Alkalinity titration questions

[cypho]

After reading a number of sources including randy's DIY alkalinity test article I set out to build an DIY automatic alkalinity test. It seems to be working better than expected. Three back to back tests resulted in:

2.621 meq/l
2.627 meq/l
2.624 meq/l

So I have the precision down, time to work on accuracy.

I don't think I have any hope of calibrating the pumps or pH probe accurately enough to match that level of precision. But I want to make sure I am at least not losing out on accuracy due to flaws in the math or testing methodology.

My understanding is that if I use a 10ml sample, and titrate with 0.01N HCl to a pH of 4.5, the alkalinity in meq/l is exactly equal to the quantity of acid used(in ml).

Is that really all there is to it?

Is the end point exactly 4.5? Not 4.51 or 4.49? And are there really no other factors to account for. I don't need to care about the salinity, temperature, CO2 level, initial pH, or anything else?

Finally, once I have the alk in meq/l, how do I convert that to dKH and PPM. I have read that 1 meq/l = 2.8 dKH = 50PPM Is that the exact conversion, or is there a more precise equation?

 

[JimWelsh]

Is that really all there is to it?

Yes.

Is the end point exactly 4.5? Not 4.51 or 4.49?

This is a great conversation to have over a beer. For your application, use 4.5.

[EDIT] You may find this helpful, or not. https://www.reef2reef.com/threads/salifert-kh-alk-testing-help.311941/page-2#post-3843220

Finally, once I have the alk in meq/l, how do I convert that to dKH and PPM. I have read that 1 meq/l = 2.8 dKH = 50PPM Is that the exact conversion, or is there a more precise equation?

That is correct.

 

[JimWelsh]

2.621 meq/l
2.627 meq/l
2.624 meq/l

So I have the precision down, time to work on accuracy.

Sorry, I forgot to give the well-deserved "attaboy" for this!!!

 

[cypho]

[EDIT] You may find this helpful, or not. https://www.reef2reef.com/threads/salifert-kh-alk-testing-help.311941/page-2#post-3843220

I think if I read it 100 more times I might begin to make sense of that discussion. I never would have guessed that the exact endpoint of the titration would still be up in the air to such a wide margin. As I approach 4.5 I am looking at pH steps of around 0.01. But the actual endpoint might actually be off by 0.2-0.3? That makes me a bit sad.

On one hand, since recommended alkalinity target ranges from 2.5 to 3.5, it is hard to say that it really matters if the accuracy of my test is off by .01 or even .1. As long as it is consistent it is a huge step up from any hobbiest test kits. On the other hand, if I can make my test more accurate I really want to even if there is no practical purpose.

Out of that I did see one potentially useful nugget in your link. Titrating past the endpoint and then calculating end point by looking for the inflection point. Would that eliminate the need for a precisely calibrated pH probe?

 

[JimWelsh]

Would that eliminate the need for a precisely calibrated pH probe?

Yes.

 

[cypho]

Thanks. My pH probe has not been calibrated in a year and even then it was calibrated with 7 and 10. So that could be a very useful tweak to the protocol (in addition to properly calibrating my probe).

And while I have your attention. I am thinking about trying Ca and Mg titrations next. Any thoughts on a indicator that I would not need to mix up daily/weekly? Will calmagite work for Ca+Mg at pH=10 and Ca only at pH=12?

 

[JimWelsh]

Calmagite is only useful as a complexometric indicator at pH values midway between its two pKa of 8.14 and 12.35, and acts as a pH indicator at pH values near its two pKa, so it is not useful for a Ca titration at high pH (but is excellent for the Ca + Mg titration). The Hach method for Ca uses Hydroxy Naphthol Blue as an indicator, which is also what I use when manually titrating Ca after precipitating the Mg as the hydroxide.

Helpful hint for the Ca titration: If you have a pretty good estimate of what your Ca level is, you can greatly improve the accuracy and precision of this titration by delivering about 90-95% of the EDTA necessary to complete the titration *before* you add the hydroxide to precipitate the Mg. Then, complete the titration to the pure blue endpoint. The endpoint will be sharper, and you should find it to be much more precise. In general, this approach will give results that are a little bit (1% to 2%) higher than the standard approach. This is because the with the standard approach, some Ca gets taken down along with the Mg as the hydroxide, and then it wants to come back into solution near the endpoint, causing you to chase the endpoint somewhat, while still giving a slight negative bias. Adding the bulk of the EDTA at the beginning of the method binds that Ca up, preventing it from being precipitated out to begin with.

