[oliphant]

I have reconstructed eqn 11.16 for a complex process.

Assume first, that the system contains citric acid and sodium hydroxide at a pH of 7.5, and the concentration of citric acid is 0.0268M.  Using this equation, it is relatively easy to show that the concentration of sodium hydroxide must be 0.0799M, which makes sense, because it is about 3 times the amount of citric acid in the solution, and, to a zeroeth approximation, all the citric acid is ionized.  I should state here, that this setup doesn't really care if the pH is 7.5 or 7.9, so relative activities are probably not important.  The purpose of this step is to merely derive some number for the concentration of sodium hydroxide.  The equation that I used, written in LaTeX is here:

$$
\frac{C_a\sum_{i=1}^n i K_{ai} [H^+]^{n-i}}{[H^+]^n+\sum_{i=1}^nK_{ai}[H^+]^{n-i}} +
\frac{K_w}{[H^+]} =
\frac{K_bC_b[H^+]}{K_w+K_b[H^+]} + [H^+]
$$

To calculate this C_b, I use K_ai = [4.07e-07; 1.7378e-05; 7.413102e-04] and K_b=0.63096.  [H^+] is calculated in the usual way, using 10^{-7.5} for this condition.


Next, hydrogen sulfide is bubbled through the solution so that the solution attains a pH of 6.8.  How much hydrogen sulfide is ionized in the solution?  To do this, I regenerated eqn 11.16 for three species, the base (NaOH), the acid (citric acid) and the other acid (hydrogen sulfide.)  Here is a LaTeX form for this equation:

$$
\frac{C_a\sum_{i=1}^n i K_{ai} [H^+]^{n-i}}{[H^+]^n+\sum_{i=1}^nK_{ai}[H^+]^{n-i}} +
\frac{K_w}{[H^+]} +
\frac{C_c\sum_{i=1}^m i K_{ci} [H^+]^{m-1}}{[H^+]^m+\sum_{i=1}^mK_{ci}[H^+]^{m-i}} =
\frac{K_bC_b[H^+]}{K_w+K_b[H^+]} + [H^+]
$$

Please see the attached file to view the equations.  The file term.m is an octave file to calculate the complex sum term. (Well, I tried to attach this but it was rejected, it is appended below.)


In this equation, I use K_ci=[1.096478e-12; 9.120184e-08] and solved for C_c = 3.94e-09.  

Is this correct?  Is my approach correct?  This seems surprisingly small.  

Please comment and critique my approach to ths question.  Thank you.



Here is the term.m file:

$$ usage:                                                                                              
$$   term(c,k,ph)                                                                                    
$$                                                                                                      
$$ Calculates the sum term where hi = 10^(-ph),                                                          
$$ the concentration of the chemical is c,                                                              
$$ and the Ka of each ionization is in k                                                              
$$ k must be an ordered row vector, where                                                              
$$ k(1) is for the first ionization,                                                                    
$$ k(2) is for the second ionization, etc.                                                              

$$ Created: March 2011                                                                                  
$$ Version: 0.1                                                                                        
$$ Keywords: pKa                                                                                        

function res = term(c,k,ph)
n = rows(k)
s1 = 0.0
s2 = 0.0
h = 10**(-ph)

for i = 1:n
  s1 = s1 + k(i) * (h**n-i)
  s2 = s2 + i * k(i) * (h**n-i)
endfor

res = (c*s2)/((h**n)+s1)
endfunction

[oliphant]

By the way, please forgive my newbidity.  I couldn't get the latex thing to work, so I had to attach the file.  Thank you for your endless understanding and deep mercy on my soul.

[Borek]

Eqn 11.16 from http://www.chembuddy.com/?left=pH-calculation&right=pH-salt-solution ?

What is the question that you are solving? I have a feeling it can be solved using much simpler approach.

[oliphant]

Yes, I modified 11.16 on chembuddy.com, it seems to me that this forum is associated to that site and Mr. Borek is the gentleman who writes chembuddy.com.  Thank you for the useful equations there.  I am enjoying this immensely.

The question is simple.  A sodium citrate buffer is prepared to create pH 7.5, the amount of citric acid in the solution must be held at 0.0268M.    Sodium hydroxide concentration is calculated to be 0.079977...M, which seems physically correct because citric acid is triprotic.  

The first question is, how much hydrogen sulfide is absorbed to bring the solution to a pH of 6.8?  A nanomolar answer seems incredulous.  

So there are three components to this problem, and I assigned citrate as species A (notice that the Ka matrix has three elements), sodium to species B (so the term on the right referring to species B is sodium hydroxide), and finally, hydrogen sulfide to species C (Kc matrix has two elements.)   I decided to use eqn 11.16 my modification because of the clear warning on the chembuddy.com web site which states that it must be used when the difference between pKa1 and pKa2 and pKa3 are less than 3.  Кстати, я также славянин и несыт без наказания.

Честно говоря, загадка не упражнение из учебника, а относится к моей работе.

[Borek]

Hard to deny I am who I am

Please read:

http://www.chembuddy.com/?left=Buffer-Maker&right=buffer-calculation

Do you need to solve the problem just once, or is it something that will be done again and again? If just once, check if it won't be faster to simply use pH calculator built into Buffer Maker - play with concentrations till you get the answer you need by trial and error. Not the most elegant approach, but you will have the answer in 5 minutes. You don't even need to buy the program, free trial will be enough.

I agree nanomolar amount doesn't sound correct, my calculations show like you need around 0.0031M.

и несыт без наказания

I must say my Russian fails me here - I got everything else, but not this part 

[oliphant]

I have to understand the equations because that's the way I am.   "несыт без наказания"-  unsatisfied without punishment.  Maybe I should have said without difficulty. 0.0031M seems more correct to me.   

Thank you for your time.

[Borek]

"несыт без наказания"-  unsatisfied without punishment.  Maybe I should have said without difficulty.

OK, got what you mean