What is the molar mass of Ba3(PO4)2?
Please record your answer with correct units and rounded to 3 places past the decimal.
The Correct Answer and Explanation is:
To calculate the molar mass of barium phosphate, (\text{Ba}_3(\text{PO}_4)_2), you need to sum the atomic masses of all atoms in the formula. Here’s the step-by-step process:
1. Atomic Masses:
- Barium (Ba): 137.327 g/mol
- Phosphorus (P): 30.974 g/mol
- Oxygen (O): 15.999 g/mol
2. Breakdown of the Formula:
- Barium (Ba(_3)): There are 3 barium atoms, so the contribution from barium is:
[
3 \times 137.327 \, \text{g/mol} = 411.981 \, \text{g/mol}
] - Phosphate (PO(_4)): The phosphate ion consists of 1 phosphorus atom and 4 oxygen atoms. There are 2 phosphate groups, so we need to calculate the molar mass of one PO(_4) group and then multiply by 2:
[
1 \times 30.974 \, \text{g/mol} = 30.974 \, \text{g/mol} \quad (\text{Phosphorus in one PO}_4)
]
[
4 \times 15.999 \, \text{g/mol} = 63.996 \, \text{g/mol} \quad (\text{Oxygen in one PO}_4)
]
[
\text{Total molar mass of one PO}_4 = 30.974 + 63.996 = 94.970 \, \text{g/mol}
]
Since there are 2 PO(_4) groups:
[
2 \times 94.970 \, \text{g/mol} = 189.940 \, \text{g/mol}
]
3. Total Molar Mass:
Now, add the contributions of all atoms:
[
411.981 \, \text{g/mol} \, (\text{Ba}_3) + 189.940 \, \text{g/mol} \, (\text{PO}_4)_2 = 601.921 \, \text{g/mol}
]
Final Answer:
The molar mass of (\text{Ba}_3(\text{PO}_4)_2) is 601.921 g/mol.
Explanation:
The molar mass of a compound is the sum of the atomic masses of all the atoms in its molecular formula. In this case, (\text{Ba}_3(\text{PO}_4)_2) contains three barium atoms, two phosphate ions, each consisting of one phosphorus atom and four oxygen atoms. Calculating the molar mass requires multiplying the atomic mass of each element by the number of atoms it contributes to the compound and then summing the results. The precision of the answer is important, especially in chemical calculations, as even slight deviations can affect the outcome in stoichiometry or other quantitative analyses. Therefore, we ensure that the atomic masses are used to three decimal places and the result is appropriately rounded for accuracy.