Look up the Fischer esterification.
Or suspend the acid and ethanol in hexane or heptane, heat to reflux and add conc H2SO4. When the reaction is finished (monitor tlc or GC) cool separate the layers collect the heptane phase wash with bicarbonate (CO2 evolution) and remove the solvent by distillation.
If necessary distill the product
So if I understand correctly - during the reaction, the produced ethyl chloroacetate is dissolved in the non-polar solvent (I assume benzene could also be used), while the water stays away from the ethyl chloroacetate as it isn't miscible with the non-polar solvent. Since this shifts the equilibrium greatly in favor of the product, the second layer should mostly be composed of water and excess of ethanol.
After the reaction is finished, the reaction mixture is cooled down, the layer composed of the non-polar solvent and ethyl chloroacetate is removed, neutralized and distilled, whereby benzene is the compound being removed from ethyl chloroacetate as it has a much lower boiling point.
Is this correct?
Also, I noticed that this is similar to the method described in Vogel's Textbook of Practical Organic Chemistry for the synthesis of ethyl bromoacetate (also similar to the one found
here). So why exactly is Dean-Stark apparatus preferred in these sources? Does it help to obtain an even higher yield, or is the reason something else?
Unfortunately, along with the relatively basic knowledge of theory related to esterifications, I don't have much personal experience with this type of reactions, so I would appreciate any additional insight and advices.