To determine the molar mass of the compound [tex]\( \text{Mg}_3(\text{PO}_4)_2 \)[/tex], we need to consider the atomic masses of its constituent elements and calculate the total molar mass of the compound. Here is a step-by-step solution:
1. Identify the formula and its components: [tex]\( \text{Mg}_3(\text{PO}_4)_2 \)[/tex]:
- This formula indicates that there are 3 magnesium (Mg) atoms, 2 phosphorus (P) atoms, and 8 oxygen (O) atoms in one formula unit of the compound.
2. Determine the atomic masses of each element (as given in the problem statement):
- Atomic mass of magnesium (Mg): 24.305 g/mol
- Atomic mass of phosphorus (P): 30.974 g/mol
- Atomic mass of oxygen (O): 15.999 g/mol
3. Calculate the contribution of each type of atom to the molar mass:
- For magnesium: There are 3 Mg atoms.
[tex]\[
\text{Mass contribution of Mg} = 3 \times 24.305 \, \text{g/mol} = 72.915 \, \text{g/mol}
\][/tex]
- For phosphorus: There are 2 P atoms.
[tex]\[
\text{Mass contribution of P} = 2 \times 30.974 \, \text{g/mol} = 61.948 \, \text{g/mol}
\][/tex]
- For oxygen: There are 8 O atoms.
[tex]\[
\text{Mass contribution of O} = 8 \times 15.999 \, \text{g/mol} = 127.992 \, \text{g/mol}
\][/tex]
4. Sum the contributions to find the total molar mass of the compound:
[tex]\[
\text{Molar mass of } \text{Mg}_3(\text{PO}_4)_2 = 72.915 \, \text{g/mol} + 61.948 \, \text{g/mol} + 127.992 \, \text{g/mol} = 262.855 \, \text{g/mol}
\][/tex]
5. Round the final molar mass to one decimal place:
[tex]\[
\text{Molar mass of } \text{Mg}_3(\text{PO}_4)_2 = 262.9 \, \text{g/mol}
\][/tex]
The molar mass of [tex]\( \text{Mg}_3(\text{PO}_4)_2 \)[/tex] rounded to one decimal place is [tex]\( 262.9 \, \text{g/mol} \)[/tex].
Hence, the correct answer is [tex]\( 262.9 \, \text{g/mol} \)[/tex].
