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The $ O-H $ bond length in $ {{H}_{2}}O $ is $ x{{A}^{0}}. $ The $ O-H $ bond length in $ {{H}_{2}}{{O}_{2}} $ is:
(A) $ (B) $ x{{A}^{0}} $
(C) $ >x{{A}^{0}} $
(D) $ 2x{{A}^{0}} $

Answer
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Hint :We know that the average length between the nuclei of two bound atoms in a molecule is known as bond length or bond distance in molecular geometry. It's a property of a bond between fixed-type atoms that can be transferred, despite the rest of the molecule being largely unaffected.

Complete Step By Step Answer:
As we know, the most basic form of peroxide is hydrogen peroxide oxygen-oxygen single bond. It's a colorless substance that's used in aqueous solutions to keep things clean. It is used as a disinfectant as well as a bleaching agent. In rocketry, concentrated hydrogen peroxide is used as a propellant because it is a highly reactive oxygen species. The distance between the nuclei of two chemically bound atoms in a molecule is measured by bond length. It is roughly proportional to the number of the two bonded atoms' covalent radii.
Bond length is proportional to bond order: the longer the bond, the more electrons involved in its creation. Bond length is also inversely related to bond strength and bond dissociation energy: a stronger bond would be shorter if all other variables remain constant. Half of the bond width is equal to the covalent radius in a bond between two similar atoms. It's a colorless liquid that's used in aqueous solutions to keep things safe. It is used as a disinfectant as well as a bleaching agent. In solid phase $ O-H $ bond length in $ {{H}_{2}}{{O}_{2}} $ ​ is $ 98.8 $ pm and in gaseous phase it is $ 95 $ pm. But $ O-H $ bond length in water is always $ 96 $ pm.
Therefore, the correct answer is option A.

Note :
Remember that the bond length is inversely proportional to bond order in covalent bonds; higher bond orders result in stronger bonds, which are followed by stronger forces of attraction that tie the atoms together. These powerful powers of attraction result in short bonds.