Seifenblasen
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I have seen glancing through a lot of discussions on using citrus (juices) in soap and some extremely low superfat numbers used. Since I am sitting at the airport doing nothing, I did some quick calculations, mainly for my own entertainment, but thought I would share the results. If it sounds like mumbo jumbo to you, or if you don't believe anything I say, that's OK, won't hurt my feelings. For those who care, I must admit I am being very sloppy with significant figures.
The conclusion is you really need not adjust your superfat when using orange juice as it changes about only 1%. It is understood that the acidity in oranges (or any other fruits) varies, due to ripeness, types, etc., but even a very tart orange juice is not going to consume enough NaOH to change the resulting superfat more than 1 or 2%.
Assumptions:
1. Specific gravity of orange juice (OJ): 1.15
2. Two acids of concern in OJ: citric acid and ascorbic acid
3. Citric acid concentration in OJ: 36 – 427 mg/fluid oz., using an average of 231.5 mg/fluid oz., equals to 7.27 mg/ml (http://www.cord.edu/dept/chemistry/CCJAC/2012_Vol_3/2012_3_57.pdf)
4. Ascorbic acid concentration in OJ: 97 mg/8 fluid oz, equals to 0.40 mg/ml (http://nutrition.about.com/od/thera...-Servings-For-A-Days-Worth-Of-Vitamin-C_2.htm)
5. Assume complete dissociation in water (I did not bother to look up the K values).
Known Facts:
1. Reaction between NaOH and citric acid:
C3H5O (COOH)3 + 3NaOH = 3H2O + C3H5O (COO)3Na3
2. Reaction between NaOH and ascorbic acid:
C6H8O6 + NaOH = H2O + C6H7O6Na
3. Molecular weight of citric acid: 192.124 g/mol
4. Molecular weight of ascorbic acid: 176.12 g/mol
5. Molecular weight of NaOH: 33.997 g/mol
If we were to make a simple soap using 1000 g of coconut oil with full water content (38% of oil = 380 g, or 380 ml), Soap Calc generated the following amounts for NaOH based on the different levels of superfatting:
183.24g NaOH – 0%
174.08g NaOH – 5%
172.25g NaOH – 6%
Based on the above equations, 1 mol of citric acid reacts with 3 mols of NaOH, and 1 mol of ascorbic acid reacts with 1 mol of NaOH.
If we replace 100% of the 380 ml water with OJ, the amounts of acids we have are:
Citric acid: 380 ml x 7.72 mg/ml = 2933.60 mg = 2.9336 g
2.9336 g / (192.124 g/mol) = 0.0153 mol
Ascorbic acid: 380 ml x 0.40 mg/ml = 152.00 mg = 0.1520 g
0.1520 g / (176.12 g/mol) = 0.0009 mol
The amount of NaOH consumed by the acids in 380 g OJ is:
3 x 0.0153 mol (amount consumed by citric acid) + 0.0009 mol (amount consumed by ascorbic acid)
= 0.0468 mol
Since the molecular weight of NaOH is 33.997 g/mol,
33.997 g/mol x 0.0468 mol = 1.5911 g
So if you replace the 100% of the water with OJ, and superfat at 5% (using 174.08 g NaOH), your NaOH “loss” due to reaction to the acids in OJ is only 1.5911 g, which would not even result in a 6% superfat (as 6% superfat would mean using 172.25 g NaOH).
174.08 g – 1.5911 g = 172.48 g
You can do the same calculation for lemon juice, lime juice, etc. Just keep in mind although those fruits are slightly more acidic than orange, it is unlikely you will replace the all the water with lemon/lime juice. So the effect is, again, quite negligible.
The conclusion is you really need not adjust your superfat when using orange juice as it changes about only 1%. It is understood that the acidity in oranges (or any other fruits) varies, due to ripeness, types, etc., but even a very tart orange juice is not going to consume enough NaOH to change the resulting superfat more than 1 or 2%.
Assumptions:
1. Specific gravity of orange juice (OJ): 1.15
2. Two acids of concern in OJ: citric acid and ascorbic acid
3. Citric acid concentration in OJ: 36 – 427 mg/fluid oz., using an average of 231.5 mg/fluid oz., equals to 7.27 mg/ml (http://www.cord.edu/dept/chemistry/CCJAC/2012_Vol_3/2012_3_57.pdf)
4. Ascorbic acid concentration in OJ: 97 mg/8 fluid oz, equals to 0.40 mg/ml (http://nutrition.about.com/od/thera...-Servings-For-A-Days-Worth-Of-Vitamin-C_2.htm)
5. Assume complete dissociation in water (I did not bother to look up the K values).
Known Facts:
1. Reaction between NaOH and citric acid:
C3H5O (COOH)3 + 3NaOH = 3H2O + C3H5O (COO)3Na3
2. Reaction between NaOH and ascorbic acid:
C6H8O6 + NaOH = H2O + C6H7O6Na
3. Molecular weight of citric acid: 192.124 g/mol
4. Molecular weight of ascorbic acid: 176.12 g/mol
5. Molecular weight of NaOH: 33.997 g/mol
If we were to make a simple soap using 1000 g of coconut oil with full water content (38% of oil = 380 g, or 380 ml), Soap Calc generated the following amounts for NaOH based on the different levels of superfatting:
183.24g NaOH – 0%
174.08g NaOH – 5%
172.25g NaOH – 6%
Based on the above equations, 1 mol of citric acid reacts with 3 mols of NaOH, and 1 mol of ascorbic acid reacts with 1 mol of NaOH.
If we replace 100% of the 380 ml water with OJ, the amounts of acids we have are:
Citric acid: 380 ml x 7.72 mg/ml = 2933.60 mg = 2.9336 g
2.9336 g / (192.124 g/mol) = 0.0153 mol
Ascorbic acid: 380 ml x 0.40 mg/ml = 152.00 mg = 0.1520 g
0.1520 g / (176.12 g/mol) = 0.0009 mol
The amount of NaOH consumed by the acids in 380 g OJ is:
3 x 0.0153 mol (amount consumed by citric acid) + 0.0009 mol (amount consumed by ascorbic acid)
= 0.0468 mol
Since the molecular weight of NaOH is 33.997 g/mol,
33.997 g/mol x 0.0468 mol = 1.5911 g
So if you replace the 100% of the water with OJ, and superfat at 5% (using 174.08 g NaOH), your NaOH “loss” due to reaction to the acids in OJ is only 1.5911 g, which would not even result in a 6% superfat (as 6% superfat would mean using 172.25 g NaOH).
174.08 g – 1.5911 g = 172.48 g
You can do the same calculation for lemon juice, lime juice, etc. Just keep in mind although those fruits are slightly more acidic than orange, it is unlikely you will replace the all the water with lemon/lime juice. So the effect is, again, quite negligible.
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