[serbianguy]

Hello guys !

I'm new in this forum, and I registered upon suggestion from my (bio)chemical friend. We disagree whether two problems have a singular or many infinite solutions. Your comments are wellcome ! Here are the problems

1. Find a, b, c, d, e, and f (unknown and desired numbers) for the following receipe:

a ml of the protein stock solution whose concentration is 10mM and pI = 8.5, Mr = 1000
b ml of 2M stoc solution of K2HPO4*7H20
c grams of ATP
d ml of 1M stock solution of sodium acetate
f ml of 1M stock solution of HEPES
-------------------------------------------
final pH=7.6
final volume V = 100 ml
final concentrations:
2mM protein,
7% K2HPO4,
10 mM ATP,
2mM sodium acetate,
1% HEPES
 
Please note: both initial and final concentrations of the reagents and both initial and final pH (and pI) are predetermined.

2.  How many mililiters and grams should be taken of each solution (substance) below, so that the pH of a final solution is pH =  6.8 and final concentrations 4mM(protein), 2mM (FeCl3), 1% (sodium acetate), 3mM (HEPES), 0.5mM (ATP) ?

a ml of 10 mM protein solution whose pI= 8.5 , Mr = 1000
b ml of 7mM FeCl3
c ml of 5 % sodium acetate,
d ml of 8 mM HEPES
e  micrograms of ATP

Looking forward to your suggestions,

Dusan

[Borek]

How many mililiters and grams should be taken of each solution (substance) below, so that the pH of a final solution is pH =  6.8 and final concentrations 4mM(protein), 2mM (FeCl3), 1% (sodium acetate), 3mM (HEPES), 0.5mM (ATP) ?

a ml of 10 mM protein solution whose pI= 8.5 , Mr = 1000
b ml of 7mM FeCl3
c ml of 5 % sodium acetate,
d ml of 8 mM HEPES
e  micrograms of ATP

It is either/either. Either you have known concentrations of all components - then your pH is given by the solution composition (and it is either 6.8 that you want or it is something else) or you have to find a, b, c d and e such that the pH of the solution is 6.8. You can't have both at the same time, just like you can't have 1M solution of HCl with pH=7.0.

In the second case there is no single solution to the question. It would be hard to analyze exactly your solution, but let's try with the other, similar example that will be easier to deal with.

Let's assume we have three reagents - benzoic acid (pKa=4.19), acetic acid (pKa=4.75), sodium hydroxide, and we want to prepare pH=4.0 buffer. We want to know how much (a, b and c) of each substance we need to prepare buffer.

First of all, we can ignore acetic acid and prepare buffer just using benzoic acid.

Second, we can ignore bezoic acid and prepare buffer just using acetic.

Third, we can mix both acids at any ratio we want and neutralize the mixture to pH=4.00.

As we can mix the solution at any ratio, there is infinite number of ways such buffer can be prepared.

Your situation is similar

[serbianguy]

How many mililiters and grams should be taken of each solution (substance) below, so that the pH of a final solution is pH =  6.8 and final concentrations 4mM(protein), 2mM (FeCl3), 1% (sodium acetate), 3mM (HEPES), 0.5mM (ATP) ?

a ml of 10 mM protein solution whose pI= 8.5 , Mr = 1000
b ml of 7mM FeCl3
c ml of 5 % sodium acetate,
d ml of 8 mM HEPES
e  micrograms of ATP

It is either/either. Either you have known concentrations of all components - then your pH is given by the solution composition (and it is either 6.8 that you want or it is something else) or you have to find a, b, c d and e such that the pH of the solution is 6.8. You can't have both at the same time, just like you can't have 1M solution of HCl with pH=7.0.

I agree, I did not express myself correctly: these are actually two problems, as you implied: to find the concentrations for a given pH, or to find the pH of a mixture ! One way or another, these two problems have a singualr solution, right ?

In the second case there is no single solution to the question. It would be hard to analyze exactly your solution, but let's try with the other, similar example that will be easier to deal with.

Let's assume we have three reagents - benzoic acid (pKa=4.19), acetic acid (pKa=4.75), sodium hydroxide, and we want to prepare pH=4.0 buffer. We want to know how much (a, b and c) of each substance we need to prepare buffer.

First of all, we can ignore acetic acid and prepare buffer just using benzoic acid.

Second, we can ignore bezoic acid and prepare buffer just using acetic.

