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

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.