time of the crime.
  8. The defendant has a criminal record at the time the crime was committed
  9. I am unable to be sure, but from what I have heard the defendant has shown little or no remorse.

So according to the nine points, using the criteria used by the legal system in Japan it appears that Shoko Asahara is a candidate for the death penalty. I have to ask however what is the point of the death penalty ? In a perverse way the “ultimate punishment” renders the criminal incapable of any further punishment. So if we wanted to impose a truely ultimate punishment then the hanging will defeat our attempts to punish the criminal. I will comment shortly on the chemistry of this case.

Nickel extraction where the reaction occurs at the interface

Dear Reader,

Recently I considered the idea of a reaction in which a BTBP reacts with a nickel cation in the aqueous phase before the nickel BTBP complex is extracted. Now let us consider a system where the chemcial reactions only occur at the interface.

We need to consider the amount of the extraction agent at the interface, I will assume for a moment that the concentration of the extractant in the bulk of the organic phase is proportional to the amount of extractant in a given area of the interface. In some real life systems this is not true.

If in a given area two BTBP molecules are present then if a nickel atom is present at the interface then they will have a given probability of being able to extract the nickel during one second. The probability that a nickel atom will be present will be proportional to the concentration of the nickel in the bulk of the aqueous phase. Thus we will have a third order reaction for the extraction of the nickel.

2BTBP(org) + Ni2+(aq) [Ni(BTBP)2]2+(org)

When this reaction exists in isolation we can write

-d[Ni2+aq]/dt = kex[BTBP]2[Ni2+aq]

We then have the backwards reaction (first order reaction) which is

[Ni(BTBP)2]2+(org) → 2BTBP(org) + Ni2+(aq)

When this exists in isolation we can write

d[Ni2+aq]/dt = kstrip[[Ni(BTBP)2]2

We can combine these two kinetics equations when the system reaches equilibrium

Kstrip[Ni(BTBP)2] = kex[BTBP]2[Ni2+aq]

Rearrange to

[Ni(BTBP)2] / [Ni2+aq] = kex[BTBP]2/ Kstrip

Then simplify to

DNi = kex[BTBP]2/ Kstrip

If we were to do some kinetics experiments in a Lewis cell, then it would be possible from both extraction experiments and stripping experiments to calculate the equilibrium distribution ratio.

Second review on serious reactor accidents

Dear Reader,

I have published an update on serious accident chemistry, partly to my horror and also partly to my amazement I understood recently that the work of critically discussing the topic seems to have no end. Keep in mind that critical does not mean carping, critical is to use rational reasoning consider something and then to make a judgement of it.

If you want carping then I have to disappoint you, you will need to look elsewhere. Some years ago as a joke I discussed with some PhD students at Chalmers the idea of the “Journal of Offensive Chemistry” where every paper, referee report, submission and editorial document has to be as rude and obnoxious as possible. We had visions of hateful, spite ridden and nasty comments. Thankfully this journal has never come to exist (well not yet). I imagine it would be rather hard work for the editor of this horrible journal to keep on coming up with new ways to be offensive about papers, I imagine that there would be a limit to the number of times each insult could be used.

I freely admit that some people will not be happy that I have chosen to write about the topic again. I am sure that there are some elements on both the pro and antinuclear side who have made up their minds on some issues before considering the evidence. I suspect that these people may not like having their bubble poked or even burst. I have during the review pointed out some issues in the work of some other writers on the subject.

Some authors on the subject who have strayed have been willing to engage in a reasonable and honest discussion with me, I tend to be more forgiving of these people. But there are some who persist in getting some things wrong even after it has been pointed out to them. As an academic I hold the view that part of my mission in life is to make the world a better place. Part of my work is to spread knowledge / skills / understanding and to confront nonsense and falsehood wherever it might be.

Now these days with the amount of nonsense which exists in the world it seems we have a lot of nonsense, false information and other things to take care of. Now one rather interesting person is Helen Caldicott who is an Australian who was shocked after reading “On the Beach”. Now for a moment I wonder what would have happened if she had read Mary Shelley’s Frankenstein. Both “On the Beach” and Frankenstein are clearly gross distortions and exaggerations of some things which exist in real life.