Third, we can mix both acids at any ratio we want and neutralize the mixture to pH=4.00.

As we can mix the solution at any ratio, there is infinite number of ways such buffer can be prepared.

I do not agree on this one. The situation is not simillar because in your example you imply chemical reaction (neutralization) whereas my example does not imply any reaction; mixing different salts isn't really a reaction (even if there is a chemical reaction, we don't care about it as long as all the ionic and molecular species present in the solution retain their identity !). Secondly, this example is not about making a buffer, but making a solution and determining its pH. Using purely mathematical logic, since the variables that determine the value of the right side of the equation are determined and the variables that determine the value of the left side of the equation are also determined, then some x (ox x-es) that are obtained by any mathematical operation applied to these variables must also be singular.
The problem is that I'm biologist and that I do not know HOW TO find these unknowns.
So, please HELP :-) !

[Borek]

Hit quote to answer

I do not agree on this one. The situation is not simillar because in your example you imply chemical reaction (neutralization) whereas my example does not imply any reaction; mixing different salts isn't really a reaction (even if there is a chemical reaction, we don't care about it as long as all the ionic and molecular species present in the solution retain their identity !).

No, situations are perfectly comparable - there is a reaction that goes in your solution. You start with HEPES (an acid) and you neutralize it with sodium acetate (Bronsted-Lewis base). Just mixing those two reagents give pH of around 6.6 (although ionic strength of the solution is a little bit too high, so calculated result can be off by 0.1 or 0.2 pH unit). See attached picture (0.624M is just a 5% solution).

There is also other reaction (or rather set of reactions) - Fe³⁺ behaves as an acid, lowering solution pH, but it also can precipitate in the form of Fe(OH)₃ and gets partially complexed by Cl^- and acetate, so the final composition of the solution can be quite complicated. But if FeCl₃ is the other acid present, you have exactly the same situation as in my example - two acids neutralized with base to get required pH. Infinite number of solutions.

Secondly, this example is not about making a buffer, but making a solution and determining its pH.

Either/either. It is either about calculating pH of the solution (in which case it is difficult equilibrium problem) that contains 4mM(protein), 2mM (FeCl3), 1% (sodium acetate), 3mM (HEPES), 0.5mM (ATP)  - these were given, or it is about preparing the solution of pH 6.8 using a, b, c, d and e amounts of reagents. It can't be both at the same time, and it is still not clear for me what do you want to do. I suppose it is the first case. If so, it is relatively simple problem of concentration conversion, but once the solution is ready you can't change its pH (unless you will ad some acid or some base).

Using purely mathematical logic, since the variables that determine the value of the right side of the equation are determined and the variables that determine the value of the left side of the equation are also determined, then some x (ox x-es) that are obtained by any mathematical operation applied to these variables must also be singular.
The problem is that I'm biologist and that I do not know HOW TO find these unknowns.

I am not sure what you refer to. Please elaborate. And remember, that you don't have one equation, but rather set of equations.

[serbianguy]

Either/either. It is either about calculating pH of the solution (in which case it is difficult equilibrium problem)

Yes, indeed, you understood well (I'm sorry I did not explain well). I'm interested how to solve this difficult equilibrium problem that you were referring to, and then how to determine the amount of acid/based needed to fit the pH to 6.8

Using purely mathematical logic, since the variables that determine the value of the right side of the equation are determined and the variables that determine the value of the left side of the equation are also determined, then some x (ox x-es) that are obtained by any mathematical operation applied to these variables must also be singular.
The problem is that I'm biologist and that I do not know HOW TO find these unknowns.

[/quote]I am not sure what you refer to. Please elaborate. And remember, that you don't have one equation, but rather set of equations.[/quote]

I was referring to the system of equations that you think of as well.

[serbianguy]

By the way, how did you get this picture using BATE ? I'm still a dummy for it (and in general dummy for computers :-)

[Borek]

Yes, indeed, you understood well (I'm sorry I did not explain well). I'm interested how to solve this difficult equilibrium problem that you were referring to, and then how to determine the amount of acid/based needed to fit the pH to 6.8

Start here:

http://www.chembuddy.com/?left=pH-calculation&right=general-pH-calculation

By the way, how did you get this picture using BATE ?

It is not BATE, it is (not yet released) pH calculator that will be part of the Buffer Maker. Release planned for December.