Calculate The Following: Mass Fraction of P in Tetraphosphorus Hexaoxide

The mass fraction of phosphorus (P) in tetraphosphorus hexaoxide (P₄O₆) is a fundamental chemical calculation that determines the proportion of phosphorus by mass in this compound. This calculation is essential for understanding the composition of the compound and is useful in various chemical and industrial applications.

What is mass fraction?

The mass fraction (or mass percentage) of a component in a compound is the ratio of the mass of that component to the total mass of the compound, expressed as a percentage. It provides a measure of how much of the total mass of the compound is made up of a particular element.

Mass fraction is calculated using the formula:

Mass fraction of component = (Mass of component / Total mass of compound) × 100%

For tetraphosphorus hexaoxide (P₄O₆), we need to determine the mass fraction of phosphorus (P) in the compound.

Calculating mass fraction

To calculate the mass fraction of phosphorus in tetraphosphorus hexaoxide, follow these steps:

Determine the molar mass of tetraphosphorus hexaoxide (P₄O₆).
Calculate the mass of phosphorus in one mole of the compound.
Use the mass fraction formula to find the percentage of phosphorus by mass.

Step 1: Calculate the molar mass of P₄O₆

The molar mass of a compound is the sum of the atomic masses of all the atoms in the compound. For tetraphosphorus hexaoxide:

Phosphorus (P) has an atomic mass of approximately 30.97 g/mol.
Oxygen (O) has an atomic mass of approximately 16.00 g/mol.

The formula P₄O₆ contains 4 phosphorus atoms and 6 oxygen atoms. Therefore, the molar mass is calculated as:

Molar mass of P₄O₆ = (4 × atomic mass of P) + (6 × atomic mass of O) = (4 × 30.97) + (6 × 16.00) = 123.88 + 96.00 = 219.88 g/mol

Step 2: Calculate the mass of phosphorus in P₄O₆

The mass of phosphorus in one mole of P₄O₆ is simply the mass contributed by the phosphorus atoms:

Mass of P in P₄O₆ = 4 × atomic mass of P = 4 × 30.97 = 123.88 g

Step 3: Calculate the mass fraction of phosphorus

Using the mass fraction formula:

Mass fraction of P = (Mass of P / Molar mass of P₄O₆) × 100% = (123.88 / 219.88) × 100% ≈ 56.33%

Therefore, the mass fraction of phosphorus in tetraphosphorus hexaoxide is approximately 56.33%.

Example calculation

Let's work through an example to illustrate the calculation:

Suppose we have 50 grams of tetraphosphorus hexaoxide (P₄O₆). We want to find out how much of this mass is phosphorus.

First, determine the mass fraction of phosphorus in P₄O₆, which we've calculated as approximately 56.33%.
Multiply the mass of the sample by the mass fraction to find the mass of phosphorus:

Mass of P = Total mass of P₄O₆ × Mass fraction of P = 50 g × 0.5633 ≈ 28.165 g

So, in 50 grams of tetraphosphorus hexaoxide, there is approximately 28.17 grams of phosphorus.

FAQ

What is the difference between mass fraction and mole fraction?: Mass fraction is the ratio of the mass of a component to the total mass of the compound, while mole fraction is the ratio of the number of moles of a component to the total number of moles in the compound. Mass fraction is expressed as a percentage, while mole fraction is a dimensionless ratio.
Why is the mass fraction of phosphorus in P₄O₆ approximately 56.33%?: The mass fraction is determined by the relative masses of phosphorus and oxygen in the compound. Since phosphorus is heavier than oxygen, it contributes a larger proportion of the total mass.
Can the mass fraction of phosphorus in P₄O₆ vary?: The mass fraction of phosphorus in P₄O₆ is a fixed value based on the compound's chemical composition. It does not vary under normal conditions.
How is mass fraction different from concentration?: Mass fraction refers to the proportion of a component by mass in a compound, while concentration typically refers to the amount of a substance per unit volume or mass of a solvent. Mass fraction is a measure of composition, while concentration is a measure of dispersion.