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Complete the following reactions:
(i) $Si{{O}_{2}}+2NaOH\to X+{{H}_{2}}O$
(ii) $Si{{O}_{2}}+4HF\to Y+2{{H}_{2}}O$
(iii) $Si+2C{{H}_{3}}Cl\xrightarrow[570K]{Cu\text{ powder}}Z$
(A) X - $N{{a}_{2}}Si{{O}_{3}}$, Y - $Si{{F}_{4}}$, Z - ${{(C{{H}_{3}})}_{2}}SiC{{l}_{2}}$
(B) X - ${{H}_{2}}Si{{O}_{3}}$, Y - $Si{{F}_{2}}$, Z - $C{{H}_{3}}SiC{{l}_{3}}$
(C) X - $N{{a}_{2}}Si{{O}_{3}}$, Y - ${{H}_{2}}Si{{O}_{3}}$, Z - ${{(C{{H}_{3}})}_{3}}SiCl$
(D) X - $N{{a}_{2}}Si{{O}_{3}}$, Y - ${{H}_{2}}Si{{F}_{4}}$, Z - ${{(C{{H}_{3}})}_{2}}SiC{{l}_{2}}$

Answer
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Hint: As we can see that in all the equations, the silicon element is reacting in some way or the other. Silicon is a metalloid having atomic number 14. It has 4 electrons in its valence shell that mean it has a valency of 4. The atomic mass of silicon is 28.085u and is most commonly used as a semiconductor.

Complete answer:
Silicon dioxide ($Si{{O}_{2}}$) reacts with sodium hydroxide to form sodium silicate ($N{{a}_{2}}Si{{O}_{3}}$) and water. The temperature of the reaction is around 900-100${}^\circ C$. The balanced chemical equation is as follows
$Si{{O}_{2}}+2NaOH\xrightarrow{900-1000{}^\circ C}N{{a}_{2}}Si{{O}_{3}}+{{H}_{2}}O$
So, X is $N{{a}_{2}}Si{{O}_{3}}$ (sodium metasilicate)
When silicon dioxide ($Si{{O}_{2}}$) reacts with a dilute solution of hydrogen fluoride (HF), silicon tetrafluoride ($Si{{F}_{4}}$) is produced along with water. The balanced chemical equation is as follows
$Si{{O}_{2}}+4HF\to Si{{F}_{4}}+2{{H}_{2}}O$
So, Y is $Si{{F}_{4}}$ (silicon tetrafluoride or tetrafluorosilane)
Finally, upon the reaction of chloromethane ($CHC{{l}_{3}}$) with silicon (Si) in the presence of gunpowder and the temperature of 570K, dimethyldichlorosilane ${{(C{{H}_{3}})}_{2}}SiC{{l}_{2}}$ is produced. The balanced chemical equation is as follows
$Si+2C{{H}_{3}}Cl\xrightarrow[570K]{Cu\text{ powder}}{{(C{{H}_{3}})}_{2}}SiC{{l}_{2}}$
So, Z is ${{(C{{H}_{3}})}_{2}}SiC{{l}_{2}}$ (dimethyldichlorosilane).
So, the answer is option (A) X - $N{{a}_{2}}Si{{O}_{3}}$, Y - $Si{{F}_{4}}$, Z - ${{(C{{H}_{3}})}_{2}}SiC{{l}_{2}}$.

Additional information:
$N{{a}_{2}}Si{{O}_{3}}$ (sodium metasilicate) can be used to produce silica gels upon reaction with acids. When dehydrated, they are used as a binding agent or cement. They are also used as preservatives for eggs.
$Si{{F}_{4}}$ (silicon tetrafluoride or tetrafluorosilane) does not have many applications but is used in synthesis of organic compounds and in microelectronics.
${{(C{{H}_{3}})}_{2}}SiC{{l}_{2}}$ (dimethyldichlorosilane) are mainly used to produce silicones and to produce polysilanes. It can also be used to form a coating layer on glass to prevent adsorption of micro-particles.

Note:
It should be noted that when referring to silicon oxide, it could either be silicon monoxide (SiO) or silicon dioxide ($S{{i}_{2}}O$). The oxidation state of silicon in silicon monoxide is +2 whereas, in silicon dioxide, it's +4. One of the most commonly occurring oxides is silicon monoxide.