Question

The percentage of ​ ${P_2}{O_5}$ in diammonium hydrogen phosphate $[{(N{H_4})_2}HP{O_4}]\;$ is:
(A) $23.48\%$
(B) $53.78\%$
(C) $46.96\%$
(D) $71.0\%$

Answer 1

$[{(N{H_4})_2}HP{O_4}]\;$ is a salt of the Phosphoric acid. It is produced when $N{H_3}$ (ammonia) reacts with ${H_3}PO{}_4$ (phosphoric acid). ${P_2}{O_5}$ is synthesized from $[{(N{H_4})_2}HP{O_4}]\;$. The molar masses of Phosphorus pentoxide and diammonium hydrogen phosphate are calculated. According to the principle of Atom Conservation (POAC), the total number of atoms of the reactants and the products should be the same. In a compound, to calculate the mass percent of a particular element, the mass of the element in 1 mole of the compound is divided by the molar mass of the compound and then multiplied this by 100.

Complete step by step answer:
-By the theory of Principal of atom conservation, 1 mole of ${P_2}{O_5}$ is obtained from 2 moles of $[{(N{H_4})_2}HP{O_4}]\;$ .
-The reaction to this statement can be written as: $2[{(N{H_4})_2}HP{O_4}]\; \to {P_2}{O_5}$
-Now, the Molar mass of diammonium hydrogen phosphate is calculated as $36 + 1 + 31 + 64 = 132g/mole$
-The molar mass of Phosphorus pentoxide is calculated as $= 62 + 80 = 142g/mole$
-So Mass of 2 moles will be $= 2(132) = 246g$
$\%$ composition of ${P_2}{O_5} = \dfrac{{Molar Mass Of{P_2}{O_5}}}{{Molar Mass Of 2 Moles Of[{{(N{H_4})}_2}HP{O_4}]\;}} \times 100$
$\%$ composition of ${P_2}{O_5} = \dfrac{{142}}{{264}} \times 100 = 53.78\%$
Hence, The percentage of ​ ${P_2}{O_5}$ in $[{(N{H_4})_2}HP{O_4}]\;$ is 53.78.

Therefore, Option (B) is correct.

Note: The stoichiometry of the reaction to calculate the right proportion of ${P_2}{O_5}$ (Phosphorus pentoxide) should be correct. Also, while substituting the values in the formula molar mass of 2 moles of $[{(N{H_4})_2}HP{O_4}]\;$ is taken. Being an inorganic phosphate and an ammoniacal salt $[{(N{H_4})_2}HP{O_4}]\;$ is majorly used as a fertilizer in India by the farmers to temporarily increase the pH of the soil. It can also be used as a fire retardant and as a yeast-nutrient in the process of making wine and mead.