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Chemistry of the Borate-Boric Acid Buffer System

C. Thorsten

CR Scientific LLC
March 2013


A note from the author:  There is some indication that boric acid and borates may be toxic to humans.  However, given the low to moderate toxicity and the fact that we're not ingesting them during laboratory work, this should not be of great concern.

Millions of people have washed their hands with borax soap, washed their clothes in borax, and used boron compounds to kill ants.  The human toxic effects from these activities comprise a data signal, as it were, that is likely much fainter than that of the many adverse effects due to (e.g.) food additives, plasticizers, PAH's, herbicides, mercury, gene remnants, etc.  There are locations in the world where diet contributes at least 5 to 10 mg of boron per day, with no ill effects of note.  There is ample evidence that boron is a necessary trace element in human biochemistry;  see for example Nutrition Reviews 66(4):183-91 (April 2008).

The classification of something as "toxic" should always include qualifiers;  for example, even air and table salt are "toxic" under the right conditions.  We should not allow the recognition of specific hazards to morph into chemophobia nor lead to overly-restrictive policies. 

As always, excercise caution appropriate to the chemicals being used.



Introduction

The borate buffer system is inorganic, but acid-base buffers in general are crucial in the study of biochemistry.  In fact, many students don't learn to prepare buffers until they take a biochemistry lab course. 
In laboratory work, buffers should be involved wherever there might be unwanted changes in pH.  For example, the product of an enzymatic reaction might shift the solution pH, causing inhibition;  a buffer would counteract these changes.
The Henderson-Hasselbalch (sometimes mis-spelled "Hasselbach") equation (Eqn. 1.) allows for the rational design of buffers.

Equation 1.  The Henderson-Hasselbalch Equation
Henderson-Hasselbalch Equation
The species " HA " and " A- " represent the conjugate acid and conjugate base, respectively, of a buffer system (Equation 2):

HA (aq.)  <------->  H+ (aq.)  +  A- (aq.)

Here, the "acid" is that which donates H+ to yield a deprotonated species, and the "base" is that which accepts H+ to yield the protonated species.  This is essentially the Arrhenius-Ostwald model of acids.
Thanks to the Henderson-Hasselbalch Equation, we know that when pH is equal to pKa, the concentration of A- should equal the concentration of HA.  The logarithmic term cancels from the equation when [A-] = [HA], since log 1 = 0.  In theory, if we dissolve equimolar amounts of a weak acid and one of its salts, we should obtain a pH equal to the pKa.  In real life it may not be exactly equal, since ionic strength has an effect;  however, it will be close, as long as we don't utilize an acid that dissociates too strongly.  For example, we could prepare an equimolar solution of acetic acid and sodium acetate, and we could expect the pH to be not far from the pKa of 4.76.    Alternatively, we could treat a solution of acetic acid with half the molar equivalent of NaOH.  Half the acetic acid would then become sodium acetate, leading to the same ratio of " A- " to " HA ".

Now we will explore a system that doesn't quite follow the Arrhenius-Ostwald model:  namely, borate buffer
There are various recipes for so-called "borate buffer", leading to some ambiguity.  We could prepare a working buffer by using H3BO3 and NaOH, or by using sodium tetraborate and HCl, or by using sodium tetraborate and H3BO3.;  in fact, it's even possible to make a buffer using sodium tetraborate and NaOH.  As we shall see, the boric acid-borate system is a difficult example because of its peculiar chemistry.
At first glance, orthoboric acid (H3BO3, also written B(OH)3  ) and borax (Na2B4O710H2O) do not appear to be stoichiometrically related;  however, when we treat a solution of boric acid with NaOH or Na2CO3, borax is indeed what crystallizes on evaporation.
Boric acid actually ionizes by accepting a hydroxide ion (and thus an electron pair) from water, rather than by donating H+.  This makes it a Lewis Acid (Equation 3):

B(OH)3 (aq.)  +  H2O  <--------->   B(OH)4-  (aq.) +  H+ (aq.)

The tetrahydroxyborate ion, in turn, can yield something that should look familiar.   Equation 4:

4B(OH)4-  (aq.) +  2H+ (aq.)     <--------->     B4O72−  (aq.)  +  9H2O

 Again, we are dealing with a Lewis Acid, not a classic "proton donor", so these equations don't give us the typical Arrhenius acid-base equilibrium expressions (yet).  Notice here the tetraborate ion, B4O72− , which occurs also with the ionization of borax.  In a borax-boric acid buffer solution (~ pH 9), tetraborate and monohydrogen tetraborate are actually the primary species, as long as the boron concentration is greater than about 0.025 M.
Equations 3 and 4 show us that a connection exists in solution between tetraborate, tetrahydroxyborate, and boric acid.
In theory, it takes four moles of boric acid to yield one mole of B4O72- in solution. If we quadruple the coefficients in Equation 3 to correspond with Equation 4, we get 4B(OH)3.    Equation 5 shows what happens when we combine the two equations:

4B(OH)3 (aq.)   <--------->   B4O72−  (aq.)  +  5H2O  +  2H+ (aq.)

