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The correct order of leaving group ability in nucleophilic substitution reaction is:
(A) \[B{r^ - } > C{l^ - } > C{H_3}C{O_2}^ - > O{H^ - } > {H^ - }\]
(B) \[{H^ - } > O{H^ - } > C{H_3}C{O_2}^ - > C{l^ - } > B{r^ - }\]
(C) \[B{r^ - } > C{H_3}C{O_2}^ - > C{l^ - } > O{H^ - } > {H^ - }\]
(D) \[C{H_3}C{O_2}^ - > B{r^ - } > C{l^ - } > O{H^ - } > {H^ - }\]

Answer
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Hint: In chemistry, a leaving group is a molecular fragment that departs with a pair of electrons during a heterolytic bond cleavage. The leaving group in a nucleophilic substitution reaction gets displaced according to a pre-defined stereochemistry.

Complete step by step answer:
First, we will discuss nucleophilic substitution reactions. Nucleophilic substitution reactions are those reactions in which a nucleophile that is rich in electrons attacks a positively charged electrophile and replaces the leaving group from the compound.
The Factors affecting leaving group ability are Electronegativity and size.
As Electronegativity Increases, Basicity Decreases, hence leaving group ability increases and as the size increases, basicity will decrease, hence, leaving group ability increases.
In the periodic table as we move from left to right, the size of the elements increases. Hence, their electronegativity increases, and basicity will decrease so leaving group ability will increase.
Same is in the case of electronegativity, as we move from left to right electronegativity increases, basicity decreases, hence the leaving group tendency will increase.
It is concluded from the above two points, that while moving from left to right in the periodic table, leaving group ability will increases.
Let’s come to our question: The elements given in it are
\[B{r^ - },C{l^ - },C{H_3}C{O_2}^ - ,O{H^ - },{H^ - }\]
When we arrange them according to their position in the periodic table from left to right the order we get is:
\[B{r^ - } > C{l^ - } > C{H_3}C{O_2}^ - > O{H^ - } > {H^ - }\]
Hence, this will be the order of leaving group ability in a nucleophilic substitution reaction.
So, Option (A) is the correct answer.

Note:
Nucleophilic Substitution reaction is a three-step process. It is generally of two types $S{N_{1\,}}\,$ and $S{N_2}$. The leaving group ability decreases as the basicity of the nucleophile increases. The presence of electron-withdrawing groups at the ortho and meta positions also favours the leaving group and increases the reactivity.