Doubt about calculating the solubility of lamivudine (3TC)

[Kathe]

For a weak base and for pH>pKa +2 $$St=[ B ]+[BH^{+}];

[ B ]=S{_{0}};
[BH^{+}]=[ B ]\cdot[H{_{3}}O]/K {_a}=S{_{0}}\cdot[H{_{3}}O]/K {_a};

St= S{_{0}}+S {_{0}}\cdot[H{_{3}}O]/K {_a}=S{_{0}}\cdot (1+[H{_{3}}O]/K {_a});$$
For pH <pKa-2
$$St=[ B ]+[BH^{+}];

[BH^{+}]=\sqrt{Kps};

[ B ]=[BH^{+}]\cdot K{_a}/[H{_{3}}O]=\sqrt {Kps}\cdot K {_a}/[H{_{3}}O];

St=\sqrt {Kps} + \sqrt {Kps}\cdot K{_a}/[H{_{3}}O]=\sqrt {Kps}\cdot (1+K {_a}/[H{_{3}}O])$$;

 

[epenguin]

]

That is clearer, at least typographically. And some changes still to make there as well, haven't you noticed?

I recognise that you are saying that for a weak base (with only one insoluble salt BHCl) total solubility S_t at lower pH is given by the last of the first set of equations, but at higher pH by the corresponding one in the second set. There is a sharp transition between the region where one or the other formula is applicable represented by a kink in the pH-solubility curves that we have seen. Whether anybody else who has not gone a bit into the theory could recognise that that is what you are saying, I have some doubts. So you are still scarcely beyond the 1st square for stating what the question is.

The point of transition between the two regimes is very sharp, given by a precise equation which you should give, rather than your very permissive inequalities which in fact I don't think even always hold.
It reads like notes towards section 1or 2 of homework help. Read a few other questions in the help forums, there is not this seeming reticence.

 

[epenguin]

To make it clear, the equations predict solubility curves like this.

 

[Kathe]

To make it clear, the equations predict solubility curves like this.

View attachment 246976

Exact! This is the typical solubility curve of a weak base. At very alkaline pH, at least 2 units higher than pKa, [ B ] >> [BH +] and [ B ] is about S0. At pH = pKa la [ B ] = [BH +] and at pH less than at least 2 units with respect to pKa we have that [BH +] >> [ B ]. In this case a further plateau is reached in which the solubility of BH + becomes equal to that of the BHCl salt. The graph of the 3tv is particular because it presents an anomaly in the behavior and consequently in the solubility curve. Moreover, it seems that this effect is due to the use of HCl (it is demonstrated by adding KCl and seeing that due to the presence of the common ion the solubility is further reduced) and not of other acids.

 

[epenguin]

Maybe I have been over-severe in trying to coax the student to set out what the question is, and maybe the question has been generally understood. In case any reader has not latched on, and to have an agreed clear starting point I will give how I would frame the question:

The total solubility S_t of a base to which a base to which acid is added, is, as a function of [H⁺] described by the equation

S_t = S₀(1 + [H⁺]/K_a). ...(1)

at high pH. There is a sharp break in the curve and the equation that describes solubility at lower pH is

S_t = √K_sp.(1 + K_a/[H⁺]). ...(2)

where K_sp is the solubility product of the (chloride – we are considering addition of HCl) salt of B

K_sp = [ BH⁺][Cl^-] ...(3)

(The student should describe exactly where this breakpoint is).

The corresponding curves have the general appearance as in #38 *

The substance (±)-3TC has the more complicated solubility curves shown in the attachment to #26 ( a calculated version is in #27). This is explained by the formation of a more complicated salt, termed the "2:1" complex, which precipitates at these intermediate pHs, has been isolated and proved to have the composition B.BH⁺Cl^- or B₂HCl.

The student has been unable to calculate the more complicated curves that would describe this situation and asks guidance.

She should now proceed to set up as per section 2 of the homework template the relevant equations, with sufficient indication of what they represent, and numbered to ease discussion. Including those already given (need typographical corrections). And then as per Section 3 of the template indicate attempts at the calculation or reasonings.

*,further commented later.

