Thank youYes and no. As with so many other soapy things, this isn't a black-and-white issue; it's important to understand the nuances.
IMO, the amount of free fat (aka superfat) in a soap MAY cause soap to go rancid quicker than if there is no superfat, but the devil is in the details, so keep reading.
You have to also consider the types of fatty acids in the soap itself as well as in the superfat. The fatty acid profile can greatly affect how likely the soap is to oxidize and go rancid.
Polyunsaturated fatty acids, which are mainly linoleic and linolenic acids in typical soap making fats, make soap more prone to rancidity. Soap made with mostly saturated fatty acids and (to a lesser degree) monounsaturated fatty acids make the soap less prone to rancidity.
Contaminants, especially metals, and any unsaponifiable content in various fats -- all of which carry over into the soap -- may also affect how quickly rancidity develops.
So there are a lot of variables to consider when trying to figure out whether a soap will have a long shelf life or not, based purely by looking at the fats in the recipe.
Also, other factors are important to reducing the chance of rancidity, incluiding proper storage (cool, low humidity, absence of light) and the correct use of antioxidants (no Vitamin E capsules used willy-nilly please!) and chelators. These will help a lot to reduce the chance of rancidity in soap.
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