In Frankenstein, it suggests that electricity can create a monster, should we now be concerned about the use of AEDs to treat heart attacks ? Equally if you watch “Wishmaster” you might be very concerned about making any wish, that is if you think it is a documentary rather than a work of pure fiction. My worry is that novels and feature films are not good education when it comes to driving cars, dating, resolving conficts or science.

Now the thing I do not like about “On the Beach” is the way in which it exagerates fallout, it ignores for example the fact that radioactivity decays away with time. Also the further you get away from the blast site the less of some of the worst of the medium lived high energy photon emitters (such as Zr-95) will be deposited on the ground by fallout. The zirconium-95 from a ground burst tends to be deposited near the blast site in coarser particles while the finer particles are lofted high into the atmosphere. These particles injected into the upper atmosphere tend to take a long time to fall to earth again. During this time they have plenty of time for radioactive decay to occur.

Now lets look for a moment at what Helen writes she wroteShute had loudly protested that the film was a “bastardization” of his work because of its American cast and what he saw as the soft-peddling of the horrors of radiation sickness, which include nausea, vomiting, fever, skin and hair loss, massive ulcers, blisters, burns, emaciation, destruction of the soft tissues, bone marrow depletion, and ultimately inflammation of the membrane around the heart, leading to a slow, agonizing death.”

I am not going to discuss the acting skills of american actors vs non american actors, that would be a mighty silly thing to waste my time on. Now I am also not going to claim that radiation is a big barrel of laughs, to be blunt with you if I did then I would be very stupid. Now Helen wrote about “Radiation Sickness”, the problem is that there is no such disease in my view. There are a series of syndromes which can be caused by radiation. The “Acute Radiation Syndrome” is the closest thing to what the general public think is “radiation sickness”. I would have thought that a medical doctor she would have known better than to use such loose and poor terminology. Now it is interesting that she comments that “inflammation of the membrane around the heart,” (Pericarditis) is the ultimate ending of this condition. I find her choice of language to be rather emotive, but I will let that slide.

I considered the question of “is cardiac issues common in people who have had an acute whole body dose ?“. Now the thing is that I will admit that it is possible to induce cardiac damage in humans with radiation, but the dose required is high. I have checked the ICRP opinion regarding early and late non carcinogenic effects in healthy tissue (ICRP 118), this is a document mainly about the side effects of radiotherapy for cancer. This document does indicate that the α/β value is 2.5 for pericarditis.

The ICRP document indicates that Emami et. al. (1991) found that for whole heart irradation that 40 Gy was required to cause 5 % of people to develop pericarditis within five years when the radiation was divided into 2 Gy fractions. A often in radiotherapy the treatment is divided into a series of doses (fractionation). Now if we assume the classic LQ model for cell survival.

S = exp -(αD + βD^2)

Then if we assume that α = 0.01, then for a 2 Gy dose we can calculate that S is equal to 0.88692. If we repeat this 2 Gy dose 20 times (with plenty of time for sublethal damage to be repaired) then we will get a S value of 0.090718

Now if we assume that the radiation is delivered at a low dose rate (where the beta term disappears) then to get a S value of (which is what we will have after 20 treatments) then the dose required can be calculated using

ln S = -αD

ln S / -α = D =  240 Gy.

Now I hold the view that 240 gray delivered over a month would be exceptionally hard for a person to tolerate for other reasons. I suspect that things like the digestive system would not be able to tolerate about 7.75 Gy per day. Also the blood forming organs would not do very well with this amount of radiation each day. I think that under this exposure senario it is unlikely that pericarditis would play a role.

If we consider a single short pulse of radiation then we can calculate a dose which would be the equilivent. This will be a little harder in terms of maths. Using my GCSE maths I will now attack the problem. We can use successive approximation to deal with the problem.

