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Out of ${{\text{H}}_{\text{2}}}{{\text{S}}_{\text{2}}}{{\text{O}}_{\text{3}}}{\text{,}}{{\text{H}}_{\text{2}}}{{\text{S}}_{\text{4}}}{{\text{O}}_{\text{6}}}{\text{,}}{{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{5}}}$ and ${{\text{H}}_{\text{2}}}{{\text{S}}_{\text{2}}}{{\text{O}}_{\text{8}}}$ peroxy acids are:
A.\[{{\text{H}}_{\text{2}}}{{\text{S}}_{\text{2}}}{{\text{O}}_{\text{3}}}{\text{,}}{{\text{H}}_{\text{2}}}{{\text{S}}_{\text{4}}}{{\text{O}}_{\text{6}}}\]
B.${{\text{H}}_{\text{2}}}{{\text{S}}_{\text{4}}}{{\text{O}}_{\text{6}}}{\text{,}}{{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{5}}}$
C.${{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{5}}}{\text{,}}{{\text{H}}_{\text{2}}}{{\text{S}}_{\text{2}}}{{\text{O}}_{\text{8}}}$
D.${{\text{H}}_{\text{2}}}{{\text{S}}_{\text{2}}}{{\text{O}}_{\text{3}}}{\text{,}}{{\text{H}}_{\text{2}}}{{\text{S}}_{\text{2}}}{{\text{O}}_{\text{8}}}$


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Answer
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Hint: Peroxy acids are sometimes all known as peracid. They are a group of compounds which have –OOH group instead of an –OH group or the compound that have a peroxy bond, i.e. an Oxygen-oxygen single covalent bond (-O-O-). Some of the examples of peroxy acids are Peroxyacetic acid, Perchloric acid.

Complete step by step answer:
To which one of the given Sulphur compounds falls under the category of peroxy acids let us look into the structure of each one of these:
${{\text{H}}_{\text{2}}}{{\text{S}}_{\text{2}}}{{\text{O}}_{\text{3}}}$: This acid is known as thiosulfuric acid.
Structure:
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Since there is no oxygen-oxygen single covalent bond, it is not a peroxy acid.
${{\text{H}}_{\text{2}}}{{\text{S}}_{\text{2}}}{{\text{O}}_{\text{6}}}$: It is known as Tetrathionic acid.
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Structure:





As you can see there is no oxygen-oxygen single covalent bond it cannot be regarded as a peroxy acid.
${{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{5}}}$: This acid is known as Peroxymonosulphuric acid.
Structure:
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As it can be seen the molecule of Peroxymonosulfuric acid contains an oxygen-oxygen single covalent bond, it is a peroxy acid of sulphur.
${{\text{H}}_{\text{2}}}{{\text{S}}_{\text{2}}}{{\text{O}}_{\text{8}}}$: This acid is known as Peroxydisulphuric acid.
Structure:
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As it can be seen in the structure this molecule of acid contains an oxygen-oxygen single covalent bond, it falls under the category of peroxy acids of sulphur.
Hence, after looking at all the structures of given acids of sulphur, we can conclude that out of the four given acids, ${{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{5}}}{\text{,}}{{\text{H}}_{\text{2}}}{{\text{S}}_{\text{2}}}{{\text{O}}_{\text{8}}}$ are the peroxy acids.
And thus option C is the correct answer.

Note:There are some very important uses of Peroxy acids. As these acids contain an extra oxygen atom, they can be used for:
Oxidising a compound: they act as oxidising agents in many organic reactions, where they themselves get reduced.
These compounds find a wide variety of uses in organic chemistry: to convert alkenes into epoxides, ketones into esters and amines into nitro compounds are some of the applications.