Calculate the mass percent composition of lithium in Li3PO4 to four significant figures. Express your answer as a percent.
The Correct Answer and Explanation is :
To calculate the mass percent composition of lithium (Li) in lithium phosphate (( \text{Li}_3\text{PO}_4 )), we need to follow a few steps:
Step 1: Determine the molar mass of ( \text{Li}_3\text{PO}_4 )
First, we find the molar masses of the elements involved:
- Lithium (Li) has a molar mass of approximately 6.939 g/mol.
- Phosphorus (P) has a molar mass of approximately 30.974 g/mol.
- Oxygen (O) has a molar mass of approximately 15.999 g/mol.
Now calculate the molar mass of ( \text{Li}_3\text{PO}_4 ):
[
\text{Molar mass of } \text{Li}_3\text{PO}_4 = (3 \times 6.939) + 30.974 + (4 \times 15.999)
]
[
= 20.817 + 30.974 + 63.996 = 115.787 \text{ g/mol}
]
Step 2: Calculate the total mass of lithium in ( \text{Li}_3\text{PO}_4 )
There are 3 lithium atoms in one formula unit of ( \text{Li}_3\text{PO}_4 ), so the total mass of lithium is:
[
\text{Mass of Li} = 3 \times 6.939 = 20.817 \text{ g/mol}
]
Step 3: Calculate the mass percent of lithium in ( \text{Li}_3\text{PO}_4 )
The mass percent composition of lithium is calculated as:
[
\text{Mass percent of Li} = \left( \frac{\text{Mass of Li}}{\text{Molar mass of } \text{Li}_3\text{PO}_4} \right) \times 100
]
[
= \left( \frac{20.817}{115.787} \right) \times 100 \approx 17.98\%
]
Final Answer:
The mass percent composition of lithium in lithium phosphate (( \text{Li}_3\text{PO}_4 )) is 17.98%.
Explanation:
The mass percent composition is a way to express the proportion of each element in a compound by mass. We first calculate the molar mass of the entire compound, which gives the total mass of one mole of that substance. Then, by finding the mass contributed by the lithium atoms and dividing it by the total molar mass of the compound, we get the mass percent of lithium in the compound. This method is crucial in understanding the relative abundance of elements within a compound and is commonly used in fields like chemistry, pharmaceuticals, and material science.