FWIW, the mixed indicator dye described in this paper produces an incredibly sharp endpoint for the Ca + Mg titration, and you can substitute Calmagite for the EBT in that recipe. It goes from red to grey to green very quickly at the endpoint, and if you consider the very first appearance of any green tint as the endpoint, you can achieve very precise results (relative standard deviation around 0.25%).

 

[Randy Holmes-Farley]

Very interesting. Thanks Jim.[emoji3]

 

[Randy Holmes-Farley]

I think if I read it 100 more times I might begin to make sense of that discussion. I never would have guessed that the exact endpoint of the titration would still be up in the air to such a wide margin. As I approach 4.5 I am looking at pH steps of around 0.01. But the actual endpoint might actually be off by 0.2-0.3? That makes me a bit sad.

On one hand, since recommended alkalinity target ranges from 2.5 to 3.5, it is hard to say that it really matters if the accuracy of my test is off by .01 or even .1. As long as it is consistent it is a huge step up from any hobbiest test kits. On the other hand, if I can make my test more accurate I really want to even if there is no practical purpose.

Out of that I did see one potentially useful nugget in your link. Titrating past the endpoint and then calculating end point by looking for the inflection point. Would that eliminate the need for a precisely calibrated pH probe?

Bear in mind that the interpretation of the exact value of total alkalinity is itself open to variability for two reasons:

1. Assuming the total alk is being used as some sort of surrogate for the amount of bicarbonate present, the starting pH substantially impacts the total alk to bicarbonate ratio since the starting pH impacts the relative contributions of bicarbonate, carbonate, and borate to total alkalinity.

2. There is a variable amount of borate in that total alkalinity, and if you have not independently measured the total boron and starting pH of the titration, you won’t know what percentage is borate alk.

 

[cypho]

Does Hydroxynaphthol Blue solution have a decent shelf life? All I see for sale is powder so I am thinking it does not.

Not so easy to pump power into the test. It's not a problem to mix the solution once - but I don't want to do it every day. That is why I was hoping calmagite would work. It comes as a liquid.

 

[JimWelsh]

EDIT: The next post addresses this.

 

[JimWelsh]

Here you go: Itoh, Atuko, and Keihei Ueno. "Evaluation of 2-hydroxy-1-(2-hydroxy-4-sulpho-1-naphthylazo)-3-naphthoic acid and hydroxynaphthol blue as metallochromic indicators in the EDTA titration of calcium." Analyst 95.1131 (1970): 583-589.

It says, "The absorbance of aqueous 6.2 * 10^-4 M hydroxynaphthol blue solution at room temperature in a dark room was almost unchanged over a period of 60 days."

 

[cypho]

Awesome!!! That is what i will use then.

Working on a routine to calculate the inflection point for alkalinity. I'll let you know how it goes.

Thanks for all of the help.

 

[pandagobyguy]

Holy god this thread is advanced.

 

[cypho]

I have tweaked the test procedure to use the inflection point as the endpoint.

1 - Titrate down to pH = 4
2 - Fit data from the pH 5 to pH 4 portion of the titration to third degree polynomial
3 - Calculate root of second derivative of the polynomial (the inflection point)
4 - Use that as the end point
5 - Also use the polynomial to estimate titrant volume at end point

The calculated endpoint was 4.7 which shifted the alkalinity down by 0.02 meq/l

So yesterday, my alkalinity was not 2.62. It was actually 2.60. Totally worth it!!!

_______________

Actually the fact that that it does not matter that my pH probe is so poorly calibrated does make it quite worthwhile. However it is a LOT slower. So much slower that I had to quadruple the amount of titrant added at each step and it still took 4x as long to run the test.

I think I will use this version of the test occasionally, perhaps once a week, as a hands free pH calibration routine. And then use the calculated inflection point as a fixed endpoint most of the time.

Thanks again for all of the help.




My alk today was low...very glad I tested.

 

[JimWelsh]

The same amount of information can be inferred from far fewer data points. Just sayin'.

 

[cypho]

You are right - now that I have a very good idea of where to look, I can shave off a lot of time by only looking at the expected endpoint +/- 0.25 Visually I can't see the inflection point with so little data, but the least squares 3rd degree poly fit does not seem to have any trouble with it!

Returns pH 4.71, alk 2.41

Or were you saying that I don't need to be taking such tiny steps between readings. I am sure that would work too, but I don't think that would actually speed things up that much. Most of the time is spent waiting for the pH reading to stabilize. Steps 2x as big would presumably take around 2x as long to stabilize.

The only way to speed things up is move forward without waiting for the pH to stabilize for a larger portion of the titration. And of course to not keep going way after the endpoint.

