Math Question - Vinegar and Superfat

[BrewerGeorge]

Let's say I make a recipe set to 33% lye concentration and 0% superfat. Normally I use a 50% lye pre-mix and "switch" the water and lye recommendations from the calculator, using 2/3 of the total as lye solution and 1/3 as additional distilled water.

If I use 5% white vinegar for that 1/3 portion instead of distilled water, what will be my approximate actual superfat and effective lye concentration? How much sodium acetate would there be?

I only ask this because I know some of you might know this already, whereas I'm going to have to do some research and a stoicheometry refresher to figure it out myself. TIA.

 

[DeeAnna]

Sometimes it's mentally easier when you convert a percentage problem into a weight problem.

Assume you have 100 g of lye solution made with --

5% vinegar @ 33.3 g
NaOH @ 33.3 g
Water for balance of solution

About 28.3 g (1 oz) of commercial 5% vinegar neutralizes 1 g NaOH. The NaOH neutralized in this particular situation is thus --

NaOH neutralized = 33.3 g vinegar X 1 g NaOH / 28.3 g vinegar ~= 1.2 g

The NaOH remaining in the solution after neutralization is --

NaOH remaining = 33.3 - 1.2 ~= 32.1 g NaOH

There is still 100 grams of solution, so this number converts directly to percentage. In other words, you'd end up with a 32% NaOH solution

If the lye discount is zero with a 33.3% NaOH solution, then adding vinegar to reduce the NaOH to 32.1% would create a 1.2% lye discount. For all intents and purposes, you can say that's a 1% lye discount. (edit -- error correction. changed 0.9% lye discount to 1.2% lye discount)

The sodium acetate made by the vinegar-NaOH reaction can be estimated using a ratio of molecular weights times the NaOH neutralized.

1 mole NaOH makes 1 mole sodium acetate, so 1:1 stoichiometric ratio
MW sodium acetate 82.0343 g/mol
MW sodium hydroxide 39.997 g/mol

Sodium acetate created ~= 1.2 g NaOH X 82.0343 / 39.997 = 2.5 g

Answers subject to correction. Let me know if you see an error.

 

[SaltedFig]

Nice write up.

Minor mathematical error at line 11 (diff s/be 1.2) - doesn't matter, they both round to roughly 1% lye discount so it doesn't change any of your conclusions

I worked the problem slightly differently DeeAnna and, other than some slight rounding differences, came to the same numbers.

Just to add one extra bit BrewerGeorge, there is 7.16% sodium acetate created (by weight of 5% vinegar you've added)
(So 100g of vinegar will make 7.16g sodium acetate, 200g 14.3g etc.)

 

[DeeAnna]

You know, I had 1.2% originally and for some reason though it was wrong and changed it. Go figure. My post above has been edited to show the correct number.

 

[BrewerGeorge]

Thank you!

So if I'm making soap with 700g of oils (one 1501's worth), using approximately 200g of lye solution and 100g vinegar, ending with 1000g finished soap, I should have about 2.5g of acetate in it.

That's not enough to bother with, is it?

 

[DeeAnna]

The original problem was for a total of 100 grams of NaOH + water + vinegar in equal proportions. For that problem, I calculated 33.3 g vinegar @ 5% acidity will make ~2.5 g sodium acetate when the vinegar fully reacts with NaOH.

Now you're increasing the total to 300 grams of mixture. Three times more vinegar than in the first problem, so the total weight of acetate also increases in proportion. 100 / 33.3 X 2.5 = 7.5 g sodium acetate.

 

[earlene]

I think the goal for SA is to harden the soap, yes? I believe when TOMH (topofmurrayhill) did it, that was his goal and he aimed for 2% of oils.

So if you are making a batch of soap using 700 grams of oils, you need 2% of 700 to give you the amount of SA to get similar results that TOMH got from his method explained here. 7.5 grams of SA is a bit over 1%, but as TOMH also mentioned, he was thinking of choosing a range around 1% - 2%, so yes, I think it is worth it.

I have done the same myself, where using a 50% masterbatch lye solution then making up the difference in vinegar to get the [33% Lye] Concentration. I found that the soap is harder, but not as hard as if I use a higher SA calculation. But if I go too high with the vinegar, the soap becomes brittle. I have not experimented enough to know the sweet spot, but I do know 100% vinegar in place of distilled water is too high and made brittle soap for me. So I've never done it again. I do have to admit that the actual soaping oils probably contributed to the brittleness and that it wasn't ONLY the amount of vinegar I used.

 

[BrewerGeorge]

The original problem was for a total of 100 grams of NaOH + water + vinegar in equal proportions. For that problem, I calculated 33.3 g vinegar @ 5% acidity will make ~2.5 g sodium acetate when the vinegar fully reacts with NaOH.

Now you're increasing the total to 300 grams of mixture. Three times more vinegar than in the first problem, so the total weight of acetate also increases in proportion. 100 / 33.3 X 2.5 = 7.5 g sodium acetate.

Ok, got it. I didn't realize you were describing 100g TOTAL. My fault; it's right there clear as day, I just missed it.

But the bigger question is that even at 7.5g in 1000g, that's not enough acetate to do what we want, right?

 

[DeeAnna]

7.5 grams sodium acetate for 1000 grams fats is 0.75% sodium acetate based on total fat weight (ppo). If you follow Earlene's info, that's on the low-ish side, but I'd think it's enough to have some effect. If you use all vinegar rather than equal parts vinegar and water, you'd double that to 1.5% ppo.

 

[penelopejane]

Thank you!

So if I'm making soap with 700g of oils (one 1501's worth), using approximately 200g of lye solution and 100g vinegar, ending with 1000g finished soap, I should have about 2.5g of acetate in it.

That's not enough to bother with, is it?

If you read Teresa’s experiment with vinegar that TOMH tested for her 25% vinegar (don’t ask me the acetic acid amount) worked almost as well as higher percentages.

In fact I prefer the lower percentages as it doesn’t replicate EDTA which I don’t like much in soap as it feels to me like plastic.

 

[SaltedFig]

Thank you!

So if I'm making soap with 700g of oils (one 1501's worth), using approximately 200g of lye solution and 100g vinegar, ending with 1000g finished soap, I should have about 2.5g of acetate in it.

That's not enough to bother with, is it?

It is easy to calculate any amount of vinegar using the percentage calculation from post #3:

The percentage of 7.16% can be multiplied by any vinegar amount, so if you are using 100g of 5% vinegar, the calculation is
100g x 7.16% = 7.2g of sodium acetate

For your 200g of lye solution at a 2:1 water to lye ratio, you would be using 66.67g of sodium hydroxide (200/3) so the calculation would be
200g/3 x 7.16% = 4.8g of sodium acetate