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So as most inorganic liquids are diamagnetic at room temperature (like water), what are some applications to paramagnetic liquids at room temperature?

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One way to generate a paramagnetic liquid is to use an active metal to generate solvated electrons. Burrows et al.[1] describe a solution of lithium in ethylenediamine plus tetrahydrofuran, which can be used in Birch reductions at ambient conditions without handling liquid ammonia.

Reference

JAMES BURROWS, SHOGO KAMO, AND KAZUNORI KOIDE (2021). "Scalable Birch reduction with lithium and ethylenediamine in tetrahydrofuran". Science 374, 741-746. DOI:10.1126/science.abk3099

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