Confusion concerning 0dKH and nitrification

[dw1305]

Hi all,

You can math it up, but essentially that means at pH 3 or higher there is no capacity for the sulphate ion to accept a proton, which means at the type of aquarium pH we are considering the sulphate ion does not affect pH at all.

Thank you. I thought that was the answer.

That means at our usual pH range, the first proton is always lost (pKa 2.16) , the third proton is always still on the phosphate (pKa 12.32), but the second proton can come on and off, so you'll have a mix of HPO3-- and H2PO3-. You get the most "buffering capacity" at the pKa, so phosphate will be an excellent buffer around pH 7 (best at pH 7.21). If you were to add a purely phosphate salt like K3PO4 to aquarium water, the K3 will all immediately come off, and the loose PO3--- will immediately grab (on average) 1.5 protons which means the pH will go up because the concentration of free H+ will go down (some got stuck on the phosphate). People usually don't want this to happen, which is why they use "hydrated" versions of potassium phosphate, typically KH2PO4.

Perfect, we have a bit of discussion of <"phosphate buffers">, but not the explanation of why (until today). This is a potassium phosphate buffer calculator <"Potassium Phosphate (pH 5.8 to 8.0) Preparation and Recipe | AAT Bioquest">

cheers Darrel

 

[aquanoobie]

For funzies we can look at (composite) carbonic acid H2CO3, with pKa1 of 6.35 and pKa2 of 10.33. That means the first proton can come on and off around pH 6-7, whilst the second proton is essentially always on below pH of 9.5, so there will be a mix of H2CO3 and HCO3- at neutral(ish) pH.

Interesting!

What is the lowest pH CO2 injection can achieve in distilled or DI water?

 

[dw1305]

Hi all,

What is the lowest pH CO2 injection can achieve in distilled or DI water?

You can pump a huge amount of CO2 into a liquid, it is a <"very soluble gas">. The only way of keeping it in solution would be to keep it contained, in the <"pop bottle"> scenario.

The problem would be that as the concentration of dissolved CO2 became larger the rate at which it escapes (due to <"Henry's Law">) from the <"gas exchange surface"> grows as well.

Have a look at @hax47 's thread <"Gas-exchange experiments">

I think the pH of cold carbonated sparkling water is around pH 4.5, although none of these would be DI water to start off with.

cheers Darrel

 

[aquanoobie]

I think the pH of cold carbonated sparkling water is around pH 4.5, although none of these would be DI water to start off with.

What would be the pH in pure water, 3.68 - 4.68 at our usual CO2 injection rates?

Carbonic acid

pH of Common Acids and Bases

hydrochemistry program

www.aqion.de

 

[dw1305]

Hi all,

What would be the pH in pure water, 3.68 - 4.68 at our usual CO2 injection rates?

I'm not entirely sure, I'm going to guess it would be somewhere in that range. The 100 mMol value is far beyond the amount of CO2 people inject.

The workings. that go back and forth from moles to ppm (mg / L) are in the <"Coca-cola thread">.

I'm not sure that pH measurements are very useful as you approach pure H2O. I prefer @_Maq_ 's acid neutralising capacity (ANC) as an approach which is probably more relevant to us: <"Some handy facts about water">.

I'm not very good at chemistry, so @hax47 and @Andy Pierce are probably your best bet for a more nuanced view.

cheers Darrel

 

[MichaelJ]

I'm not sure that pH measurements are very useful as you approach pure H2O. I prefer @_Maq_ 's acid neutralising capacity (ANC) as an approach which is probably more relevant to us: <"Some handy facts about water">.

I'm not very good at chemistry, so @hax47 and @Andy Pierce are probably your best bet for a more nuanced view.

On a similar note, that is an area where I want to further my practical understanding in terms that are relevant to our hobby. For instance, what's the relationship between dKH (HCO3 contents) and pH in terms of what range the pH can be allowed to change naturally at a given dKH. We know that low dKH (low alkalinity essentially) will enable us to easily lower our pH with say botanicals and other natural means which is generally beneficial for our planted soft water tanks in terms of uptake etc. ... whereas high dKH makes it much harder or impossible given the increased capacity to neutralize acid - what we call buffering. But what's the underlying mechanism/math that would allow us to make reasonable ballpark predictions for a given dKH which is what hobbyists are mostly concerned about?

