How is #"propionic acid"#, #"H"_3"CCH"_2"CO"_2"H"#, synthesized?

#H_2C=CH_2 + C=O + H_2O rarr H_3C-CH_2C(=O)OH#

In the laboratory, propionic acid could be formed the reaction of ethyl magnesium chloride with dry ice, or cyanide with ethyl chloride.

If we start from ethanol, then we can use #"PBr"_3# in pyridine to turn ethanol into ethyl bromide, which can then be converted to a Grignard reagent by reacting with magnesium solid in dry ether, followed by a reaction with carbon dioxide.

1. #\mathbf("PBr"_3)# acts as an electrophile for the alcohol to attack, while pyridine acts as a proton acceptor. A #""^(-)"O"-"PBr"_2# (bromophosphite) group leaves when the bromide that left from #"PBr"_3# attacks again as a nucleophile (Organic Chemistry, Bruice, Ch. 10.2).
2. Formation of a Grignard reagent; you should know this if you have taken second-semester organic chemistry for a few weeks. It must be dry to prevent deactivation of the nucleophile.
3. Grignard reagents can react in an #"S"_N2# reaction with #\mathbf("CO"_2)#.
4. A bit of aqueous acid finishes up the reaction by protonating the carboxylate and hydrolyzing the #"MgBr"^(+)#, neutralizing any remaining Grignard reagent as well by (easily) protonating the ethyl anion.