To calculate the grams of zinc (Zn) in a sample containing 1.867 mol of zinc phosphate ($\text{Zn}_3(\text{PO}_4)_2$), we follow these steps:

1. Determine the molar mass of zinc phosphate ($\text{Zn}_3(\text{PO}_4)_2$):

   • Zinc ($\text{Zn}$) has an atomic mass of 65.38 g/mol.
   • Phosphorus ($\text{P}$) has an atomic mass of 30.97 g/mol.
   • Oxygen ($\text{O}$) has an atomic mass of 16.00 g/mol.

   The formula for zinc phosphate is $\text{Zn}_3(\text{PO}_4)_2$, which means:

   • 3 zinc (Zn) atoms
   • 2 phosphorus (P) atoms
   • 8 oxygen (O) atoms

   The molar mass of $\text{Zn}_3(\text{PO}_4)_2$ is calculated as:

   $\text{Molar mass of } \text{Zn}_3(\text{PO}_4)_2 = 3(65.38) + 2(30.97) + 8(16.00)$

   $= 196.14 + 61.94 + 128.00 = 386.08 \, \text{g/mol}$

2. Find the number of moles of zinc in the sample:

   Each mole of $\text{Zn}_3(\text{PO}_4)_2$ contains 3 moles of zinc (Zn). Thus, the total moles of zinc in the sample is:

   $\text{Moles of Zn} = 1.867 \, \text{mol of} \, \text{Zn}_3(\text{PO}_4)_2 \times 3 = 5.601 \, \text{mol of Zn}$

3. Convert moles of zinc to grams:

   Now, multiply the number of moles of zinc by the molar mass of zinc (65.38 g/mol):

   $\text{Mass of Zn} = 5.601 \, \text{mol} \times 65.38 \, \text{g/mol} = 366.0 \, \text{g of Zn}$

Therefore, the sample contains 366.0 grams of zinc.

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Related Questions:

1. What is the molar mass of zinc phosphate for other hydrate forms?
2. How do you calculate moles if only the mass of a substance is provided?
3. What are common applications of zinc phosphate in industry?
4. Can this method apply to other compounds containing zinc?
5. How would the calculation change if the sample contained a mixture of compounds?

Tip:

Always check the formula of the compound to determine the ratio of atoms when calculating molar masses.