Notice that the H+ is now on the right, which is consistent with the fact that boric acid yields an acidic solution.  Because H2B4O7 is not a strong acid, though, it does not completely ionize. 

First ionization (Equation 6):

H2B4O7 (aq.)   <--------->   HB4O7- (aq.)  +  H+ (aq.)

Second ionization (Equation 7):

HB4O7- (aq.)   <--------->   B4O72- (aq.)  +  H+ (aq.)

Now we have something straight from the Arrhenius-Ostwald model.  The second ionization (Eq. 7) is the more important one at pH 9.  The monohydrogen tetraborate ion has a pKa of 9;  hence, in our buffer system we would expect about equal amounts of HB4O7- and B4O72-.  The species "H2B4O7", having a pKa of about 5 (Latimer and Hildebrand, 1940), would not be present in significant amounts at pH 9.  Conversely, a pH low enough to favor it according to pKa would also cause hydrolytic degradation of the tetraborate structure.
The mono-protonated species HB4O7-  does exist, increasing in concentration around pH 5 (Trejo et al. 2012) and upward.  However, the borax-boric acid system does not produce tetraborate exclusively, since there are other species present (e.g., B3O3(OH)4- ).   The system is actually so complex that it remains difficult to characterize.  Trejo et al. (2012) mention that there are ten different equilibrium reactions in solution.  However, as said before, the tetraborate species would predominate at pH 8 or above.
Borax has a molar mass about 6.2 times that of boric acid.  If we need only 1/4 mole of borax for every mole of boric acid in our buffer, we would need (6.2)(1/4) or about 1.5 grams of borax for every gram of boric acid.
Now, here's the question.  Does this really produce a solution of pH 9.0?  If not exactly, then how close is it?
Let's prepare a buffer and see how well it works.  We'll make it about 0.05 M in borax and 0.2 M in boric acid.  We'll also try making a buffer with borax and HCl.


Materials 

Boric acid (orthoboric acid), H3BO3
Sodium tetraborate decahydrate (borax), Na2B4O710H2O
Distilled-deionized water
Volumetric flask (250 mL)
Lab balance
0.01-molar and 0.1-molar HCl solutions
Droppers
Wide-range pH paper or Wide-range pH indicator kit.
pH meter (optional)


Procedure

Formula weights:

Borax (Na2B4O710H2O)..............381.43 g / mole

Boric Acid (H3BO3)........................61.84 g / mole

We will prepare two different buffers.  One is based on the calculated 4:1 molar ratio of borax to boric acid;  the other utilizes a 2:1 molar ratio of borax to HCl.

Buffer A.   4 moles boric acid per mole borax

Weigh out 3.06 grams of boric acid and 4.75 grams of borax (sodium tetraborate decahydrate). 
Add these to a 250 mL volumetric flask and add a small amount of de-gassed, de-ionized water. Swirl until the solids dissolve, then add enough distilled water to make the total volume up to 250 mL. The boric acid may take a while to dissolve, especially if it has formed lumps.

Buffer B.   1/2 mole HCl per mole borax

Weigh out 4.75 grams of borax (sodium tetraborate decahydrate). Add this to a 250 mL volumetric flask and add a small amount of de-gassed, de-ionized water. Swirl until the solids dissolve. 
Next, add enough HCl so that the solution will be 0.0025 M when diluted up to 250 mL.  Starting with 6M HCl, this would require about 0.10 ml.  This amount could be delivered with a micropipettor, or by simply adding two drops from a dropper (because 1 drop = approx. 0.05 ml).
Finally, add enough distilled water to make the total volume up to 250 mL. The boric acid may take a while to dissolve, especially if it has formed lumps.

Testing the pH:

Put 5 drops of Buffer A into a clean well in the spot plate. Add 1 drop of wide range pH indicator solution to this (or put a drop on a piece of wide range pH test paper) and immediately note the color. Check the color against the chart to determine approximate pH.

Do the same with Buffer B, using a different well in the spot plate.

If either buffer actually has [A-] = [HA] and thus pH = pKa, then the measured pH should be about 9.0 to 9.5   1 


Testing the buffering capacity:

Measure out 50. mL of Buffer A and put it into a beaker.  Add 2 drops of 0.01-molar HCl.  Stir with a glass rod, taking care not to spill any. Then, take five drops of the resulting solution and place in a clean well on the spot plate. Add 1 drop of wide range pH indicator and note the color. What is the approximate pH, according to the chart?  

If possible, test the buffer solution with a calibrated pH meter.

Repeat with Buffer B. 

What differences, if any, do you notice?  Is there any discrepancy in buffering capacity or pH?


If you were to add the same amount of 0.01-molar HCl to an unbuffered solution of pH 9.2 2 , what would you expect the new pH to be? 3 What difference, if any, is there between actual and expected results?
Try the experiment using 0.1-molar HCl instead of 0.01-molar HCl. Does the buffer solution still "absorb" it without appreciably changing in pH?  Why or why not?  What happens if you use 1.0-molar HCl?  At what concentration of HCl would you predict the buffering capacity to be exceeded?


