How is diethyl ether prepared by continuous etherification process?

Hint: Etherification is a simple reaction in which ether \[(R-O-R)\]is formed is formed from an alcohol on distilling it with concentrated \[{{H}_{2}}S{{O}_{4}}\]by intermolecular dehydration reaction. This is commonly practiced with both aliphatic and aromatic alcohols. In the case of simple aliphatic alcohols acid catalysis is sufficient to produce the ether.
  \[\Rightarrow 2R-O-H\xrightarrow[\Delta ]{conc.{{H}_{2}}S{{O}_{4}}}R-O-R\]
Here, we can see that once an alkyl alcohol is used for the etherification process the respective ether is produced. To produce diethyl ether we have to take ethyl alcohol

Complete step by step answer:
To produce diethyl ether we have to take the primary reactant as ethyl alcohol
Step 1: Ethyl alcohol reacts with concentrated \[{{H}_{2}}S{{O}_{4}}\] and form ethyl hydrogen sulphate with water. The reaction is given below
  \[\Rightarrow {{C}_{2}}{{H}_{5}}OH+HO-S{{O}_{3}}H\xrightarrow{room.temp}{{C}_{2}}{{H}_{5}}-O-S{{O}_{3}}H+{{H}_{2}}O\]
Step 2: The product ethyl hydrogen sulphate then reacts with an excess of ethyl alcohol at 413K and forms diethyl ether. The reaction is given below;
  \[\Rightarrow {{C}_{2}}{{H}_{5}}-O-S{{O}_{3}}H+{{C}_{2}}{{H}_{5}}OH\xrightarrow{413K}{{C}_{2}}{{H}_{5}}-O-{{C}_{2}}{{H}_{5}}+{{H}_{2}}S{{O}_{4}}\]
The produced ether is distilled over. The regenerated \[{{H}_{2}}S{{O}_{4}}\] is reused in the first step. Thus a small amount of \[{{H}_{2}}S{{O}_{4}}\] can convert a large amount of alcohol into ether and the process becomes continuous. Hence, the process is called a continuous etherification process.
So we can write whole reaction in one step as;
  \[\Rightarrow 2{{C}_{2}}{{H}_{5}}-OH\xrightarrow[\Delta ]{Conc.{{H}_{2}}S{{O}_{4}}}{{C}_{2}}{{H}_{5}}-O-{{C}_{2}}{{H}_{5}}\]
Hence, diethyl ether is formed

Note:
Diethyl ether has high volatility and low flash point and has been used with petroleum distillates as a starting fluid for petroleum engines. It was widely used as anaesthetic agent, but because of its flammability and post-anaesthetic side effects has been replaced with halogenated ethers. The effects of diethyl ether on the central nervous system are mainly attributed to interactions with neuronal membranes and ion channels.