This is a can of worms, there are two main routes to DCM, the one you have chosen is the direct chlorination route which suffers (or is an advantage )
from it making multiple chlorinated methanes. Then comes the fun of separating them. The byproduct is lots of HCL.
The other technique is to use HCL and methanol to form methyl chloride under catalytic Friedel- Craft conditions if done in the gas phase, or using
metal chlorides in the liquid phase, and then chlorinate it with chlorine. This makes more of what you want but methyl chloride isn't something you
want in your near vicinity for very long in any appreciable concentration.
Then there is the use of copper chlorides to chlorinate methane. Cuprous chloride is converted to cupric chloride to make methyl chloride. HCl is a
byproduct which can be used to regenerate the cuprous chloride when 1/2 mol O2 is introduced per mol of cupric chloride.
Other schemes have been devised to close this cycle and an innovative and elegant one is to react methane, HCl, chlorine and air in a tube furnace to
essentially combust the HCl to generate chlorine. Cuprous chloride, as well as potassium and zinc chlorides are used catalytically.
In a non industrial setting addition of air in these reactions has the potential to form the deadly phosgene, so it's chemically elegant but not
something to get wrong.
Other milder chlorinating agents like sulfuryl chloride can be used, and there are exotic combinations of metal chlorides and sulphur trioxides to
consider.
All of these use or generate potentially deadly gasses. High temperatures use of specific materials for the reactions and separations make this more
than just a challenge.
I'd tread very carefully with this project.
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