Cheers,
Michael

 

[Andy Pierce]

What would be the pH in pure water, 3.68 - 4.68 at our usual CO2 injection rates?

If you inject to a final concentration of 30 ppm (30 mg/l) CO2 that makes a CO2 concentration of around 680 uM (0.03g CO2 per litre divided by the molecular weight of CO2 of 44 g/mole). When dissolved in pure water the ratio of CO2:H2CO3 is about 588:1 so you'd have 1.16 uM H2CO3. The pKa of H2CO3 (actual H2CO3, not the hydrated composite) is 3.6 so putting that into a weak acid pH calculator with the 1.16 uM acid concentration shows pH of around 4.75. The other way you could arrive at this would be to use the CO2 concentration of 680 mM and the pKa of composite carbonic acid of 6.3 which gives you about the same result. You won't have pure water of course in your aquarium...

 

[dw1305]

Hi all,

........ and @Andy Pierce are probably your best bet for a more nuanced view.

If you inject to a final concentration of 30 ppm (30 mg/l) CO2 that makes a CO2 concentration of around 680 uM (0.03g CO2 per litre divided by the molecular weight of CO2 of 44 g/mole). When dissolved in pure water the ratio of CO2:H2CO3 is about 588:1 so you'd have 1.16 uM H2CO3. The pKa of H3CO3 (actual H2CO3, not the hydrated composite) is 3.6 so putting that into a weak acid pH calculator with the 1.16 uM acid concentration shows pH of around 4.75.

There we are, that is definitely a "more nuanced view".

cheers Darrel

 

[John q]

There we are, that is definitely a "more nuanced view".

Well you did summon the Chemist.

 

[MichaelJ]

If you inject to a final concentration of 30 ppm (30 mg/l) CO2 that makes a CO2 concentration of around 680 uM (0.03g CO2 per litre divided by the molecular weight of CO2 of 44 g/mole). When dissolved in pure water the ratio of CO2:H2CO3 is about 588:1 so you'd have 1.16 uM H2CO3. The pKa of H3CO3 (actual H2CO3, not the hydrated composite) is 3.6 so putting that into a weak acid pH calculator with the 1.16 uM acid concentration shows pH of around 4.75. The other way you could arrive at this would be to use the CO2 concentration of 680 mM and the pKa of composite carbonic acid of 6.3 which gives you about the same result. You won't have pure water of course in your aquarium...

I like this... and working my way through it - meticulously! ... Tentatively: Andy, if your ever up for "adoption" please PM me

There is a great quote by Richard P. Feynman when asked to explain his additions to Paul Dirac's theory of Quantum Electrodynamics in simple terms: He quipped: "If I could explain it to the average person, It wouldn't have been worth the Nobel Prize" ... sometimes stuff is just complicated for the uninitiated.

Cheers,
Michael

 

[hax47]

On a similar note, that is an area where I want to further my practical understanding in terms that are relevant to our hobby. For instance, what's the relationship between dKH (HCO3 contents) and pH in terms of what range the pH can be allowed to change naturally at a given dKH. We know that low dKH (low alkalinity essentially) will enable us to easily lower our pH with say botanicals and other natural means which is generally beneficial for our planted soft water tanks in terms of uptake etc. ... whereas high dKH makes it much harder or impossible given the increased capacity to neutralize acid - what we call buffering. But what's the underlying mechanism/math that would allow us to make reasonable ballpark predictions for a given dKH which is what hobbyists are mostly concerned about?

Cheers,
Michael

I am unsure if this answers your question, but... When the pH is lowered with anything outside CO2, basically the KH / alkalinity is lowered. The less KH you have, the bigger the further pH changes with a unit of KH change you get (the relative changes matter). If you look at this plot, you can see the bigger pH differences the closer we are to 0 KH at a CO2 level of 3 ppm (note that the x-axis is logarithmic):

So if you have an alkalinity of 2 dKH, and you want to keep at least 1 dKH, you should not drop the pH by more than ~0.3. 10x change in KH makes 1 pH change, 3x about 0.5, 2x about 0.3.

