Methacrylic acid & benzoyl chloride (1:2 molar ratio) [containing very little hydroquinone] are mixed in a r.b.flask. Simple distillation is applied at a moderate rate. Methacryloyl chloride will go to the dry receiving flask (it has a boiling point of 95-96 oC). A good practice is to put a drying agent (e.g CaCl2) in the receiving flask & to decant the liquid monomer only afterwards.
Please take care since methacryloyl chloride is toxic& is highly reactive with, e.g. moisture. So the distillation is done in the fume hood & the monomer is used immediately.
you can try using coupling reagents to react the acid with your other reagent in one pot rather than making the acid chloride. anyhydride can also react with certain substrates but less reactive than acid chloride, may need to heat
Other ways to make the acid chloride include SOCl2, and oxalyl chloride with a drop of DMF in DCM.
Compound methacrylic acid or methyl methacrylate (0.01mole,) dissolved in thionyl chloride (25mL) and refluxing was continued for (3 hrs). Then, the excess Thionyl chloride evaporated in reduced pressure by rotary.
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If you are worried about HCl from the reaction adding across the double bond, you could try, e.g. triphenylphosphine with carbon tetrachloride. The tetrachloride is hard to get these days, but I once ran a similar reaction with the phosphine and ethyl trichloroacetate. The other products are triphenylphosphine oxide and either chloroform or ethyl dichloroacetate,