 

[epenguin]

Note on #40

I had to illustrate the general appearance of these curves in #38 because there are actually no adequate illustrations of it in the textbook extract given by the student. Such curves have a characteristic feature – the vertical distanceFrom the peak singularity to the height where the curve levels off at low pH is equal to B₀. Student should be able to work out why, and why this corresponds to the formula which may also not be evident at first sight. At first sight also the textbook curves 34.2, 34.3 seem to be missing this unavoidable feature - at the top they look just flat. But this is because the solubility is being expressed logarithmically – there are three orders of magnitude difference between B₀ and the concentration of a saturated salt solution, so the low-pH dip is practically not noticeable.The vertical coordinate in the case our problem (fig 34.4) is on the other hand linear.

 

[Kathe]

Maybe I have been over-severe in trying to coax the student to set out what the question is, and maybe the question has been generally understood. In case any reader has not latched on, and to have an agreed clear starting point I will give how I would frame the question:

The total solubility S_t of a base to which a base to which acid is added, is, as a function of [H⁺] described by the equation

S_t = S₀(1 + [H⁺]/K_a). ...(1)

at high pH. There is a sharp break in the curve and the equation that describes solubility at lower pH is

S_t = √K_sp.(1 + K_a/[H⁺]). ...(2)

where K_sp is the solubility product of the (chloride – we are considering addition of HCl) salt of B

K_sp = [ BH⁺][Cl^-] ...(3)

(The student should describe exactly where this breakpoint is).

The corresponding curves have the general appearance as in #38 *

The substance (±)-3TC has the more complicated solubility curves shown in the attachment to #26 ( a calculated version is in #27). This is explained by the formation of a more complicated salt, termed the "2:1" complex, which precipitates at these intermediate pHs, has been isolated and proved to have the composition B.BH⁺Cl^- or B₂HCl.

The student has been unable to calculate the more complicated curves that would describe this situation and asks guidance.

She should now proceed to set up as per section 2 of the homework template the relevant equations, with sufficient indication of what they represent, and numbered to ease discussion. Including those already given (need typographical corrections). And then as per Section 3 of the template indicate attempts at the calculation or reasonings.

*,further commented later.

Thanks 1000 Epiguin ! In fact now the question is well formulated and I hope someone else can intervene to help us resolve the issue. My only doubt is that perhaps users could "snub" old posts in favor of new ones. Maybe, initially, having badly formulated the question, I involuntarily dismissed many users but I hope that they will reconsider and at least take a look at the question. Thank you so much for what you are doing!

 

[epenguin]

Nobody here is likely to help until they see you help yourself by setting out the necessary equations as per paragraph 2 of the homework help template, of which 3 are ready but not complete as I have pointed out, and others are necessary, then possibly a stab at para 3, Attempt at solution.

The problem is more challenging than average for this section of the site, but limited to calculating the curve in question is not as difficult as all that.

 

[jim mcnamara]

@Kathe
We cannot help you without your help. For me, most of your posts are exceedingly hard to decipher. I actually tried to decipher some broken latex and fixed it to give you some help on how to do that. PF helpers cannot go much further than that. Please note that the "ball is in your court" now, it is your turn to step up and help us to help you. We get that it is an interesting problem. Pharmacologists and chemists of all types need to know latex in order to communicate with peers, for example.

 

[Kathe]

@Kathe
We cannot help you without your help. For me, most of your posts are exceedingly hard to decipher. I actually tried to decipher some broken latex and fixed it to give you some help on how to do that. PF helpers cannot go much further than that. Please note that the "ball is in your court" now, it is your turn to step up and help us to help you. We get that it is an interesting problem. Pharmacologists and chemists of all types need to know latex in order to communicate with peers, for example.

Hello Jim Mcnamara, I tried to use Latex but it came out a very long formula that I had to break with ";" because I didn't know how to wrap up. I also didn't understand which formula to use for the division and that's why I kept using the "/". Unfortunately if I have been reluctant to use it it is because it is not a language familiar to me and using mostly the smartphone it became even more complex to write any formula. But I understand that it makes the reading of the formulas easier for this I will undertake to make the posts more understandable!

 

[Kathe]

Not knowing how to use the Latex well, I attached a word file where I reported the equations in an orderly manner.

