Carbonate/bicarbonate buffer

[alanrockwood]

Does anyone use a carbonate/bicarbonate buffer? The pKa for the second dissociation of the carbonic acid/bicarbonate/carbonate system is about 10.25, or maybe it's 10.23, but anyway assuming it is 10.25, an equimolar mixture of carbonate and bicarbonate should give a pH of about 10.25.

I gather from discussions about pH and development that a pH of 10.25 would put a developer in the active range, but not extremely active, and the buffering capacity would be high, depending of course somewhat on the absolute concentrations.

At a molar ratio of [CO3--]/[HCO3-] the pH would be about 9.25, and the buffering capacity would be moderate, again depending somewhat on the absolute concentrations.

If I recall correctly, a pH of 9.25 is below the threshold of strong developer activity for ascorbate and is close the the practical threshold of moderate to strong developer activity for para aminophenol.

Taking these broad concepts to a specific developer formulation concept (i.e. raising a second topic of discussion for this thread), maybe making a pH 9.25 bicarbonate/carbonate buffer with (a super additive) para aminophenol and ascorbate developer combination could be interesting. The pH might be low enough to tame ascorbate's tendency to fog film by keeping it from being he main developer, but high enough to allow the para aminophenol to be the main developer. Because the buffering capacity of this buffering system at pH 9.25 would be relatively low, the tendency for oxidation of ascorbate to lower the pH may be only partially compensated by the buffer, especially if the total buffer concentration is kept low, so there may be a moderate compensating effect and/or edge effect when using this mixture.

One nice thing about this proposed system is that it would be possible to make it at home using relatively common ingredients, a desirable thing, but not necessarily the main idea of this thread.

Of course, I haven't tested this. I am just throwing out this concept for discussion.

 

[Photo Engineer]

At one time or another, I have run most of the experiments you describe above. We took, on average, that the best position for buffering at 20 deg C for the Carbonate/Bicarbonate was at 10.1. You will see that in use in the RA and C-41 developers most notably.

Lowering pH brings many advantages but none of which are easily described, but basically the biggest example is that at lower pH, a developer becomes less sensitive to CO2 from the air, and also it becomes less sensitive to oxidation. These interesting facts bring on a lot of possibilities. Also, Carbonate is not the best choice as you lower pH.

PE

 

[Alan Johnson]

In the case where photo chemicals are not available its probably easier to make sodium aminophenolate from acetaminophen capsule contents as in making PaRodinal then add vit C ascorbic acid to adjust the pH.But is there any real evidence that p-aminophenol and ascorbate are superadditive?

 

[Kirk Keyes]

At a molar ratio of [CO3--]/[HCO3-] the pH would be about 9.25, and the buffering capacity would be moderate, again depending somewhat on the absolute concentrations.

My understanding from titrating thousands of water samples for alkalinity content, pH 8.3 is the endpoint. That's where you should have a 50/50 ratio of carbonate/bicarbonate.

As far as buffering capacity, that's a function of how many moles of each you have in solution, and not the pH of that solution...

 

[alanrockwood]

As far as buffering capacity, that's a function of how many moles of each you have in solution, and not the pH of that solution...

Actually, buffering capacity is a function of both the pH and the number of moles. However, the pH dependence is indirect.

The fundamental quantities that determine buffering capacity are the mole ratio of the acid and conjugate base and the total number of moles of acid and conjugate base.

Maximum buffering capacity is achieved at equal mole ratio of acid and conjugate base. The rule of thumb chemists use is that when a mole ratio between 0.1 and 10 is the useful range.

This ratio range corresponds to a range of +/- 1 pH unit relative to the pKa of the acid. Outside of this range the buffering capacity is dropping very fast compared to the maximum, i.e. compared to an equimolar buffer. This is why buffering capacity depends on pH, or more correctly speaking, the pH relative to the pKa of the acid.

The buffering capacity also depends, as mentioned above, on the total concentration of the acid and conjugate base. I won't go into the reason for this because I think you agree and it is probably obvious to everyone else as well.

Regarding the end point of a titration, that is not where the acid and conjugate base are in 50/50 ratio, but rather the point at which one or the other (depending on the direction of the titration) is virtually completely used up.

 

[alanrockwood]

I should add one other comment. You are correct when you say that buffering capacity depends on the number of moles of each (acid and conjugate base) present. This is an alternative and equivalent description to my description of using the mole ratio and the total number of moles.

 

[Kirk Keyes]

Actually, buffering capacity is a function of both the pH and the number of moles. However, the pH dependence is indirect.

I'd say the pH is a function of the the ratio and number of moles of buffer present, the capacity is a function of the number of moles of that buffer ratio present.

Buffer first, pH second.

Keep in mind that alkalinity is not buffering capacity, but does measure the amount of carbonate, bicarbonate, and hydroxyl ion as well.