By the way - each dot represents 500 pH readings statistically analyzed to remove outliers and then averaged. So there is a mountain of data represented in that plot. Good thing computers can process a mountain of data in the blink of an eye!

 

[Randy Holmes-Farley]

I think he meant the tiny steps. Having a wide enough spread is desirable to get the inflection properly.

 

[cypho]

Once I have the alk in meq/l, how do I convert that to dKH and PPM. I have read that 1 meq/l = 2.8 dKH = 50 PPM Is that the exact conversion, or is there a more precise equation?

Those conversion factors have been weighing on me. 50 and 2.8 just seemed like way too round of numbers. I think I have finally figured out the math behind those conversions.

meq/l to ppm is:
molar mass of CaC03 / 2 = 100.0869 / 2 = 50.04345

meq/l to dKH is:
molar mass of CaO / 20 = 56.0774 / 20 = 2.80387

The difference is very small, but it does slightly change the results displayed by by titrator.

Before 3.000 meq/l = 8.400 dKH = 150.0 ppm
Now 3.000 meq/l = 8.411 dKH = 150.1 ppm

 

[Randy Holmes-Farley]

Those conversion factors have been weighing on me. 50 and 2.8 just seemed like way too round of numbers. I think I have finally figured out the math behind those conversions.

meq/l to ppm is:
molar mass of CaC03 / 2 = 100.0869 / 2 = 50.04345

meq/l to dKH is:
molar mass of CaO / 20 = 56.0774 / 20 = 2.80387

The difference is very small, but it does slightly change the results displayed by by titrator.

Before 3.000 meq/l = 8.400 dKH = 150.0 ppm
Now 3.000 meq/l = 8.411 dKH = 150.1 ppm

I'd be careful to not carry this concern too far. Besides being a possible sign of OCD ( ), it may also not be the full story.

FWIW, many of the things the we do or assume in reefkeeping chemistry do not survive very close inspection. They end up being simplifications of very complicated issues. Very few reefers dig deep enough to encounter them, and those of us who do often are left oversimplifying in discussions so people don't glaze over and walk away.

In this case, I think there are even bigger errors than just rounding off the conversions.

The biggest one is likely the error in assuming that 1 ppm = 1 mg/L in seawater (it does not exactly equate).

If we really have total alkalinity of 3.000000 meq/l, and the salinity is 35 ppt, that means 3.0000000 meq/1.0264 kg

So by your conversion numbers we have 3.00000 meq/L = 3 x 50.04345 mg/L = 150.1304 mg/l

but that 1 l does not weigh 1 kg, but rather weighs 1.0264 kg

So 150.1304 mg/l = 150.1304 mg/1.0264 kg = 146.269 mg/kg = 146.269 ppm

Looking deeper, when doing a total alkalinity titration, there are different ways to do it that give slightly different answers.

For example, titrations either titrate to a specific pH endpoint, or determine by the shape of the curve where the endpoint is. If you elect a specific endpoint, you need to decide what endpoint. There are different values mentioned in the scientific literature, and we have discussed them, but have never come to a good understanding of why some scientists get or use a slightly different value in the range of pH 4.2-4.5. This value is known to change slightly as the alkalinity and CO2 levels change. So no matter what fixed endpoint you use, it will not be 100% perfect for every starting alkalinity and CO2 level in the water.

For alk test kits, there's a whole other layer of uncertainty beyond simple user inability to distinguish colors perfectly. Is the color change exactly at the pH endpoint of the titration? Salinity can impact the pKa of ions in water, so can alter the pH range at which color indicating dyes transition from one color to another. Did the kit manufacturer select a proper dye or set of dyes to give a "correct" endpoint, or is it a kit that was ultimately derived from freshwater data and the manufacturer never even checked the difference between freshwater pKa and seawater? That effect is small for soem dyes,a nd bigger for some, but if we are worrying about alkalinity to four significant figures, it could be important.

We discuss color interpretation issues here, for example:
https://www.reef2reef.com/threads/s...r-results-for-alkalinity.341599/#post-4275414

The pH shift in dyes can be seen from this data for seawater compared to freshwater. It is always easier to make the higher charge form of any ion in seawater than in freshwater:

https://www.sciencedirect.com/science/article/pii/0304420389900613?via=ihub
http://www.3rd1000.com/chem301/p00413.htm
http://www.wiredchemist.com/chemistry/data/acid-base-indicators

Dye...............................pKa in seawater..................pKa in freshwater
Thymol Blue....................1.439................................1.6
Bromophenol Blue..........3.695................................3.85
Bromcresol green............4.410..................................4.7
Bromcresol purple..........5.972..................................6.3
Phenol Red......................7.492.................................7.9