[Babcock_Hall]

I was helping a group of undergraduate students prepare a 0.100 M sodium carbonate buffer at pH 10.0 from Na₂CO₃ and HCl yesterday.  I had asked them to estimate the amount of HCl that they would need using the H-H equation and a pK_a value of 10.33 (from Appendix III in Perrin and Dempsey's "Buffers for pH and Metal Ion Control."  I had also told them that the ionic strength could affect the apparent pK_a value.  They used much less HCl than they had calculated (I now think that 10.33 is the thermodynamic pK_a value).

In looking into bicarbonate/carbonate a bit further, I found Table 10.40 in the same book.  It details a buffer made by Delory and King Biochemical Journal (1945).  These workers used 0.10 M solutions of bicarbonate and carbonate in varying ratios.  At 20 °C a 50/50 ratio of the two solutions produced a pH value of 9.90.  My question is whether or not one could use 9.90 as an estimate of the practical pK_a value under the conditions of Delory and King.

[Babcock_Hall]

I am examining the data of Bates and Bower (Analytical Chemistry, 1956, 1322), who also prepared a bicarbonate/carbonate buffer.  Assuming that I did my calculations correctly, I obtained an ionic strength of 0.0494 M for this buffer at pH 10.10, where the concentrations of NaHCO₃ and Na₂CO₃ are nearly equal (0.0128 M and 0.0122 M, respectively).  By doing a crude interpolation from their data, I can estimate a practical pK_a of 10.12 for the Bates and Bower Buffer.

For the Delory and King buffer, I calculate that the ionic strength is 0.200 M, and my estimate of the practical pK_a is 9.90, as I mentioned in my previous post.  It seems to me that in both of these calculations, I am implicitly taking the final concentrations of bicarbonate and carbonate as being the same as their initial concentrations.  I wonder whether or not this is valid.

I am not especially bothered that the two values are not the same, because the ionic strength is not the same.  It seems to me that the trend is in the expected direction. 

[AWK]

Starting from 0.1 M sodium carbonate you buffer with pH ~10 will show ionic strength above 0.2.
At such ionic strength it is difficult to estimate activity coefficients with simple formulas. For this ionic strength a practical pK_a will be close 9.8 and activity coefficient for H₃O⁺ about 0.75.
Using program aq_solutions prepared under IUPAC project I calculated table for real(concentration) pK_a of some acids and bases for ionic strength values from 0(thermodynamic value) to 1.
Intermediate values for pK_a and f(H₃O⁺) may be interpolated at logarithm scale (pK_a, f(H₃O⁺, and pK_w - if needed)
http://www.kchn.pg.gda.pl/didactics/skrypt_cw/Stale7.pdf (table contains a few word in Polish, but I do hope that is easily understandable even without comments in English.
pH=-log(f(H₃O⁺⁾·K_a·[conc_Bronsted_acid]/[conc_Bronsted_base])

Calculation added later: for I=0.2 you should add 0.0435 mole of HCl (gaseous) to 1 L 0.1 M sodium carbonate. Final I = 0.21. Further corrections may be neglected.

[Babcock_Hall]

In retrospect a better idea than starting with sodium carbonate and HCl would have been starting with sodium bicarbonate and NaOH.

[AWK]

or NaHCO₃ (solubility at 20 C ~1 mol/L) and Na₂CO₃.
Diluted NaOH reacts with CO₂ from air.