I stand corrected with your statement that the endpoint is where one ion has been consumed and is converted into the other ion. In other words:
H+(aq) + CO3=(aq) --> HCO3-(aq) at pH 8.3

I had 5 hours of sleep last night after flying 1700 miles...

 

[Murray Kelly]

The last half of your original post reminds me of Pat Gainer's 'Begone Fog!'
contribution in the Unblinking Eye article 'Appreciating Rodinal'.
http://unblinkingeye.com/Articles/Rodinal/rodinal.html
I can attest to the extreme fog of PaRodinal and ascorbate mixed - just haven't gotten around to adding some borax. Initially I would expect any free caustic to form metaborate with added borax but with persistence, enough borax would pull the pH down to about 9.2. An excellent buffer, too.
Doesn't add anything to your carbonate/bicarbonate conjecture but the general idea is the same.
Murray

Big SNIP ----

If I recall correctly, a pH of 9.25 is below the threshold of strong developer activity for ascorbate and is close the the practical threshold of moderate to strong developer activity for para aminophenol.

Taking these broad concepts to a specific developer formulation concept (i.e. raising a second topic of discussion for this thread), maybe making a pH 9.25 bicarbonate/carbonate buffer with (a super additive) para aminophenol and ascorbate developer combination could be interesting. The pH might be low enough to tame ascorbate's tendency to fog film by keeping it from being he main developer, but high enough to allow the para aminophenol to be the main developer. Because the buffering capacity of this buffering system at pH 9.25 would be relatively low, the tendency for oxidation of ascorbate to lower the pH may be only partially compensated by the buffer, especially if the total buffer concentration is kept low, so there may be a moderate compensating effect and/or edge effect when using this mixture.
More SNIP ----

 

[Alan Johnson]

I just tried adding ascorbic acid to PaRodinal 1:50, pH with given weights of ascorbic acid added to 500ml was: +0g >12, +1g >12, +2g=11.8, +2.5g=10,+3g=8.2.
T-max 100 developed in the 1:50 with 3g ascorbic acid/500ml 10m 68F gave very thin negatives.
Adding ascorbic acid without a buffer causes IMO unacceptable pH changes.

I wonder roughly how much sodium carbonate I should put in with the PaRodinal 1:50 +3g ascorbic acid before trying to adjust the pH to say 9.25 with sodium bicarbonate,ie enough buffer to fix the pH so that one could suggest a formula for use,eg would 10g/L sodium carbonate be OK?
All these except sodium sulfite are locally available chemicals.I cannot get borax from local pharmacies,some sell boric acid and do not know the difference.

 

[Kirk Keyes]

The pKa2 of cabonic acid (bicarbonate going to carbonate) is at pH 10.25 at 25 °C. So a 50/50 mix of them should give that pH. If you add more bicarbonate to the mixture, you can force the pH lower, about 1 pH unit and still have reasonable buffering.

If you add the ascorbic and lower the pH down to 8.2, and then add carbonate to bring the pH back to where you want, you will have some buffering from that.

There are online buffering calculators that you can use to help determine how much you need to add.

 

[Alan Johnson]

Quite a good table for the pH of carbonate/bicarbonate buffers here:
www.sigmaaldrich.com/life-science/c.../buffer-reference-center.html#sodiumcarbonate
Sodium carbonate is as soda crystals I believe.

 

[Photo Engineer]

There is a very easy way to get the optimum ratio and buffer capacity for any buffer system. It is rule of thumb, but works.

I'll leave it to the OP to figure it out and let us know. (Kirk, don't give him the answer! )

Much easier than the table or anything else.

PE

 

[alanrockwood]

There is a very easy way to get the optimum ratio and buffer capacity for any buffer system. It is rule of thumb, but works.

I'll leave it to the OP to figure it out and let us know. (Kirk, don't give him the answer! )

Much easier than the table or anything else.

PE

If, by optimum ratio you mean maximum buffer capacity for a given amount of reagent, it occurs at an equimolar mixture of acid and conjugate base. At this ratio the pH equals the pKa of the acid. (I think I might have mentioned these points in earlier posts.) The pH for other mole ratios can be calculated by the Henderson-Hasselbalch equation.

An equation for buffer capacity can be derived by taking the derivative of the concentration of added base with respect to pH. You would use the Henderson-Hasselbalch equation when taking the derivatives. Being too lazy to work out the math myself, I looked up the answer, and for an equimolar mixture of acid and conjugate base the result for buffer capacity is given approximately by 2.3*C/4, where C is the sum of the concentrations of the acid and conjugate base, or as an extremely rough approximation the buffer capacity is about equal to half of C, or in other words about equal to the concentration of either the acid or conjugate base. When the mole ratio goes to 0.1 or 10 the buffer capacity is about one third the buffer capacity of the buffer capacity of an equimolar ratio. Outside of these bounds the buffer capacity drops rather precipitously, and people therefore usually avoid extreme ratios when preparing buffers, unless of course one intends to produce a buffer with a low buffering capacity.

