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The reaction of ${P_4}$ with X leads selectively to ${P_4}{O_6}$. The X is :
a.) dry ${O_2}$
b.) a mixture of ${O_2}$ and ${N_2}$
c.) moist ${O_2}$
d.) ${O_2}$ in presence of aq. NaOH

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Answer
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Hint: This reaction requires less supply of oxygen. So, some other element will be used that will competitively inhibit the full supply of oxygen.

Complete step by step answer:
For this, first, we will see the reaction of formation of ${P_4}{O_6}$.
${P_4} + 3{O_2}\xrightarrow[{{N_2}}]{{{O_2}}}{P_4}{O_6}$
Phosphorus trioxide is prepared by heating phosphorus in a limited supply of oxygen and nitrogen.
Oxygen supply is provided in a limited quantity because if it is in more quantity then ${P_4}{O_6}$ will further oxidize to ${P_4}{O_6}$.

Thus, option b.) is the correct answer.

Additional information:
Phosphorus exists in two major forms – white phosphorus and red phosphorus.
Phosphorus is highly reactive. So, it is never found as a free element. Many oxides of phosphorus are formed in nature.
Phosphorus trioxide is a colourless solid. It is the anhydride of phosphoric acid. So, in reaction with water, we get phosphorous acid.
It is a good ligand for transition metals.
Further, low temperature is required during its formation.
Phosphorus trioxide is found to have a tetrahedral point group. This was determined from electron diffraction data.
It consists of P – O – P bonds as well.

Note:
Nitrogen when present along with oxygen limits its supply so that further oxidation can be prevented. Absence of nitrogen will give a complete supply of oxygen and this can lead to oxidation of the product further.