Of course, the exact pH will depend on the CO2 levels, but the pH steps are the same. 1-30 ppm range:

 

[MichaelJ]

I am unsure if this answers your question, but...

Yes @hax47 this is great!! I think it at least partially answers my question... however, and to be specific, what is the underlying math function(s) (its my thing, so don't hold back lol) governing these graphs ?

Cheers,
Michael

 

[aquanoobie]

If you inject to a final concentration of 30 ppm (30 mg/l) CO2 that makes a CO2 concentration of around 680 uM (0.03g CO2 per litre divided by the molecular weight of CO2 of 44 g/mole). When dissolved in pure water the ratio of CO2:H2CO3 is about 588:1 so you'd have 1.16 uM H2CO3. The pKa of H2CO3 (actual H2CO3, not the hydrated composite) is 3.6 so putting that into a weak acid pH calculator with the 1.16 uM acid concentration shows pH of around 4.75. The other way you could arrive at this would be to use the CO2 concentration of 680 mM and the pKa of composite carbonic acid of 6.3 which gives you about the same result. You won't have pure water of course in your aquarium...

The Best explanation ever!

 

[hax47]

Yes @hax47 this is great!! I think it at least partially answers my question... however, and to be specific, what is the underlying math function(s) (its my thing, so don't hold back lol) governing these graphs ?

Cheers,
Michael

It is the Henderson–Hasselbalch equation, which is used to calculate the pH of a buffer:

pH = pKa + log10([Base]/[Acid])

Where pKa is the negative base-10 logarithm of the acid dissociation constant. From the equation, one can see, that pKa is the pH value by which the concentration of the base and acid is the same (since log 1 is 0).

In the case of the bicarbonate buffer, we have bicarbonate as the base and H2CO3 as the acid. As @Andy Pierce wrote, the amount of H2CO3 is very low compared to CO2. But we can use CO2 instead since it is in equilibrium with H2CO2, although CO2 is not an acid, strictly speaking. Although the reaction resulting in HCO3- from CO2 is a multi-step process, we can still determine the dissociation constant as it was a single-step reaction:
CO2 + H2O <----> H+ + HCO3-

The right pKa here is a question but from a paper @Andy Pierce's linked we can calculate it as 6.52. In some pH/KH/CO2 tables, people use different values, but this one seemed to be giving reasonable results also in my measurements.

So basically we have a pKa value, and then we add the base-10 logarithm of the bicarbonate/CO2 ratio:

pH = 6.52 + log10([bicarbonate]/[CO2])

Concentrations here are molar concentrations, but those are linear functions of ppm. Also, we usually take bicarbonate concentration as a linear function of KH, which is only true at pH values under about 9, but this is what range is usually interesting for us.

From the above equation, we can see that 10x change in the ratio makes a change of one in pH, no matter if the ratio is changed because of CO2 or bicarbonate/KH. So that is why smaller KH changes have a bigger effect at low KH values. One dKH drop at 2 dKH halves the ratio, while at 10 dKH has an almost negligible effect.

Edit: in the linked Henderson-Hasselbach page, the pKa used for bicarbonate buffer is 6.1, but that is true for ion concetrations and temperature present in blood.

 

[aquanoobie]

In the case of the bicarbonate buffer, we have bicarbonate as the base and H2CO3 as the acid. As @Andy Pierce wrote, the amount of H2CO3 is very low compared to CO2. But we can use CO2 instead since it is in equilibrium with H2CO2, although CO2 is not an acid, strictly speaking.

This must be the first H2CO2 formic acid ants venom weapon reference on UKAPS.

Do we have that in CO2 injected water?

 

[MichaelJ]

So basically we have a pKa value, and then we add the base-10 logarithm of the bicarbonate/CO2 ratio:

pH = 6.52 + log10([bicarbonate]/[CO2])

Concentrations here are molar concentrations, but those are linear functions of ppm. Also, we usually take bicarbonate concentration as a linear function of KH, which is only true at pH values under about 9, but this is what range is usually interesting for us.

Thanks @hax47 ... Appreciated!

the pKa used for bicarbonate buffer is 6.1, but that is true for ion concetrations and temperature present in blood.

I will keep that in mind next time I travel in Transylvania.

Cheers,
Michael