Question

The percentage of \[{{\text{P}}_2}{{\text{O}}_5}\] in diammonium hydrogen phosphate is;
A.\[77.58\]
B.\[46.96\]
C.\[53.78\]
D.\[23.48\]

Answer 1

Hint: To calculate the percentage of \[{{\text{P}}_2}{{\text{O}}_5}\] we need to write the dissociation reaction of diammonium hydrogen phosphate. From the balanced chemical equation we will get the number of moles of \[{{\text{P}}_2}{{\text{O}}_5}\] produced and hence we will calculate the mass of \[{{\text{P}}_2}{{\text{O}}_5}\] present.

Complete step by step solution:
The formula for diammonium hydrogen phosphate is \[{({\text{N}}{{\text{H}}_4})_2}{\text{HP}}{{\text{O}}_4}\].
Two moles of diammonium hydrogen phosphate dissociate to give phosphorus oxide, ammonia and nitrogen oxide. The reaction occurs as follow:
\[2{({\text{N}}{{\text{H}}_4})_2}{\text{HP}}{{\text{O}}_4} \to {{\text{P}}_2}{{\text{O}}_5}\]
From the above equation, we gets to know that two moles of \[{({\text{N}}{{\text{H}}_4})_2}{\text{HP}}{{\text{O}}_4}\] produces one mole of \[{{\text{P}}_2}{{\text{O}}_5}\].
Molar mass of a substance is the mass of 1 mole of a substance. Let us calculate the molar mass in each case:
Molar mass of \[{({\text{N}}{{\text{H}}_4})_2}{\text{HP}}{{\text{O}}_4}\] is \[(14 + 4 \times 1) \times 2 + 1 + 31 + 16 \times 4 = 132\].
But in the question we are using 2 moles, so mass of 2 moles of \[{({\text{N}}{{\text{H}}_4})_2}{\text{HP}}{{\text{O}}_4}\] will be \[132 \times 2 = 264\]
The molecular mass of \[{{\text{P}}_2}{{\text{O}}_5}\] is \[31 \times 2 + 16 \times 5 = 142\].
Two mole of \[{({\text{N}}{{\text{H}}_4})_2}{\text{HP}}{{\text{O}}_4}\] give 1 mole of \[{{\text{P}}_2}{{\text{O}}_5}\], this means that 264 gram of \[{({\text{N}}{{\text{H}}_4})_2}{\text{HP}}{{\text{O}}_4}\] will give us 142 gram of \[{{\text{P}}_2}{{\text{O}}_5}\]. Hence the percentage of \[{{\text{P}}_2}{{\text{O}}_5}\] will be calculated as:
\[\dfrac{{142}}{{264}} \times 100 = 53.78\% \]

Hence the correct option is C.

Note: \[{{\text{P}}_2}{{\text{O}}_5}\] is called phosphorus pentoxide. \[{{\text{P}}_2}{{\text{O}}_5}\] is the empirical formula for the compound \[{{\text{P}}_4}{{\text{O}}_{10}}\]. \[{{\text{P}}_2}{{\text{O}}_5}\] Exists in dimer state as \[{{\text{P}}_4}{{\text{O}}_{10}}\]. It is a very good dehydrating agent. It is a deliquescent that is it absorbs moisture from air and turns sticky when we leave it open. Diammonium phosphate is commonly called DAP. It is used as a fertilizer. It increases the pH of soil but when left over a long period it makes the solid acidic.