To address this question, each mineral's name must be paired with its chemical formula, and the incorrect association identified.
- Fluorspar - The correct formula for fluorspar is \(CaF_2\), not \(BF_3\). This pairing is erroneous.
- Cryolite - The provided formula, \(Na_3AlF_6\), accurately represents cryolite. This pairing is correct.
- Fluoroapatite - The formula stated, \(3Ca_3(PO_4)_2 \cdot CaF_2\), is the correct chemical representation for fluoroapatite. This pairing is correct.
- Carnallite - The given formula, \(KCl \cdot MgCl_2 \cdot 6H_2O\), is the correct formula for carnallite. This pairing is correct.
The erroneous pairing identified is:
Fluorspar - \(BF_3\)
This is incorrect because fluorspar's actual chemical composition is \(CaF_2\).