For modern homesteaders, who might have a scale and measuring cup handy, it would be much more precise just to measure the density of the lye solution directly. (A graduated cylinder would make this calculation--and other density calculations you might want to do--more precise, but a measuring cup, used judiciously, should be good enough.
Another technique is to use a pH indicator and either dilute a small (representative) portion of the lye water or titrate it with an acid (such as vinegar) to find the strength of it. The pH indicator would also be useful during the soapmaking process to check the progress of the saponification reaction.
Let's take a look at each of those techniques in more detail.
To make soap, we normally use a ratio of something like 2.89 oz NaOH to 7.87 oz water, which works out to about 26.9 wt% NaOH. According to the above calculator, that should give us a solution density of 1.29 g/mL. (The analogous numbers for KOH lye would be 4.06 oz KOH to the same amount of water, giving 34.0 wt% KOH, and a density of 1.33 g/mL.) If we take an egg density of 1.1 g/mL, we can calculate the amount of water that should be displaced by the egg if we know the volume of it.
A typical large egg has a mass of 57 g, corresponding to a volume of 51.8 mL. Buoyancy dictates that the egg should displace 57 g of the lye solution, which will correspond to a volume less than 51.8 mL if the lye solution is more dense than the egg (which it should be if the egg is floating). As an approximation, we can find an equation for an egg and make a graph to see how much of the egg should be above the water for a quarter-sized interface.
|The egg equation came from here, but we normalized it to match the dimensions of an actual egg. We assumed that an egg was sufficiently symmetrical to use a 2-D projection and calculate areas instead of using a 3-D model and calculating volumes. In reality, the egg will sit with the skinny end slightly lower in the water since the air pocket is toward the flatter end. In any case, leaving an area the size of a quarter above the surface would require a lye density of 1.13 g/mL, which is considerably less dense than our standard recipe, which has a density closer to 1.3 g/mL. If the egg were a little less dense (toward the 1.03 g/mL end), it would sit higher. As a point of reference, a potato has a density near 1.09 g/mL, in the same range as an egg.|
|For example, using data found here (and their related NaOH calculator), we can make a correlation, measure the density of the lye directly, and use the correlation to calculate the concentration. It would help to have a digital scale and a graduated cylinder, but you can probably get at least as close as the egg/potato method with an old spring-loaded scale and a measuring cup. We dripped a small batch of lye recently and were doing tests with it, but accidentally spilled it in the kitchen sink before we could test this method. For lye dripped from ashes, use the KOH equation. Note that if our solution density is 1.3 g/mL, our lye concentration (as KOH) is about 34 wt%, or 5.2 molar. This density method will be our favorite lye strength test going forward.|
|Another way to test the strength is with a pH indicator. One natural pH indicator is cabbage juice, which contains anthocyanidin pigments. (As an aside, we noticed similar color changes in elderberry juice and wondered why; elderberries have a similar set of pigments.) These pigments change structure as the pH of a solution changes, with each structure having a different color. See here for more info.|
|The pigment structures of the cabbage anthocyanidins look something like this, with the different colors as shown. Part of the reason the change from red to purple happens over such a wide pH range is the colorless intermediate. Similarly, the yellow compound starts to form at pH > 8, but doesn't become the dominant form of the molecule until much higher pH (the presence of both yellow and blue make the solution green, kind of like a Ziploc bag). The "R" groups are glucosides (i.e. substituted glucose molecules). Sources for this figure came from here, here, and here. If you took note of the concentrations above (i.e., that our standard soap recipe calls for 5.2 molar lye) and you are familiar with the pH scale, you might realize that there's a bit of a problem here. That is, our lye should be at pH 14.7, but our indicator will be yellow at every pH > 11.|
|Guess we'll just have to dry it down with waste heat from the oven (after baking bread or something) and store it in a jar until we can make some more!|
|Also, in case you're interested, here's how we made the pH indicator solution. We chopped about a third of a cabbage to give around four cups chopped cabbage.|
|Then we poured about two cups boiling water onto the cabbage and let it steep for about two hours.|
Have you dripped lye from wood ashes? What did you use it for? How did you test the strength? Let us know in the comments section below!