Potassium Phosphate Buffer

[qbslug]

So I want to make a Potassium Phosphate Buffer from monobasic and dibasic forms of potassium phosphate because it was recommended for doing circular dichroism scans due to its low absorption in the UV region. However I don't understand the proportions of mono basic and dibasic forms of potassium phosphates used.

The pKa of potassium Phosphate is 7.2. So if I want a buffer with pH 7.2 then according to the henderson-hasselbalch equation the recipe should call for equal parts of KH2PO4 and K2HPO4. However according to a chart I found the proportions depend on total concentration and it turns out the molar fraction of dibasic form is closer to 0.678 for a 0.05M concentration at pH 7.2. Obvious disagreement with H-H equation which would give molar fraction of 0.5.

So why does the henderson hasselbalch equation seems to fail and how do I correctly calculate the molar ratio of the two potassium phosphate forms?
Or maybe there is a better buffer for circular dichroism (i.e. low UV absorption) experiments?

 

[Borek]

The more concentrated the solution the higher the ionic strength and the more important are thermodynamic corrections. HH equation holds, but it requires use of activities, not concentrations.

Compare www.chembuddy.com/?left=pH-calculation&right=ionic-strength-activity-coefficients

 

[epenguin]

Yes, these effects are surprisingly strong, especially with phosphate where half the ions have two charges. What final molarity do you want? Practical workers do not calculate it - they make two solutions of mono- and bi-phosphate both of that concentration and add one to the other while stirring, monitoring with a pH meter until the desired pH is reached.

If you have to play around with the concentration of the substance whose dichroism (or any other property) you are investigating remember to dilute it into this same buffer, not into water if the pH is important, because if you dilute it into water you will change its pH.

 

[qbslug]

Thanks, that makes some sense. But now wouldn't we be caught in a catch 22; we need the concentrations to figure out the ionic strength but then we also need the ionic strength to figure out the concentrations from the altered pKa and HH equation. This got complicated real quickly.
I don't have a reliable pH meter which is why I need to know how calculate it precisely.

 

[qbslug]

Im trying to make a buffer for tubulin and using circular dichroism - I just need the buffer to be ~ pH 7.4 and to be transparent in the 185-240nm region. This mono/dibasic potassium phosphate buffer does this but seems needlessly complicated. Would monobasic potassium phosphate with sodium hydroxide be sufficient also? But once again I'm not sure how to calculate the proper proportions of KH2PO4 and NaOH - do I assume NaOH dissociated completely and just figure out the KH2PO4 concentration?

 

[Borek]

Using NaOH/KH₂PO₄ doesn't change anything - it is the final composition of the solution that counts, not the way the solution was prepared. And while you replace some of the K⁺ with Na⁺, final ionic strength of the solution is identical in both cases.

If you can't find good and ready recipe, check this - it should calculate a correct, ionic strength corrected buffer recipe, at least as long as ionic strength is not too high. Generally speaking we don't have a good theory allowing such calculations for ionic strengths higher than about 0.1-0.2, in some cases 0.5. Some even limit this range to just 0.1.

 

[Darwin123]

So I want to make a Potassium Phosphate Buffer from monobasic and dibasic forms of potassium phosphate because it was recommended for doing circular dichroism scans due to its low absorption in the UV region. However I don't understand the proportions of mono basic and dibasic forms of potassium phosphates used.

The pKa of potassium Phosphate is 7.2. So if I want a buffer with pH 7.2 then according to the henderson-hasselbalch equation the recipe should call for equal parts of KH2PO4 and K2HPO4. However according to a chart I found the proportions depend on total concentration and it turns out the molar fraction of dibasic form is closer to 0.678 for a 0.05M concentration at pH 7.2. Obvious disagreement with H-H equation which would give molar fraction of 0.5.

So why does the henderson hasselbalch equation seems to fail and how do I correctly calculate the molar ratio of the two potassium phosphate forms?
Or maybe there is a better buffer for circular dichroism (i.e. low UV absorption) experiments?

