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The acid strength of oxoacids of halogens is in order:
A. $HOF > HOCl > HOBr > HOI$
B. $HOI < HOBr < HOCl < HOF$
C. $HOI > HOCl > HOBr > HOF$
D. $HOCl > HOBr > HOI > HOF$

Answer
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Hint: Acid strength is based on how easily a compound can donate/let go of the hydrogen atom present in it as a proton. The ease with which this occurs is based on the electronegativity of the other atoms bonded directly to hydrogen, or in the close vicinity of it.

Complete step by step solution:
To tackle this problem, let us first closely examine the structure of oxoacids of halogens. They have the basic formula $H - O - X$, where $X$ stands for the halogen atom. Thus, we can see that it is actually the oxygen atom which is directly bonded to the hydrogen atom.
 Now, acid strength is based on the ease with which the hydrogen atom can leave as a proton (${H^ + }$). For this to happen, clearly the partial charge on hydrogen should be as positive as possible. In other words, the oxygen must be able to pull the shared pair of electrons of the ${\kern 1pt} O - H$ bond towards itself. For this to happen easily, the electronegativity of the halogen atom should be as high as possible, so that it pulls the shared pair of electrons of the $X - O$ bond towards itself, making oxygen partially electron deficient, resulting in it pulling the shared electrons of the ${\kern 1pt} O - H$ bond towards itself, making the liberation of the ${H^ + }$ ion easy.
Therefore, higher the electronegativity of the halogen atom, higher is the acid strength. As we know, as we move down a group, atomic size increases and this reduces the nuclear pull (attraction between the nucleus and the electrons), as electrons become further away from the nucleus. This leads to a decrease in electronegativity down a group. Hence, acid strength of oxoacids of halogens decrease as we move down the group.
 So, in this case, the correct options are A and B, as both these options have the same series, the only difference being that one is written in increasing order and the other in decreasing order.
Hence, correct order: $HOF > HOCl > HOBr > HOI$ OR $HOI < HOBr < HOCl < HOF$

Note:
Electronegativity is the property of an atom to pull electrons towards itself, and is inversely proportional to atomic size. Out of all the elements, fluorine is the most electronegative atom. Note that the acidic nature of oxoacids is due to the highly polar nature of the bond between hydrogen and oxygen.