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Soapstone is a metamorphic mineral with a number of constituent compounds including principally:
What would be a typical procedure to analyze a sample of soapstone and determine the proportions of its constituents?
Given its heat resistance to thermal decomposition and the high chemical inertness of soapstone, as noted in this source, for example, to quote:
Soapstone is chemically inert, resistant to heat and durable, yet also malleable...As a metamorphic rock, it is very resistant to heat. In fact, soapstone is often used for casting metals, such as lead, pewter and silver...Because soapstone is primarily talc, which is chemically inert, it is highly resistant to etching and chemical reactions that may mar it’s beauty.
I would suggest placing a small amount of finely powdered soapstone in a vessel with highly alkaline aqueous mix of Sodium hydroxide (NaOH). Apply conventional heating or, given an iron oxide presence, microwave heating. This is an attempted relatively safe synthesis of, for example, Sodium aluminate.
The proposed reaction is a hot alkaline attack of any of the several metal oxides present, including, for example, aluminum oxide, which could proceed as follows:
$$\ce{Al2O3 (s) + 2 NaOH (s) + 3 H2O (l) -> 2 Na[Al(OH)4] (aq) }$$
Support is provided per this reference, to quote:
All the solutions removed some $\ce{SiO2, Al2O3, and Fe2O3}$ from the samples, but the quantities were small. Sodium hydroxide attacked the kaolin group minerals more strongly...
I would then neutralize the soluble salts with $\ce{CO2}$, creating corresponding carbonate (or oxide, in the case of Aluminum ions) precipitates.
Please read the cited reference for more information on procedures (albeit, as alluded to per this 1971 source).