The solubility and equilibrium constants of many reactions vary with the concentration of ions due to the Yukawa-type screening of Coulomb potentials. The effect of electrolytic concentration is usually characterized by a parameter referred to as the “ionic strength”. One approximation commonly used to characterize the effect of electrolytes is the Debye-Hukel formula.
Here is an article on ionic strength.
http://en.wikipedia.org/wiki/Ionic_strength
“The ionic strength of a solution is a measure of the concentration of ions in that solution. Ionic compounds, when dissolved in water, dissociate into ions. The total electrolyte concentration in solution will affect important properties such as the dissociation or the solubility of different salts. One of the main characteristics of a solution with dissolved ions is the ionic strength.
…
The ionic strength plays a central role in the Debye–Hückel theory that describes the strong deviations from ideality typically encountered in ionic solutions. It is also important for the theory of double layer and related electrokinetic phenomena and electroacoustic phenomena in colloids and other heterogeneous systems. That is, the Debye length, which is the inverse of the Debye parameter (κ), is inversely proportional to the square root of the ionic strength. Debye length is characteristic of the Double layer thickness. Increasing the concentration or valence of the counterions compresses the double layer and increases the electrical potential gradient.”

Here is an article on the Debye-Hukel theory, which I think is sufficiently accurate for your purposes.
http://en.wikipedia.org/wiki/Debye–Hückel_theory
“The Debye–Hückel theory was proposed by Peter Debye and Erich Hückel as a theoretical explanation for departures from ideality in solutions of electrolytes.[1] It was based on an extremely simplified model of the electrolyte solution but nevertheless gave accurate predictions of mean activity coefficients for ions in dilute solution. The Debye-Hückel equation provides a starting point for modern treatments of non-ideality of electrolyte solutions.[2]

Here is an article where the Debye-Hukel formulas are derived.
http://www.public.iastate.edu/~xsong/paper/xs_45.pdf
“A molecular Debye-Hückel theory and its applications
to electrolyte solutions
In this report, a molecular Debye-Hückel theory for ionic fluids is developed. Starting from the macroscopic Maxwell equations for bulk systems, the dispersion relation leads to a generalized Debye-Hückel theory which is related to the dressed ion theory in the static case. Due to the multi-pole structure of dielectric function of ionic fluids, the electric potential around a single ion has a multi-Yukawa form.”

Here is an article in which I think the Debye-Hukel theory is used.
http://www.aseanfood.info/Articles/13006695.pdf
“ROLE OF IONIC STRENGTH IN BIOCHEMICAL PROPERTIES OF SOLUBLE FISH PROTEINS ISOLATED FROM CRYOPROTECTED PACIFIC WHITING MINCE
Biochemical characteristics of Pacific whiting muscle proteins extracted at acidic, neutral and alkaline conditions were investigated as affected by various ionic strength levels.”

 

[Darwin123]

So I want to make a Potassium Phosphate Buffer from monobasic and dibasic forms of potassium phosphate because it was recommended for doing circular dichroism scans due to its low absorption in the UV region. However I don't understand the proportions of mono basic and dibasic forms of potassium phosphates used.

The pKa of potassium Phosphate is 7.2. So if I want a buffer with pH 7.2 then according to the henderson-hasselbalch equation the recipe should call for equal parts of KH2PO4 and K2HPO4. However according to a chart I found the proportions depend on total concentration and it turns out the molar fraction of dibasic form is closer to 0.678 for a 0.05M concentration at pH 7.2. Obvious disagreement with H-H equation which would give molar fraction of 0.5.

So why does the henderson hasselbalch equation seems to fail and how do I correctly calculate the molar ratio of the two potassium phosphate forms?
Or maybe there is a better buffer for circular dichroism (i.e. low UV absorption) experiments?

