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The structure of beryllium chloride in the solid-state and vapor phase, respectively, are:
(A) chain and dimeric
(B) chain and chain
(C) dimeric and dimeric
(D) dimeric and chain

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Answer
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Hint: In solid-state, beryllium chloride forms continuous coordinate bonds with surrounding chlorine atoms which is analogous to the structure of aluminium chloride. While in gaseous state two Be atoms are joined through a bridge of chlorine atoms. The bond formation takes place to complete the octet of atoms.

Complete answer:
Beryllium chloride is an inorganic compound. It is a colorless solid which can be dissolved in many polar solvents. Beryllium has 2 valence electrons and according to Valence bond theory, beryllium chloride has linear geometry in which the Be atom is sp-hybridized.
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However, beryllium tends to form different structures in the solid and vapor phase to fulfill the number of electrons required to complete its octet.
In the vapor phase, it exists as a dimer in which two electrons in the valence bond of beryllium form covalent bonds with two chlorine atoms. But then two orbitals in beryllium remain unoccupied. So, it is called an electron-deficient compound.
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On the other hand, in its solid-state, beryllium tends to build a polymeric chain in which two electrons in the valence bond of beryllium forms covalent bonds with two chlorine atoms. But then two orbitals in beryllium remain unoccupied. So, it forms a coordinate covalent bond with another two chlorine atoms which forms a bridge-like structure as shown below:
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Hence, the correct answer is (A) chain and dimeric.

Note:
Beryllium chloride is hygroscopic in nature that means it readily absorbs moisture through adsorption and thus it exists as a tetrahydrate - $\text{BeC}{{\text{l}}_{\text{2}}}\text{.4}{{\text{H}}_{\text{2}}}\text{O}$.