pH Buffer Capacity

[chem geek]

The following gives a rough idea of pH buffering strength with 50 ppm Borates vs. 80 ppm CYA vs. 70 ppm carbonate alkalinity where the strength is buffer capacity in millimoles/liter/pH (that is, the amount of acid per volume needed to move the pH by one unit, but in an infinitesimal sense). I also list the effect of 50 ppm Borates and 80 ppm CYA on TA.

.................................................... 50 ppm ............... 80 ppm ................ 70 ppm
pH .... Borate_TA ... CYA_TA ... Borate Strength ... CYA Strength ... Carbonates Strength ... CYA+Carbonates ... CYA+Carbonates+Borate
7.0 ......... 1.7 ........... 18.8 ............. 0.08 .................... 0.32 ....................... 0.51 ......................... 0.83 ............................. 0.91
7.1 ......... 2.2 ........... 20.3 ............. 0.10 .................... 0.30 ....................... 0.41 ......................... 0.71 ............................. 0.81
7.2 ......... 2.7 ........... 21.6 ............. 0.12 .................... 0.28 ....................... 0.34 ......................... 0.62 ............................. 0.74
7.3 ......... 3.3 ........... 22.9 ............. 0.15 .................... 0.25 ....................... 0.27 ......................... 0.52 ............................. 0.67
7.4 ......... 4.1 ........... 23.9 ............. 0.19 .................... 0.22 ....................... 0.23 ......................... 0.45 ............................. 0.64
7.5 ......... 5.2 ........... 24.9 ............. 0.23 .................... 0.20 ....................... 0.18 ......................... 0.38 ............................. 0.61
7.6 ......... 6.5 ........... 25.6 ............. 0.29 .................... 0.17 ....................... 0.15 ......................... 0.32 ............................. 0.61
7.7 ......... 8.1 ........... 26.3 ............. 0.36 .................... 0.14 ....................... 0.13 ......................... 0.27 ............................. 0.63
7.8 ....... 10.0 ........... 26.8 ............. 0.44 .................... 0.12 ....................... 0.11 ......................... 0.23 ............................. 0.67
7.9 ....... 12.5 ........... 27.2 ............. 0.54 .................... 0.10 ....................... 0.09 ......................... 0.19 ............................. 0.73
8.0 ....... 15.5 ........... 27.6 ............. 0.67 .................... 0.09 ....................... 0.08 ......................... 0.17 ............................. 0.84

You can see not only how 50 ppm Borates increases pH buffering overall, but is a nice complement to the carbonates and CYA pH buffering and provides stronger buffering as the pH rises. So basically you have the carbonates and CYA preventing the pH from quickly dropping too much while you have the borates preventing it from quickly rising too much. Additional info is in this post.

The peak pH buffering occurs when the pH is at the pKa of the weak acid and its conjugate base so for carbonic acid / bicarbonate this is at pH 6.3, for bicarbonate / carbonate this is at pH 10.2 while for H₃CY/H₂CY^- this is at pH 6.8, for H₂CY^-/HCY^2- this is at pH 11.3, for HCY^2-/CY^3- this is at pH 13.3, for boric acid / borate ion this is at pH 9.1.

As noted in this link, the buffer capacity can be calculated from the formula ln(10)*C_buf*K_a*[H⁺]/(K_a+[H⁺])² and the amount of acid or base needed to change the pH by a specific amount can be calculated by the difference in C_buf*K_a/(K_a+[H⁺]) at two different pH values and summing these differences for all of the buffer species. Calculating the effect on pH when acid or base is added when multiple buffer species are present requires iteration since the inverse formula cannot be solved in closed form.

 

[RGB]

Thanks chem geek, that table is another useful resource.

