[jayjay5531]

I'm a biology undergrad working in a lab, and I've only ever taken general chemistry and organic chemistry (I'm actually not sure if this question belongs in the "general chemistry" or "analytical chemistry" page, since I'm really trying to do a calculation and not actually do any titrations or anything). But anyways, I'm making agar plates with media containing different concentrations of ammonium sulfate (a very wide range going from 0.1 μM to 0.5 M). I'm trying to keep the pH constant for each treatment, but obviously adding more ammonium sulfate will lower the pH. Therefore I want to add a base (maybe sodium sulfate?), and add higher amounts to the treatments with higher amounts of ammonium sulfate, so that the pH remains constant across treatments. To further complicate things, the plate medium I'm using has a phosphate buffer (made with a mix of K₂HPO₄ and KH₂PO₄).

I know the concentrations of KH₂PO₄ and K₂HPO₄, as well as the different concentrations of (NH₄)₂SO₄ I will be using in the different treatments. How do I calculate the amount of base I need to add in order to keep the pH constant across treatments?

I don't know how to account for the ammonium, sulfuric acid, and phosphoric acid equilibria simultaneously. I don't have a pH meter, and pH paper may not really work because it's not precise enough and the medium becomes a gel as it cools (I'm thinking that a pH meter may also not work for that same reason, even if I had one?).

Thanks so much!!

[jayjay5531]

(To clarify, I mean "how much base to add for each particular treatment"; and of course it will depend on the Kb of the base that I use)

[hypervalent_iodine]

Normal practice is to adjust with NaOH or HCl using a pH meter. The media solutions you are working with are too complex to accurately calculate how much of something you’d need to get to your desired pH. Paper could work in a pinch, but it won’t give you very precise results. Can you not see if someone around you has a pH meter you can borrow (assuming you’re doing this in an actual lab)?

[billnotgatez]

Would a pH indicator be appropriate?
https://en.wikipedia.org/wiki/PH_indicator

I guess it might not due to the potential of being biologically active in the experiment.
That is depending on which indicator you use.

[billnotgatez]

I have mentioned in another thread about the concern of pH versus ions effect in a biological environment.
http://www.chemicalforums.com/index.php?topic=95273.msg337971#msg337971

I am not sure if it applies to this study, but never the less it might be a consideration.

[billnotgatez]

I am also wondering if you would be allowed to use buffered agar plates?

[Borek]

Hint: technically you are looking for such a ratio of [NH₃]/[NH₄⁺] that pKa + log([NH₃]/[NH₄⁺]) = 7.

[billnotgatez]

I am sorry -- I missed this when first reading the original post

...
To further complicate things, the plate medium I'm using has a phosphate buffer (made with a mix of K₂HPO₄ and KH₂PO₄).
...

[jayjay5531]

Hint: technically you are looking for such a ratio of [NH₃]/[NH₄⁺] that pKa + log([NH₃]/[NH₄⁺]) = 7.

The ratio would be 0.00575 to 1. However, how do I simultaneously account for the sulfuric acid? I can assume that the first proton will fully dissociate, but the second proton also dissociates (pK_a2 = 1.92)

[Borek]

At pH 7 you can safely assume sulfuric acid is completely dissociated. (Hint: you can use the same equation to find the ratio [SO₄^2-]/[HSO₄^-, it works for every acid, it is just a rearranged acid dissociation constant).

[jayjay5531]

I started to try to solve it like this:

I'm simplifying the situation: my goal is to get a mixture of H₂SO_4(aq) and NH_3(aq) that will give me a pH of 7. Specifically, I want a formula that will calculate [NH₃]_initial (where [NH₃]_initial is the concentration of aqua ammonia I need to add), for any given initial concentration of sulfuric acid [H₂SO₄]_initial, in order to get pH = 7.

So, I know [H₂SO₄]_initial (which is the same as [HSO₄⁻]_initial or [H⁺]_initial, since I assume complete dissociation of the first proton), and I know the final proton concentration that I want: [H⁺] = 10⁻⁷.

I have five unknowns: [HSO₄⁻], [SO₄²⁻], [NH₃], [NH₄⁺], and [NH₃]_initial (which is the thing I'm trying to solve for), so I need five equations.

The first four are obvious:

(1)     K_a(HSO4⁻) [HSO₄⁻] = [SO₄²⁻] [H⁺]   (definition of K_a),
         and since [H⁺] = 10⁻⁷, we have K_a(HSO4⁻)[HSO₄⁻] = 10⁻⁷ [SO₄²⁻]

(2)     K_a(NH4⁺) [NH₄⁺] = [NH₃] [H⁺]   (definition of K_a)
         and since [H⁺] = 10⁻⁷, we have K_a(NH4⁺) [NH₄⁺] = 10⁻⁷ [NH₃]

(3)     [H₂SO₄]_initial = [HSO₄⁻] + [SO₄²⁻]   (balance S)

(4)     [NH₃]_initial = [NH₃] + [NH₄⁺]   (balance N)


I need one more equation. I was thinking this, is this valid:  ??

(5?)     [NH₄⁺] − [NH₃] = [H₂SO₄]_initial + [HSO₄⁻] − [SO₄²⁻]

which describes the claim that the net H⁺'s gained by NH₃ (to make NH₄⁺) came from either the initial [H⁺]_initial (which equals [H₂SO₄]_initial), or from the dissociation of the second proton ([HSO₄⁻] − [SO₄²⁻]). Is this 5th equation valid? If so, I can combine them all and solve for [NH₃]_initial.

[Borek]

I know [H₂SO₄]_initial (which is the same as [HSO₄⁻]_initial or [H⁺]_initial, since I assume complete dissociation of the first proton)

Depends on the concentration, in 0.01 M sulfuric acid about 50% of HSO₄^- is already dissociated, in 0.1 M around 10 %, so the assumption is rather doubtful.

Most obvious fifth equation is the charge balance (solution is neutral, so sum of negative charges must equal sum of positive charges).

The approach is more or less correct, but the result you will get from these calculations will be off, as long as you ignore the ionic strength of the solution. And even when you take it into account, mixing the compounds as calculated can give solution that has pH that is a unit or even more off. You are far from buffering effects of the ammonia and it means tiny inaccuracies in solution concentration/volume measurement have a large effect on the final pH.

If anything, you can play with the Buffer Maker, it will easily calculate what to mix. But even then it will give just a rough estimate of what to mix, to get really precise result you will need to adjust the solution composition against the pH meter.

[jayjay5531]

Thanks Borek — I definitely will use a pH meter for this if I can get access to one, I think I’m mainly still interested in my original question just out of curiosity at this point lol. I was wondering, what would the charge balance equation look like?

Thanks everyone for your responses! I appreciate it

[Borek]

I think I’m mainly still interested in my original question just out of curiosity at this point

http://www.chembuddy.com/?left=pH-calculation&right=toc

There will be charge balance equations on pages describing individual cases.

For pure water it is just [OH^-] = [H⁺], add any ions and you need to add them on both sides (taking their charges into account, so for example 2[SO₄^2-] for fully dissociated sulfuric acid anion).