What is the percent composition of zinc phosphate (Zn3(PO4)2)

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What is the percent composition of zinc phosphate (Zn3(PO4)2)? Find the percentage for each element and show work

The Correct Answer and Explanation is:

To find the percent composition of zinc phosphate, Zn₃(PO₄)₂, we need to determine the molar mass of the compound and then calculate the mass percent of each element in it.

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

First, break the formula into the number of atoms of each element:

  • Zn: 3 atoms
  • P: 2 atoms
  • O: 8 atoms (since each PO₄ has 4 O, and there are 2 PO₄ groups)

Use the periodic table to get atomic masses (rounded to 2 decimal places):

  • Zn (zinc) = 65.38 g/mol
  • P (phosphorus) = 30.97 g/mol
  • O (oxygen) = 16.00 g/mol

Now calculate the molar mass:Zn3=3×65.38=196.14 g/molP2=2×30.97=61.94 g/molO8=8×16.00=128.00 g/mol\text{Zn}_3 = 3 \times 65.38 = 196.14 \text{ g/mol} \\ \text{P}_2 = 2 \times 30.97 = 61.94 \text{ g/mol} \\ \text{O}_8 = 8 \times 16.00 = 128.00 \text{ g/mol}Zn3​=3×65.38=196.14 g/molP2​=2×30.97=61.94 g/molO8​=8×16.00=128.00 g/mol

Total molar mass of Zn₃(PO₄)₂:196.14+61.94+128.00=386.08 g/mol196.14 + 61.94 + 128.00 = 386.08 \text{ g/mol}196.14+61.94+128.00=386.08 g/mol

Step 2: Find percent composition

Now calculate each element’s percent by dividing its total mass by the molar mass:

  • Zinc:

196.14386.08×100≈50.80%\frac{196.14}{386.08} \times 100 \approx 50.80\%386.08196.14​×100≈50.80%

  • Phosphorus:

61.94386.08×100≈16.04%\frac{61.94}{386.08} \times 100 \approx 16.04\%386.0861.94​×100≈16.04%

  • Oxygen:

128.00386.08×100≈33.16%\frac{128.00}{386.08} \times 100 \approx 33.16\%386.08128.00​×100≈33.16%

Final Answer:

  • Zinc (Zn): 50.80%
  • Phosphorus (P): 16.04%
  • Oxygen (O): 33.16%

Textbook-Style Explanation (≈300 words):

Percent composition is the percentage by mass of each element in a compound. It helps chemists understand how much of each element is present in a given compound. To determine the percent composition of zinc phosphate, Zn₃(PO₄)₂, we must first calculate its molar mass by summing the masses of all the atoms in the compound.

Zinc phosphate contains 3 atoms of zinc (Zn), 2 atoms of phosphorus (P), and 8 atoms of oxygen (O). Using the periodic table, we find the atomic masses: zinc is 65.38 g/mol, phosphorus is 30.97 g/mol, and oxygen is 16.00 g/mol. Multiplying each atomic mass by the number of atoms in the formula gives us:

  • Zinc: 3 × 65.38 = 196.14 g/mol
  • Phosphorus: 2 × 30.97 = 61.94 g/mol
  • Oxygen: 8 × 16.00 = 128.00 g/mol

Adding these values gives the total molar mass of zinc phosphate:
196.14 + 61.94 + 128.00 = 386.08 g/mol.

To find the percent composition, divide the total mass of each element by the compound’s molar mass and multiply by 100:

  • %Zn = (196.14 ÷ 386.08) × 100 ≈ 50.80%
  • %P = (61.94 ÷ 386.08) × 100 ≈ 16.04%
  • %O = (128.00 ÷ 386.08) × 100 ≈ 33.16%

These values show the mass proportion of each element in zinc phosphate. This information is useful in chemical analysis, stoichiometry, and quality control in manufacturing.

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