To determine the mass of phosphorus (P) in the sample of Zn₃(PO₄)₂, we need to follow these steps:

Step 1: Find the molar mass of Zn₃(PO₄)₂

The molecular formula is Zn₃(PO₄)₂, which consists of:

• 3 Zinc (Zn) atoms
• 2 Phosphate (PO₄³⁻) groups, each containing 1 Phosphorus (P) and 4 Oxygen (O) atoms.

Now, let's calculate the molar mass of each component:

• Zinc (Zn): Atomic mass = 65.38 g/mol $3 \times 65.38 = 196.14 \, \text{g/mol}$

• Phosphorus (P): Atomic mass = 30.97 g/mol $2 \times 30.97 = 61.94 \, \text{g/mol}$

• Oxygen (O): Atomic mass = 16.00 g/mol $8 \times 16.00 = 128.00 \, \text{g/mol}$

So, the total molar mass of Zn₃(PO₄)₂ is: $196.14 \, \text{g/mol} \, (\text{Zn}) + 61.94 \, \text{g/mol} \, (\text{P}) + 128.00 \, \text{g/mol} \, (\text{O}) = 386.08 \, \text{g/mol}$

Step 2: Determine the mass percentage of phosphorus (P) in Zn₃(PO₄)₂

There are 2 phosphorus atoms in Zn₃(PO₄)₂.

$\frac{61.94 \, \text{g/mol (P)}}{386.08 \, \text{g/mol (Zn₃(PO₄)₂)}} \times 100 = 16.04\%$

Step 3: Calculate the mass of phosphorus in the 158.379 g sample

Now, to find the mass of phosphorus in the sample, multiply the mass percentage by the total sample mass:

$158.379 \, \text{g} \times \frac{16.04}{100} = 25.40 \, \text{g}$

Final Answer:

There are 25.40 grams of phosphorus in a 158.379 g sample of Zn₃(PO₄)₂.

Would you like further details or have any questions?

Here are 5 related questions:

1. How would you calculate the amount of oxygen in the same compound?
2. What is the molar mass of one mole of Zn₃(PO₄)₂?
3. How many moles of phosphorus are in the sample?
4. How do the percentages of zinc, phosphorus, and oxygen compare in the compound?
5. How would the mass of phosphorus change if the sample were doubled?

Tip: Always check your significant figures based on the given data to ensure precision!