I have estimated that a single short duration dose of about 9.6 Gy is able to give a person a 5 % chance of the pericarditis within five years. Now I know from the literature that people who get doses of about 10 Gy do not typcially live more than about 1 month. So I think it would be very unlikely for a person to be able to get pericarditis from a one off whole body dose, the only time this radiation effect is likely to be seen is for medical paitents who typically get a very uneven irradation, these uneven irradations are very unlikely under nuclear warfare conditions. Unless the person getting the dose is a worker assembling a nuclear bomb who makes a horrible mistake and causes a criticality to occur during the assembly process.

Now I have to ask the question of why is Helen making these bold claims that simple GCSE maths show to be wrong, I hold the view that things like radiation are sufficently bad that we do not need Helen to invent new horrors.

Solvent extraction of nickel

Dear Reader,

I was thinking about solvent extraction recently, now solvent extraction a bit more than “shake A and B, and the nickel extracts”. Rather than merely shaking things and seeing that the metal goes from one layer to the other (and stopping there) it is important to understand that a lot of things can control the equilibrium position. I was recently thinking about nickel with BTBP.

I made the assumption in this model of the thermodynamics that the nickel reacts with the BTBP in the bulk of the aqueous phase and that no reaction occurs in the organic phase. I make a lot of use of Hess’s law.

Some years ago I was involved in a study of the solvent extraction chemistry of nickel with the BTBP reagents. Here are some equations which I have written which help explain things.

Extraction behavior of nickel(II) using some of the BTBP-class ligands, Ekberg, C., Dubois, I. Fermvik, A., Retegan, T., Skarnemark, G., Drew, M. G. B.,Foreman, M. R. S. and Hudson, M. J. SOLVENT EXTRACTION AND ION EXCHANGE, Volume: 25, Issue: 5, Pages: 603-617, DOI: 10.1080/07366290701512634, Published: SEP-OCT 2007

At low concentrations of C6-BTBP the following equation is true.

Log D = Log K + log [BTBP]

Where D is the distribution ratio, K is an extraction constant and [BTBP] is the concentration of the BTBP in the organic phase. But when the concentration of the BTBP is higher then this equation

Log D = Log K’ + 2.5 log [BTBP]

When it is even higher the best equation becomes

Log D = Log K”

This paper clearly in figure 4 shows that the nickel distribution ratio reaches a plateau when the BTBP concentration reaches a value of about 1 mmol for C6 BTBP.

What I want you to do is to consider a BTBP which distributes between the organic and the aqueous phase.

Kd(BTBP) = [BTBP]org/[BTBP]aq

Then if the BTBP is able to bind to the nickel we can write the following two equations

k1 = [NiBTBP]aq/[Ni]aq[BTBP]aq

β2 = [Ni(BTBP)2]aq/[Ni]aq[BTBP]2aq

And then we combined these equations we get

[Ni]aq / total aqueous nickel = 1 / (1 + k1[BTBP]aq + β2[BTBP]2aq)

[NiBTBP]aq / total aqueous nickel = k1[BTBP]aq / (1 + k1[BTBP]aq + β2[BTBP]2aq)

[Ni(BTBP)2]aq / total aqueous nickel = β2[BTBP]2aq / (1 + k1[BTBP]aq + β2[BTBP]2aq)

Now we are about to add the physical distribution of the three forms of nickel between the aqueous and organic layers, we will use equations like this

Kd(Ni) = [Ni]org/[Ni]aq

Kd(NiBTBP) = [NiBTBP]org/[NiBTBP]aq

Kd(Ni(BTBP)2) = [Ni(BTBP)2]org/[Ni(BTBP)2]aq

I want you to combine these equations to get to now give us (take a deep breath), and trust me this will be pleasureable !

DNi = (Kd(Ni) / (1 + k1[BTBP]aq + β2[BTBP]2aq) + (k1[BTBP]aq/Kd(NiBTBP) / (1 + k1[BTBP]aq + β2[BTBP]2aq)) + ( β2[BTBP]2aqKd(Ni(BTBP)2)/ (1 + k1[BTBP]aq + β2[BTBP]2aq))

Now we take another step to include the constant Kd(BTBP) we get an even bigger equation which is harder to write here on wordpress. But I imagine that you will have no problem with it.

%d bloggers like this: