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In solid state \[{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{5}}}\] exists as:
A. \[{\left[ {{\text{N}}{{\text{O}}_{\text{3}}}} \right]^{\text{ - }}}{\left[ {{\text{N}}{{\text{O}}_{\text{2}}}} \right]^{\text{ + }}}\]
B. \[{\left[ {{\text{N}}{{\text{O}}_{\text{2}}}} \right]^{\text{ - }}}{\left[ {{\text{N}}{{\text{O}}_{\text{3}}}} \right]^{\text{ + }}}\]
C. \[{\left[ {{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{4}}}} \right]^{{\text{2 + }}}}{{\text{O}}^{{\text{2 - }}}}\]
D. \[\left[ {{\text{N}}{{\text{O}}_{\text{3}}}} \right]\left[ {{\text{N}}{{\text{O}}_{\text{2}}}} \right]\]

Answer
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Hint: \[{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{5}}}\] is dinitrogen pentoxide. It is the anhydride form of nitric acid. It is prepared as white crystals, by dehydration of nitric acid with diphosphorus pentoxide or by oxidizing nitrogen dioxide with ozone. It is a salt in solid form.

Complete step by step answer:
 \[{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{5}}}\] is an unstable compound, it decompose spontaneously at room temperature forming nitrogen dioxide and oxygen. Dinitrogen pentoxide is highly dissociated. It is also called nitrogen pentoxide and nitro nitrate.
It reacts with water and forms nitric acid. The balanced chemical equation is given as,
\[{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{5}}}{\text{ + }}{{\text{H}}_{\text{2}}}{\text{O }} \to {\text{ 2HN}}{{\text{O}}_{\text{3}}}\]
The dinitrogen pentoxide undergoes reaction with sodium hydroxide forming sodium nitrate and water. The chemical equation can be written as,
\[{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{5}}}{\text{ + 2NaOH }} \to {\text{ 2NaN}}{{\text{O}}_{\text{3}}}{\text{ + }}{{\text{H}}_{\text{2}}}{\text{O}}\]
Solid \[{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{5}}}\]​ is a salt, it contains separated anions and cations. Here, the cation is the linear nitronium ion \[{\text{N}}{{\text{O}}^{{\text{2 + }}}}\]​ and the anion is the planar nitrate \[{\text{N}}{{\text{O}}^{{\text{3 - }}}}\]ion. Thus, the solid is also nitronium nitrate. Here, both the nitrogen centres have an oxidation of state +5.

Hence, the answer is Option A. \[{\left[ {{\text{N}}{{\text{O}}_{\text{3}}}} \right]^{\text{ - }}}{\left[ {{\text{N}}{{\text{O}}_{\text{2}}}} \right]^{\text{ + }}}\].

Note: \[{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{5}}}\] is a strong oxidizing agent that produces explosive mixtures with organic compounds and with ammonium salts. A highly toxic gas, nitrogen dioxide gas is formed by the decomposition of dinitrogen pentoxide.
\[{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{5}}}\] has many applications, it can be used as a robust oxidizer in high-fuel rockets, it is used in non-polar solvents so, the molecules that are very sensitive to water can be nitrated easily. It is also used as a nitrating agent in modern synthetic organic chemistry, the mixture of \[{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{5}}}\] and nitric acid is also a good and strong nitrating agent.