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If $ {H_2}COH.C{H_2}OH $ heating with periodic acid gives
 $\left( a \right)2C{O_2} \\
  \left( b \right)2HCOOH \\
  \left( c \right)CHO - CHO \\
  \left( d \right)2HCHO \\ $

Answer
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Hint :Iodine's strongest oxoacid is periodic acid, in which the iodine has an oxidation state of $ + 7 $ . It can be found in two ways, as all periodates: orthoperiodic acid $ \left( {{H_5}I{O_6}} \right) $ and meta periodic acid $ \left( {HI{O_4}} \right) $ .

Complete Step By Step Answer:
 $ \left( a \right)2C{O_2} $ : Carbon dioxide is a one carbon substance with the formula $ C{O_2} $ , in which the carbon atoms are joined by a double bond on each oxygen atom. Ethylene glycol on heating with periodic acid does not give carbon dioxide. Hence this is not the correct answer.
 $ \left( b \right)2HCOOH $ : Ethylene glycol on heating with periodic acid does not give $ 2HCOOH $ . Hence this is not the correct answer.
 $ \left( c \right)CHO - CHO $ : The organic compound glyoxal has the molecular formula $ OCHCHO $ . It is the smallest dialdehyde. It is an aldehyde containing compound with two aldehyde groups. Ethylene glycol on heating with periodic acid does not give $ CHO - CHO $ . Hence this is not the correct answer.
 $ \left( d \right)2HCHO $ : As a $ 1,2 - diol $ like ethylene glycol is treated with $ HI{O_4} $ , $ HI{O_4} $ converts each alcoholic group to a carbonyl group. Since all $ - OH $ groups in glycol are terminal, oxidation will result in two formaldehyde molecules.
 $ {H_2}COH.C{H_2}OH + HI{O_4} \to 2HCHO + HI{O_3} $
Hence this is the correct answer.
Ethylene glycol $ \left[ {{H_2}COH.C{H_2}OH} \right] $ on heating with periodic acid gives $ 2HCHO $ .
Therefore, the correct option is $ \left( d \right)2HCHO $ .

Additional Information:
Periodic acid Schiff (PAS) is a staining technique for detecting polysaccharides like glycogen, as well as mucosubstances like glycoproteins, glycolipids, and mucins in tissues.

Note :
Perchloric acid is the strongest acid, while hypochlorous acid is the weakest acid. The number of oxygens bound to chlorine is the only distinction between these acids. The acid intensity increases as the number of oxygens increases; this is due to electronegativity.