What is the molar mass of barium phosphate? Steps: first derive formula, then calculate molar mass. (2 point)
The Correct Answer and Explanation is :
Deriving the Formula for Barium Phosphate:
- Identify the ions involved:
- Barium (( \text{Ba}^{2+} )) is a Group 2 element, meaning it has a ( +2 ) charge.
- Phosphate (( \text{PO}_4^{3-} )) is a polyatomic ion with a ( -3 ) charge.
- Determine the ratio of ions for neutrality:
To balance the charges, we need three ( \text{Ba}^{2+} ) ions (( +6 ) total) to combine with two ( \text{PO}_4^{3-} ) ions (( -6 ) total).
Thus, the chemical formula is:
[
\text{Ba}_3(\text{PO}_4)_2
]
Calculating the Molar Mass:
- Atomic masses (from the periodic table):
- Barium (( \text{Ba} )): ( 137.33 \, \text{g/mol} )
- Phosphorus (( \text{P} )): ( 30.97 \, \text{g/mol} )
- Oxygen (( \text{O} )): ( 16.00 \, \text{g/mol} )
- Number of each atom in ( \text{Ba}_3(\text{PO}_4)_2 ):
- ( 3 \times \text{Ba} )
- ( 2 \times \text{P} )
- ( 8 \times \text{O} )
- Calculate molar mass:
[
\text{Molar mass of Ba}_3(\text{PO}_4)_2 = (3 \times 137.33) + (2 \times 30.97) + (8 \times 16.00)
]
[
= 411.99 + 61.94 + 128.00
]
[
= 601.93 \, \text{g/mol}
]
Explanation (300 words):
The molar mass of barium phosphate is calculated by first determining the correct chemical formula, ( \text{Ba}_3(\text{PO}_4)_2 ). This is derived by balancing the charges of barium (( \text{Ba}^{2+} )) and phosphate (( \text{PO}_4^{3-} )) ions to ensure neutrality. The total positive charge from three ( \text{Ba}^{2+} ) ions equals ( +6 ), which balances the ( -6 ) charge from two ( \text{PO}_4^{3-} ) ions.
Next, the molar mass is calculated by summing the contributions of each atom type in the formula. The atomic masses of barium, phosphorus, and oxygen are multiplied by their respective quantities in ( \text{Ba}_3(\text{PO}_4)_2 ): three barium atoms (( 3 \times 137.33 )), two phosphorus atoms (( 2 \times 30.97 )), and eight oxygen atoms (( 8 \times 16.00 )). Adding these values gives a total molar mass of ( 601.93 \, \text{g/mol} ).
This value is critical in stoichiometric calculations, where precise amounts of substances are used or analyzed in reactions involving barium phosphate. Understanding how to derive the formula and calculate its molar mass ensures accuracy in laboratory and industrial applications.