The effect of Debye-Hukel screening will always be there at high ionic strengths. I don’t think you can eliminate the effect by using another buffer.
I suggest that you use the phosphate buffer. Maybe you should use a mixture of buffer that is less concentrated than the amount recommended on the package.. Mix the buffer the way you want and then measure the pH that results.
Buffer is cheap. So trial and error won't cost too much. If you want to do biologically relevant measurements, you may want to use a buffer solution with an ionic strength comparable to that of the biological system under consideration.
Manufacturers like to recommend high concentrations of buffer comparable so the changes in ionic strength are negligible in your experiment. However, maybe you want to take into account the ionic strength in the biological system that you are studying. So you may not want to use the buffer strength on the package.
If you still feel that you want a different buffer, consider the following.
http://www.life.illinois.edu/biochem/455/Lab%20exercises/Photometry/spectrophotometry.pdf
“Buffers that contain carboxyl and/or amino groups absorb light below 220 nm, and therefore should not be used when working in this wavelength range. Buffers with very low absorbance in the far-UV include phosphate, cacodylate and borate.”

http://what-when-how.com/molecular-biology/absorption-spectroscopy-molecular-biology/
“Buffers with negligible absorbance in the far-UV include phosphate, cacodylate, and borate. Detailed procedures for the measurement of difference spectra are found in Ref. 1.”


When you do your experiment, or read about a previously done experiment, please keep in mind both the pH and the ionic strength of the system that is being studied.
The ionic strength makes a difference. See my other post.

 

[Darwin123]

Im trying to make a buffer for tubulin and using circular dichroism - I just need the buffer to be ~ pH 7.4 and to be transparent in the 185-240nm region. This mono/dibasic potassium phosphate buffer does this but seems needlessly complicated. Would monobasic potassium phosphate with sodium hydroxide be sufficient also? But once again I'm not sure how to calculate the proper proportions of KH2PO4 and NaOH - do I assume NaOH dissociated completely and just figure out the KH2PO4 concentration?

The common assumption is that a strong base like NaOH dissociates completely. I think this is a good assumption. However, the KH2PO4 has several ionization states. Each ionic state has its own pK associated with it, which change with ionic strength. So it is the KH2PO4 that presents the main problem. Here are some suggestions.
1) Buy a good pH meter and learn how to maintain it. There are some inexpensive pH meters on the market. A pH meter can be a valuable item for all sorts of reasons. However, the maintenance of a pH meter is tricky. There are different electrodes for different pH ranges. The electrode has to be kept wet. The wetting solution has to be in a buffer with a pH in the general vicinity of the solutions that you wish to study. However, the maintenance is inexpensive and easy once you know how. The pH meter will be worth the cost and effort of maintenance. If you can't get a pH meter, then you may have to use other methods of estimating pH which are not as reliable as a pH meter.
2) Another method is to use the Debye-Hukel formula to predict what pH of the solution. The Debye Hukel formula can extrapolate what the pK would be for each ionization state provided that you know the effective radius and activity coefficient of each ion.
The effective radius and activity coefficient of the simple ions are known. There are tables. I am sure that the data is available for the different ions of phosphate. In fact, I have a table right in front of me now. I can give you this data in this reply.
The following is a reference of a book that is no longer published but which has an appropriate table:
"Analytical Chemistry Third Edition" by Douglas Skoog and Donald West (Holt 1979) p 109.
Table 5.3 provide and effective diameter and the activity coefficient for ionic strengths between 0.001 and 0.1.

H2PO4- , Effective diameter 4.2 Angstroms, Activity Coefficient at an ionic strength of 0.01 is 0.914, Activity Coefficient at an ionic strength of 0.001 is 0.964;
HPO4-- , Effective diameter 4.0 Angstroms, Activity Coefficient at an ionic strength of 0.01 is 0.660, Activity Coefficient at an ionic strength of 0.001 is 0.867;
There is no data on PO4---. Maybe you can assume that PO4--- is not present in the solution. For this and other reasons, I do not strongly recommend relying on the Hukel-Debye formula for pH.

3) Use litmus paper!
Just joking. Don't try it. Indicator papers are not very accurate. However, they can serve as a sanity check.


4) Borrow a pH meter.
A pH meter is invaluable. Referees may not trust your data unless you can independently verify the pH of your system. If you have a pH meter, you may be able to do a study where both the pH and the ionic strength of your system is varied in a controlled way.

 

[Borek]

Debye-Hü_c_kel.

 

[Darwin123]

Debye-Hü_c_kel.

Yes. I misspelled it. Sorry.

 

[Borek]

I would not correct if not for the fact you were very consistent about the wrong spelling