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Reaction of sulfuric acid and methanol?

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If methanol and H2SO4 react:

 

2 MeOH + H2SO2 → (Me)2SO4 + 2 H2O

 

but then (Me)2SO4 reacts with water:

 

H2O + (Me)2SO4 → H2SO4

 

Wouldn't this mean when the H2SO4 reacts with the methanol, that the methanol would produce dimethyl sulfate then react with the water and start the cycle again?

Edited by Aaron_S

IIRC, Dimethyl ether is most likely outcome, Then you could use that after with sulpher trioxide to make your Dimethyl sulphate.

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IIRC, Dimethyl ether is most likely outcome, Then you could use that after with sulpher trioxide to make your Dimethyl sulphate.

So you mean it wouldn't produce dimethyl sulfate but dimethyl ether + SO3?

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