One last fine point. Strictly speaking the relationships do not use concentrations of acid and conjugate base, but rather the thermodynamic activities of acid and conjugate base. For extremely dilute solutions one can use concentrations in place of activities. This is the so-called ideal condition. For ionic solutions (all buffers are ionic solutions) the solutions are rather non-ideal at practical concentrations, and the equations using concentrations will only give approximate results.

 

[Photo Engineer]

Much too complicated.

KISS rules.

PE

 

[alanrockwood]

Much too complicated.

KISS rules.

PE

50:50 ratio of acid and conjugate base gives maximum buffering capacity. In the case of carbonate/bicarbonate that would be an equi-molar ratio of carbonate and bicarbonate.

Of course, it all depends on what one wants to accomplish. For some purposes you might want a weaker buffer. In physiology, the body uses the carbonic acid/bicarbonate system to adjust the pH of blood. They are in about a 10:1 ratio. (I should know which one is in the higher concentration, but I don't recall at the moment.) This is near the edge of the effective range for buffering for this system. By the way, hemoglobin is the main buffering agent in blood, but the body uses the carbonic acid/bicarbonate system to fine tune the blood's pH.

 

[Gerald C Koch]

An equimolar mixture of sodium bicarbonate and sodium carbonate forms a solution of sodium sesquicarbonate or trisodium hydrogen dicarbonate. A 1% solution has a pH of 9.9.

http://www.hillbrothers.com/msds/pdf/n/sodium-sesquicarbonate.pdf

 

[Photo Engineer]

Still too complex. Just add 25 - 50 g/l Na2CO3 to water and then adjust to the pH you want with Bicarb or even better Acetic Acid, and you end up with a quite nice buffered solution.

PE

 

[alanrockwood]

post deleted.

 

[Photo Engineer]

Maybe I should be more explanatory than I was in the post above.

In a common B&W developer you might have Metol and Sulfite as well as Carbonate. But Metol is a Sulfuric Acid salt and Sulfite itself has buffering power. Add to that some Quadrofos (sequestrant) and the HQ, and in an MQ developer you now have 5 or more compounds that can supply ions with potential buffering ability.

It is thus beyond the power of most chemists to just quote a mixture of Carbonate/Bicarbonate which would give the best buffer. All of the rest of the ions are in the mix as well and are contributing to whatever the "best" pH should be.

The selection is not a simple matter and you should just take the pH you get from the mix or adjust it with an acid or base. The Atmosphere will change it in a few days or even a few hours.

PE

 

[alanrockwood]

Maybe I should be more explanatory than I was in the post above.

In a common B&W developer you might have Metol and Sulfite as well as Carbonate. But Metol is a Sulfuric Acid salt and Sulfite itself has buffering power. Add to that some Quadrofos (sequestrant) and the HQ, and in an MQ developer you now have 5 or more compounds that can supply ions with potential buffering ability.

It is thus beyond the power of most chemists to just quote a mixture of Carbonate/Bicarbonate which would give the best buffer. All of the rest of the ions are in the mix as well and are contributing to whatever the "best" pH should be.

The selection is not a simple matter and you should just take the pH you get from the mix or adjust it with an acid or base. The Atmosphere will change it in a few days or even a few hours.

PE

Good discussion PE. The calculation of pH when multiple buffers are involved can be very complex and usually can't be done by hand, so an experimental approach is often warranted.

Some additional information: In the case of the Sulfurous acid/bisulfite/sulfite system the two relevant species at high pH would be sulfite and bisulfite. I am finding very conflicting information about pKa of the bisulfite ion. Some sources say 1.99 and some say 6.97. Either way, at the pH of many developers (pH>9) it will be virtually completely ionized to the doubly charged form, and it should have relatively little effect on the pH of the solution. This conclusion would need to be modified if the concentration of sulfite is extremely high compared to the other potential buffering components.

 

[Photo Engineer]

Well, there is also the slow but real reaction of HQ with O2 and SO4= to produce HQMS and the resultant observed pH change over about 1 day and which leads many to say that MQ developers should stand for a day or so to equillibrate. There is also the reaction of Metol with O2 (and CO2 for that matter) along with OH- and H+ leading to a lot of changes over days until things equillibrate.

Myself, I expect different results from fresh Dektol or D76 and that mixed up about 2 days earlier. From then on, things are stable and gradually the developer begins to die. This is a combination of Oxidation and pH changes induced by the inevitable equillibria of basic reductants in an acidic oxidative environment.

PE