It may be worth noting here a point that you have explained elsewhere: Buffering works in both directions. Over the same pH range the capacity of the same buffer is identical against pH rise and pH fall. Those who need regularly to reduce pH will find that with borate present they need to add higher acid doses, albeit less frequently, to restore their target pH. The buffer reduces the pH rise from addition of alkali (for example NaOH in commercial bleach) but equally it reduces the pH drop from addition of acid (for example HCl). Total acid usage will be identical, with or without the buffer (borate in this scenario).

Digging a bit deeper about borate, which may help to explain different experiences from different pools: The apparent pKa of boric acid is about 9.24 in fresh water at 25 C, and it declines with increased ionic strength or temperature (Owen and King 1943; Manov 1946). pKa is lower in the presence of small amounts of Ca or Mg than in pure NaCl solutions (Hershey et al. 1986). It is likely to be around 9.0 at the salt levels in many SWG pools. A practical consequence of all this is that in warm SWG pools, borate may show greater pH buffer strength than expected ‘at first glance’, especially as pH rises to around 8.

Owen BB, King EJ (1943) The effect of sodium chloride upon the ionization of boric acid at various temperatures. J Am Chem Soc 65:1612-1620
Manov GG, Delollis NJ, Lindvall PW, Acree SF (1946) Effect of sodium chloride on the apparent ionization constant of boric acid and the pH values of borate solutions. J Res Natl Bureau Standards 36:543-558
Hershey JP, Fernandez M, Milne PJ, Millero FJ (1986) The ionization of boric acid in NaCl, Na-Ca-Cl and Na-Mg-Cl solutions at 25 degrees C. Geochimica et Cosmochimica Acta 50:143-148

 

[chem geek]

The table accounts for ionic strength but without any extra added salt. So the pKa for boric acid at zero ionic strength at 80ºF would be 9.195, but accounting for ionic strength with 300 ppm CH, 100 ppm TA, 30 ppm CYA and 50 ppm borates it is 9.143. With 3000 ppm chloride (measured as ppm sodium chloride implying 3465 ppm TDS) the pKa for boric acid is 9.100. So the ionic strength effect is low enough to pretty much ignore with regard to buffer strength unless one looks at much higher ionic strength such as in ocean water. The ionic strength has a more pronounced effect on the calcite saturation index where this example would have the CSI lowered by about 0.2 units when the salt is increased to 3000 ppm.

I think the difference seen with different pools has much more to do with differences in outgassing of carbon dioxide and in other sources of pH rise such as the excess lye from some chlorine sources or from new or deteriorating plaster or from undissolved chlorine gas outgassing (from SWG pools). Without 50 ppm borates, then adding 10 ppm and having 20% of the chlorine not dissolve and instead outgassed would have the pH rise from 7.7 to 8.0. With 50 ppm Borates, the pH rise is limited to 7.8.

 

[JamesW]

Over the same pH range the capacity of the same buffer is identical against pH rise and pH fall.

The only time a buffer would have the same capacity against rise or fall is when the pKa was equal to the pH. That is when half is in the form of acid and half is in the form of base. For boric acid/borate, at normal pool pH, most is in the form of boric acid, and will have a much greater capacity against pH rise than fall.

When there are multiple buffers, then each has to be calculated independently.

Total Alkalinity is a measure of resistance to pH drop, whereas Total Acidity is the measure of resistance to pH rise.

 

[RGB]

Thanks chem geek. The caution to think also about saturation index is important. But focussing on pH for now:

Many SWG pools are run way above 3000 ppm salinity. For example, Watermaid recommend 6000 ppm NaCl plus about 200 ppm MgCl₂ (and there will be additional small molar contributions from borate, cyanurate and calcium bicarbonate in the usual concentration ranges). At 25 C this will reduce the apparent pKa of borate to just below 9 (from 9.24 in fresh water) (Owen and King 1943; Hershey et al. 1986). The apparent pKa of other weak acids is also affected by salinity. For example, the apparent pKa for bicarbonate will drop to about 6.05 at this salinity (from 6.3 in fresh water) (Millero et al. 2006). The overall effect is that borate buffers better (closer to pKa) whereas bicarbonate contributes less (further from pKa) in a salt pool. When working about 1 pH from the pKa, the effect of a shift of 0.2 in effective pKa will be quite noticeable: buffer capacity will improve by about 50% (or in practical terms there will be about a 50% increase in the volume of HCl needed to reduce pool pH from 8.0 to 7.8).