 

[epenguin]

I don't know what you see on your iPhone but clicking on your attachment all I see on my iPad is

A (eg. by 2 units)

once repeated.I guess on i-phone you can see posts including your own as they are meant to be seen. Even before posting using the preview button bottom right. Re LaTex if you can do subscripts and superscripts for one thing that needs them, you can do them for another, therefore your #36 looks careless, especially after your attention has already been drawn to this.
Fractions: For the fractions in the equations so far it would be acceptable to keep them on one line as they are, but soon you will probably need the fraction thing. I do not know if you are using some other version of LaTex; if slightly tedious there is nothing enormously difficult about them in the site version https://www.physicsforums.com/help/latexhelp/. You can save some subscripts if you write [H⁺] as most people prefer instead of [H₃⁺O].

In the usual thread on this forum a student posts #1 consisting of standard homework template paras. 1, 2, 3 and then we can start to solve the problem collaboratively in as many posts as it takes – you can see what the sort of average of that is. Here we are on #40 and have not got as far as completing section 2 of #1. This is becoming unreasonable. I Will not answer your next post unless it is an attempt at a complete para 2, and a shot at 3 .

 

[Kathe]

I don't know what you see on your iPhone but clicking on your attachment all I see on my iPad is

A (eg. by 2 units)

once repeated.I guess on i-phone you can see posts including your own as they are meant to be seen. Even before posting using the preview button bottom right. Re LaTex if you can do subscripts and superscripts for one thing that needs them, you can do them for another, therefore your #36 looks careless, especially after your attention has already been drawn to this.
Fractions: For the fractions in the equations so far it would be acceptable to keep them on one line as they are, but soon you will probably need the fraction thing. I do not know if you are using some other version of LaTex; if slightly tedious there is nothing enormously difficult about them in the site version https://www.physicsforums.com/help/latexhelp/. You can save some subscripts if you write [H⁺] as most people prefer instead of [H₃⁺O].

In the usual thread on this forum a student posts #1 consisting of standard homework template paras. 1, 2, 3 and then we can start to solve the problem collaboratively in as many posts as it takes – you can see what the sort of average of that is. Here we are on #40 and have not got as far as completing section 2 of #1. This is becoming unreasonable. I Will not answer your next post unless it is an attempt at a complete para 2, and a shot at 3 .

I explain to you! As latex I used an automatic editor

https://www.codecogs.com/latex/eqneditor.php
But from the mobile it turns out to me however complicated because you click on a box and another one is selected.
With PC I used word and in fact I have attached a docx file to make the formulas understandable. I read from the phone but since you can't do it I thought I'd convert it to pdf. I also tried to turn word into latex but I couldn't. Let me know if you can open and view the pdf.

 

[epenguin]

OK I can read that now. Unfortunately I do not have the software or the skills to change that into something others can read here. Hopefully, someone else will volunteer to do this for you. Once you have one formula in LaTex code you can cannibalise it and get any other formula in latex code that needs only the same symbols. Awaiting this, I can give some positive advice.

About the first word. Please translate this into English.

We think order of things reflects comprehension as well as comprehensibility. So you should take out the equations that are always true and put them before the section which concerns things only sometimes, or conditionally, true e.g. under the different pH conditions. So generally true equations (I refer to them by line number not equation number) to take out and put first are 14, 15, 13, 2 (=11 and should have subscript). More equations than necessary will be unhelpful, we can safely eliminate Lines 4-6 even if they are true and stay part of your background knowledge. (12 is actually derived from 13, you could indicate this in the text with 12 ⇒ 13. The derivation depends on another very general equation that comes into all ionic equilibria that it is indispensable to include in the general equation section.) You could condense 8,9 and 17, 18 into single lines. Set out like this it will also be more helpful for your later revision than just a mass of formulae you might not easily see clear though any more. It would be convenient for others trying to follow if you list the numerical constants of the particular example we are treating. And number the equations.

For substance, you will not be able to understand the the complicated system of the problem unless you first understand the simpler case you are talking about above and that produces the behaviour in #38. Your comments so far do not give total confidence that you do understand this. You would have to be able to obtain the pH and other details of that maximum point, more than once asked. If your textbook seem a bit sketchy on that, the authors probably think it is the sort of thing pretty obvious to their readers. Make an attempt, this might go in either section 2 or 3. This is all about the background and a simple case. This will not suffice to to treat the complex case of the question because you have not yet included an equation specific to this question.

It begins to sound like quite a formidable lot of stuff to do but this would all be considered ordinary, even elementary routine in your field!