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What is ${\text{X}}$ in the following reaction?
${\text{KHS}}{{\text{O}}_{\text{4}}} + {{\text{F}}_{\text{2}}} \to {\text{HF}} + {\text{X}}$
A) ${{\text{K}}_2}{\text{S}}{{\text{O}}_{\text{4}}}$
B) ${{\text{K}}_2}{{\text{S}}_2}{{\text{O}}_{\text{4}}}$
C) ${{\text{K}}_2}{{\text{S}}_2}{{\text{O}}_{\text{3}}}$
D) ${{\text{K}}_2}{{\text{S}}_2}{{\text{O}}_{\text{8}}}$

Answer
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Hint: In the given reaction $KHSO_4$ is reacting with $F_2$. One compound formed is given as HF and the other compound formed will be potassium persulphate. We have to determine the chemical formula for potassium persulphate.

Complete answer:
The given reaction is as follows:
${\text{KHS}}{{\text{O}}_{\text{4}}} + {{\text{F}}_{\text{2}}} \to {\text{HF}} + {\text{X}}$
In the given reaction, potassium bisulphate reacts with fluorine. Hydrogen fluoride and potassium persulphate are formed in the reaction. The reaction occurs at room temperature.
Potassium bisulphate is the potassium salt of sulphuric acid. It is white solid in appearance. It is soluble in water.
The name of the compound having molecular formula ${{\text{K}}_2}{\text{S}}{{\text{O}}_{\text{4}}}$ is potassium sulphate. Thus, option (A) is not correct.
The name of the compound having molecular formula ${{\text{K}}_2}{{\text{S}}_2}{{\text{O}}_{\text{4}}}$ is potassium dithionite. Thus, option (B) is not correct.
The name of the compound having molecular formula ${{\text{K}}_2}{{\text{S}}_2}{{\text{O}}_{\text{3}}}$ is potassium thiosulphate. Thus, option (C) is not correct.
The name of the compound having molecular formula ${{\text{K}}_2}{{\text{S}}_2}{{\text{O}}_{\text{8}}}$ is potassium persulphate. Thus, option (D) is correct.
The complete reaction is as follows:
${\text{KHS}}{{\text{O}}_{\text{4}}} + {{\text{F}}_{\text{2}}} \to {\text{HF}} + {{\text{K}}_2}{{\text{S}}_2}{{\text{O}}_{\text{8}}}$
The balanced chemical reaction is as follows:
${\text{2KHS}}{{\text{O}}_{\text{4}}} + {{\text{F}}_{\text{2}}} \to 2{\text{HF}} + {{\text{K}}_2}{{\text{S}}_2}{{\text{O}}_{\text{8}}}$
Potassium persulphate is also known as potassium peroxydisulfate. Potassium persulphate is white solid in appearance. Potassium persulphate is sparingly soluble in cold water but soluble in warm water. Potassium persulphate is a very powerful oxidising agent and it is used to initiate polymerization reactions.

Thus, the correct option is (D) ${{\text{K}}_2}{{\text{S}}_2}{{\text{O}}_{\text{8}}}$.

Note: The reaction ${\text{2KHS}}{{\text{O}}_{\text{4}}} + {{\text{F}}_{\text{2}}} \to 2{\text{HF}} + {{\text{K}}_2}{{\text{S}}_2}{{\text{O}}_{\text{8}}}$ is the preparation reaction of potassium persulphate. Potassium persulphate can also be prepared by an electrolysis of cold potassium bisulphate solution in sulphuric acid. Potassium persulphate can also be prepared by adding potassium bisulphate to ammonium peroxydisulphate $\left[ {{{\left( {{\text{N}}{{\text{H}}_{\text{4}}}} \right)}_{\text{2}}}{{\text{S}}_{\text{2}}}{{\text{O}}_{\text{8}}}} \right]$.