How many grams of phosphorus (P) are in a 158.379 g sample of Zn3(PO4)2? Express your answer in units of grams using at least three significant figures.

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!

Learn how to calculate the mass of phosphorus in a 158.379 g sample of Zn3(PO4)2. This detailed solution covers stoichiometry, molar mass calculations, and mass percentage. Suitable for high school chemistry students, with a focus on accurate use of significant figures.

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