Millero FJ, Graham TB, Huang F, Bustos-Serrano H, Pierrot D (2006) Dissociation constants of carbonic acid in seawater as a function of salinity and temperature. Mar Chem 100:80-94

JamesW, I think your point is about buffer capacity from the same starting pH. As you quoted, the original point was "over the same pH range". Put in practical terms, the same number of moles of HCl will be needed to reduce pH from 8.0 to 7.8 as the number of moles of NaOH (for example in commercial bleach) that increased pH of the same buffered pool from 7.8 to 8.0.

 

[chem geek]

Starting with pH 8.0, TA 80 ppm, FC 4.0 ppm, CYA 80 ppm, CH 300 ppm, 50 ppm Borates, TDS 900 ppm, 80ºF, then it takes 18.55 fluid ounces of full-strength Muriatic Acid (31.45% Hydrochloric Acid) to lower the pH to 7.8. Interestingly, if one did not have the 50 ppm Borates, then it only takes 4.8 using the same 900 ppm TDS assumption. With 50 ppm borates and if the TDS were 6500 ppm for around 6000 ppm salt (chloride as ppm sodium chloride) level, then it takes 19.97 fluid ounces. I don't know where you are getting an increase of 50%. If I use 35,000 ppm TDS for something more like ocean water, then it takes more like 22.4 fluid ounces, but that's still not 50% more which would be 27 fluid ounces.

Where exactly are you seeing the calculation where it takes 50% more acid due to a higher TDS at a pH in the 7.8 to 8.0 range?

 

[RGB]

Hi chem geek. I think we agree that there will be about a 50% increase in buffer capacity if pKa shifts about 0.2 units towards an operating pH about 1 pH unit from the pKa. This shows in the general curve (which can be explored graphically at http://academic.pgcc.edu/~ssinex/buffer_cap.xls) and in your table above (for example 44 to 67 is a 52% increase).

So the question may be about the effect of salinity on pKa? In case it helps I have plotted data from the references given above on a salinity ppm X axis.

I think the work in those references about effect of salinity on pKa is quite robust (the effect on carbonate has received a lot of scientific attention because of relevance to the global carbon cycle). If your model is generating pKa results that differ substantially from those papers, I hope the references will help you to refine your model.

I think the other point you may be emphasising (with JamesW) is that in any given pool at any given time, the overall buffer capacity is the sum of the capacities from all the different buffers present. You are right of course, and I can not add much there. I have not seen any compelling test of the effects of salinity on pKa of CYA or HOCl (or all the complexes that can form involving these along with borate and bicarbonate). And of course HOCl can vary dramatically during the day, and bicarbonate over time through outgassing, even in the same pool. So for simplicity I have focused the examples on borate, which we have seen accounts for an increasing share of overall buffer capacity (relative to the other buffers with pKa below the working pH) at increased salinity.

 

[chem geek]

Ah I see the discrepancy. You are saying the pKa moves by 0.2, but you aren't accounting for the fact that you aren't starting with 0 salinity. With usual TA and CH and with 50 ppm Borates, you are already starting out at nearly 900 ppm TDS (with no borates, you start out at around 500 ppm TDS with usual TA and CH for plaster pools). So the pKa is already down quite a ways from the zero salinity level so changes by something closer to 0.1, not 0.2. That explains the difference.

Nevertheless, your references show a faster drop in pKa compared to the Debye-Hückel (or Davies as an alternative) activity coefficient calculations as a function of ionic strength that I used in my spreadsheet. Thanks for the data and references.