Question

In diammonium hydrogen phosphate, \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4}\), percentage as: a. \(\mathrm{P}\) is maximum b. \(\mathrm{N}\) is maximum c. \(\mathrm{P}_{2} \mathrm{O}_{5}\) is \(53.78 \%\) d. \(\mathrm{NH}_{3}\) is \(25.76 \%\)

Short answer

The maximum percentage of P is 23.45%, of N is 21.21%, P2O5's percentage is incorrectly claimed as 53.78%, while NH3 is correctly 25.76%.

Step-by-step solution

Understanding the Problem

We need to determine the maximum percentage of phosphorus (P) and nitrogen (N) in diammonium hydrogen phosphate (NH4)2HPO4. Additionally, we will verify if the percentage calculations for P2O5 (53.78%) and NH3 (25.76%) are correct. Understanding the problem requires knowing the molecular weight of each element and the molecular formula.

Calculating Molar Mass

First, calculate the molar mass of (NH4)2HPO4 by summing up the atomic masses of all constituent atoms: N = 14.01, H = 1.01, P = 30.97, and O = 16.00. Thus, the molar mass of (NH4)2HPO4 = 2(14.01 + 4*1.01) + 1.01 + 30.97 + 4*16.00 = 132.07 g/mol.

Maximum Percentage of Phosphorus

Calculate the mass percentage of phosphorus in (NH4)2HPO4. The molar mass of P is 30.97. Therefore, the percentage of P is (30.97 / 132.07) * 100 ≈ 23.45%.

Maximum Percentage of Nitrogen

Calculate the mass percentage of nitrogen in (NH4)2HPO4. The molar mass of N in (NH4)2HPO4 is 2 * 14.01 = 28.02. Hence, the percentage of N is (28.02 / 132.07) * 100 ≈ 21.21%.

Verifying Percentage of P2O5

Convert the relevant part of (NH4)2HPO4 to P2O5. Given: 2 moles of HPO4 can theoretically make 1 mole of P2O5. The molar mass of P2O5 is 2(30.97) + 5(16.00) = 141.94 g/mol. Calculating percentage relative to 132.07 g/mol gives: (141.94 / 132.07) * 100, which does not equal 53.78%, indicating that the claim might not be accurate.

Verifying Percentage of NH3

Calculate the impact of NH3 in (NH4)2HPO4. NH3 = 17.03 g/mol, and two moles come from (NH4)2, so percentage of NH3 is (2 * 17.03 / 132.07) * 100 = 25.76%, verifying the claim.

Key concepts

Mass Percentage Calculation

Mass percentage calculation is a fundamental concept in chemistry. It involves calculating the mass of a specific component in relation to the total mass of the compound. This helps in understanding the composition of the compound by knowing what fraction of the total mass comes from each element. To calculate the mass percentage, use the formula:\[\text{Mass percentage of an element} = \left( \frac{\text{Molar mass of the element in the compound}}{\text{Total molar mass of the compound}} \right) \times 100\%\]

• Identify the molar mass of each element in the compound.
• Add up all the individual molar masses to find the total molar mass of the compound.
• Divide the molar mass of the element of interest by the total molar mass.
• Multiply the result by 100 to convert it into a percentage.

This process is essential for determining the percentage composition of elements in a compound, which is a crucial step for further chemical analysis and reaction calculations.

Molar Mass

Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol). It is calculated by adding up the atomic masses of all the atoms present in the molecule. The atomic masses of elements can be found on the periodic table and are usually given in atomic mass units (amu), which are the same as grams per mole when considering molar mass.For example, in the compound diammonium hydrogen phosphate,

• Each nitrogen (N) atom has a mass of 14.01 g/mol.
• Each hydrogen (H) atom has a mass of 1.01 g/mol.
• Phosphorus (P) has a mass of 30.97 g/mol.
• Oxygen (O) has a mass of 16.00 g/mol.

The molar mass of (NH₄)₂HPO₄ is then calculated by summing up the components:\[2(14.01 + 4\times1.01) + 1\times1.01 + 30.97 + 4\times16.00 = 132.07\, \text{g/mol}\]Understanding molar mass is fundamental because it allows us to convert between moles and grams, which is necessary for stoichiometry, balancing chemical equations, and performing accurate quantitative analyses.

Diammonium Hydrogen Phosphate

Diammonium hydrogen phosphate, chemical formula \((NH_4)_2HPO_4\), is a compound used in a variety of applications including fertilizers and fire retardants.This compound is composed of:

• Two ammonium ions \((NH_4)^+\), which contribute positively charged nitrogen and hydrogen atoms.
• A hydrogen phosphate ion \((HPO_4)^{2-}\), which includes phosphorus and oxygen atoms.

Key points about diammonium hydrogen phosphate:- It contains essential elements like nitrogen (N) and phosphorus (P), making it valuable in agriculture as a source of these nutrients.- It has a molecular structure that allows it to release ammonia (NH₃) slowly when dissolved, providing a controlled release of nitrogen.- It's important in industrial chemical reactions where phosphorus is required.Analyzing its mass percentages, like in calculations for phosphorus and nitrogen, is essential for determining its suitability for particular industrial or agricultural applications. By mastering both its general properties and specific calculations, one can better leverage its benefits in various practical contexts.