Discussion

Acid-base buffer solutions tend to resist changes in pH.  This is essential to living organisms. Simple processes such as eating, breathing, drinking, or taking medicine would throw the body into fatal imbalance if it weren't for our natural buffering systems.
Ideally, the intended buffering pH of a solution should be close to the pKa of the buffering species. At room temperature, the boric acid / borate system has a pKa about 9; therefore, a borate-boric acid buffer solution should be expected to buffer most effectively at a pH between 8 and 10.
The borax-boric acid system presents a challenging example, partly because it doesn't conform to the Arrhenius model.   We've seen that instead of donating a hydrogen ion, boric acid actually takes a hydroxyl ion from water.  Furthermore, borates in solution yield polymeric species that don't lend themselves to readily-balanced equations. 
Nevertheless, the borax-boric acid buffer is still used in biochemistry and histology.  A recipe appears in Methods in Enzymology, Vol. I (1955). 
Some, however, start with sodium tetraborate and add HCl until the desired pH is attained.  This is sometimes called "borax-HCl buffer". Alternatively, one may start with boric acid and add NaOH.  The ionic species involved in the two different methods are probably not identical;  Quantitative Chemical Analysis by Daniel Harris (5th ed., 1999) notes, as we have here, that boric acid and sodium tetraborate have somewhat different acid-base chemistries in solution.  The old saying "You can't get there from here" comes to mind.  To add some perplexity, however, one can in fact obtain sodium tetraborate from a solution of boric acid, simply by treating it with the appropriate amount of NaOH or Na2CO3.  As we've seen, the most plausible answer is that boric acid at pH > 7 yields significant amounts of HB4O7- and B4O72-.
There is, by the way, also a "borax-NaOH" buffer (Methods in Enzymology Vol. I).  This is possible because tetraboric acid is diprotic;  addition of NaOH yields a buffer with pH between 9 and 10, rather than pH 8 to 9.
Like the sodium thiosulfate-copper (II) system, the boric acid-borate system is much more complex than it initially seems.  There is still probably much opportunity for research to determine what ionic species are actually present under various circumstances.



References

Latimer, Wendell and Joel Hillebrand.  Reference Book of Inorganic Chemistry.  New York:  Macmillan Company, 1940.

Trejo G., Frausto-Reyes C., Gama S.C., Meas Y., Orozco G.  "Raman Study of Benzylideneacetone on Silver".  Int. J. Electrochem. Sci., 7(9):8436-8443 (2012).



Citing this article:
If you found this article useful, please provide a citation in your bibliography:

Thorsten, C.  "Chemistry of the Borate-Boric Acid Buffer System". CR Scientific LLC.  Web.  March 2013. <http://www.crscientific.com/experiment4.html>.



Notes:

1 this should be the case if there is no carbon dioxide dissolved in the water. Aqueous CO2 creates carbonic acid and lowers the pH. There's another problem: ionic strength of the buffer solution also affects the pH.  Theoretical buffer pH and real buffer pH are usually two different numbers. For best accuracy, it's recommended to use a pH meter. While monitoring the solution's pH, small amounts of either HCl or NaOH in dilute solution are added until the pH reaches the desired value.
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2 We'll assume the unbuffered solution is made pH 9.2 by preparing approx. 16 micromolar NaOH in water.   The use of carbonates or bicarbonates would create a buffer system of their own. 
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3 If we were using pure water (pH 7), the calculation of "expected" pH after adding acid or base would be more straightforward. When adding acid to a basic solution (or the other way around) and trying to calculate the final pH, one must of course take into account the amount of H+ that will combine with OH- to form water.  
     To the solution we added 2 drops, which translates to about 0.1 mL.  In the case of 0.01M HCl there will be 1 micromole of H+ ions added to the solution. If the solution is pH 9.2 to begin with, we must calculate how many moles of OH- ions there are to react with any added H+.  In a non-buffered system, subtraction tells us how many moles of H+ this will leave.  This will allow us to calculate the final pH of the unbuffered solution. 
      At pH 9.2, [OH-] is antilog{-(14 - 9.2)} = antilog(-4.8) = 1.6 x 10-5 moles per liter.  50 mL of this solution translates to 8.0 x 10-7 moles of OH-.  If 1 micromole of H+ was added, that is 1 x 10-6 moles H+, minus 8.0 x 10-7moles that react with OH- (or 0.8 x 10-6 moles, to make calculation easier).  That leaves 0.2 x 10-6 moles H+ (which equals 2x10-7 moles H+).  This many moles dissolved in 50 mL of solution gives a [H+] of 4 x 10-6 M.  The expected pH would be about 5.4 with no buffering. 
       According to a preliminary test run with wide-range pH paper, the buffered solution was still around pH 9 after addition of the same amount of HCl.  That is a gigantic difference in hydrogen ion concentration: pH 5.4 versus pH 9.
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