"...How much glycerin is produced using 1g of the 90% KOH sold by Essential Depot? ..."
I'm going to give you the set-up for this problem. See if you can come up with the answer, okay?
First thing to know is the chemical conversion between the two lyes:
1 g of NaOH is the equivalent of 1.4 g of KOH.
Said another way, 1 g of KOH is the equivalent of 0.7 g NaOH.
I have already said that 1 g of NaOH will produce 0.77 g of glycerin, so there's another piece of the puzzle.
First, figure the "ideal" amount of glycerin produced by 100% pure KOH.
Next, figure the glycerin for impure KOH. For a 90% purity KOH, the glycerin it can make is 90/100 of the ideal.
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"...Is it the length of the carbon chain that also determines the cleansing factor of the soap as well?..."
Um, yes and no. Sorry to be vague, but there is no short-n-sweet answer to this question. There are two issues at work here -- solubility in water and "fat dissolving" abililty.
Let's start simple by talking only about soap made from a single pure saturated fatty acid. In this case, your idea is definitely correct. Shorter chain fatty acids create soap that is more soluble in water and is a stronger cleanser than soap made with longer chain fatty acids. The more soap that can dissolve quickly into water, the more likely the soap will be a strong cleaner. The shorter the carbon chain also means the soap will be a stronger cleanser from a fat-dissolving point of view.
The solubility of soap made from saturated fatty acids, from high solubility to low: Sodium laurate (12 carbon atoms) > sodium myristate (14 carbon atoms) > sodium palmitate (16 carbon atoms) > sodium stearate (18 carbon atoms).
But there are UNsaturated fatty acids that are the same length as saturated fatty acids. Once you start comparing soap made from pure UNsaturated fatty acids and pure saturated fatty acids, then your idea breaks down a little bit when we look at solubility. For example, stearic, oleic, linoleic, and ricinoleic acids all have 18 carbons, but stearic is saturated and the others are unsaturated.
Let's stick the pure sodium oleate soap into the solubility list, since I have solubility data for that soap. The relative solubilities of all of these pure soaps would be this: Sodium oleate (18 carbon atoms, UNsat) > Sodium laurate (12 carbon atoms, sat) > sodium myristate (14 carbon atoms, sat) > sodium palmitate (16 carbon atoms, sat) > sodium stearate (18 carbon atoms, sat).
Looking at "fat dissolving" power, however, sodium oleate with its UNsaturated nature is not going to be as effective at cleaning as the shorter chain saturated soaps (laurate and myristate).
Some of this seems to run counter to "common sense", but that's chemistry for you!
Everything I've said so far relates to a PURE soap made from a single fatty acid. When you mix the fatty acids together and make soap, as is normally the case in a real-life bar of soap, the solubility and fat-dissolving power of the soap-as-a-whole will be entirely different than the properties of the individual pure soaps that make up the bar.
In general, a real-life soap will tend to be somewhere between the extremes, but the solubility and cleansing ability will often be higher than one might guess. The reason why this is true is because bar soap is a type of crystalline material. In a crystal, molecules are packed together in a more or less regular structure. Molecules that are similar in size and shape pack nicely and make tidy, dense soap crystals that are not as soluble in water. Molecules that are lumpy bumpy (UNsaturated fatty acids) or molecules in a variety of sizes can't pack together as nicely, so they make untidy, irregular soap crystals that are more soluble.
This is a complicated topic that I really don't know well. Even so, I probably know more than most and I hope I've given y'all a little bit of insight.
