I thought a large dipole moment meant the substance was polar, so I'm confused by the following statement (from Wikipedia) that "With a dipole moment of 3.92 D, acetonitrile dissolves a wide range of ionic and nonpolar compounds...." Why would it dissolve many nonpolar compounds?
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$\begingroup$ Just because something has a dipole doesn't mean that it can't interact with other, less polar, compounds. The dipole might help get some ionic compounds into solution but acetonitrile has plenty of scope to mix with non polar compounds via dispersion forces which are still there in acetonitrile. $\endgroup$– matt_blackApr 30, 2021 at 23:56
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It's all about the energetics (assuming an isolated system--happy to elaborate in the comments): as acetonitrile has a large dipole moment, it can readily stabilize the individual ions. See this discussion of solvation energy.
The more subtle case is in the case of nonpolar compounds. In this case, the large dipole can create an induced dipole in the nonpolar molecule. Then the dipole-induced dipole attraction would be larger in magnitude than the spontaneous dipole-spontaneous dipole interactions present in nonpolar-nonpolar interactions (which are also still present as small fluctuations in the polar-nonpolar case). See this discussion of how charges/dipoles/multipoles induce dipoles and then subsequently attractively interact with said dipoles.
