Question

Calculate the percent composition by mass of all the elements in calcium phosphate \(\left[\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\right]\), a major component of bone.

Short answer

Calcium: 38.76%, Phosphorus: 19.97%, Oxygen: 41.27%.

Step-by-step solution

Find Molar Mass of Calcium Phosphate

Calculate the molar mass of calcium phosphate, \( \text{Ca}_3(\text{PO}_4)_2 \). The molar mass can be found by summing the atomic masses of all atoms in the formula. - Calcium (Ca): 40.08 g/mol, and there are 3: \( 3 \times 40.08 = 120.24 \text{ g/mol} \).- Phosphorus (P): 30.97 g/mol and there are 2: \( 2 \times 30.97 = 61.94 \text{ g/mol} \).- Oxygen (O): 16.00 g/mol and there are 8 (4 per phosphate ion \( \text{PO}_4 \)): \( 8 \times 16.00 = 128.00 \text{ g/mol} \).Adding these values gives: \[ \text{Total Molar Mass} = 120.24 + 61.94 + 128.00 = 310.18 \text{ g/mol} \]

Calculate Mass Contribution of Each Element

Now, calculate the mass contribution of each element in the compound.- Calcium's mass contribution: \( \frac{120.24}{310.18} \times 100\% \approx 38.76\% \).- Phosphorus's mass contribution: \( \frac{61.94}{310.18} \times 100\% \approx 19.97\% \).- Oxygen's mass contribution: \( \frac{128.00}{310.18} \times 100\% \approx 41.27\% \).

Verify the Calculations

Ensure the percentages add up to 100% to verify correctness.Calculate:\[ 38.76\% + 19.97\% + 41.27\% = 100.00\% \]The sum is 100%, confirming the calculations are correct.

Key concepts

Molar Mass Calculation

Understanding molar mass is crucial for determining the percent composition of compounds. Molar mass represents the mass of one mole of a substance. It is typically expressed in units of grams per mole (g/mol). To calculate it, we sum the atomic masses of all the atoms present in the molecular formula of the compound. For instance, in calcium phosphate, with the formula \( \text{Ca}_3(\text{PO}_4)_2 \), we calculate the molar mass by adding together the products of the atomic masses and the number of each type of atom present in the formula.

- For calcium (Ca), we have: \( 3 \times 40.08 \text{ g/mol} = 120.24 \text{ g/mol} \).
- For phosphorus (P), there are: \( 2 \times 30.97 \text{ g/mol} = 61.94 \text{ g/mol} \).
- For oxygen (O), within the phosphate (PO₄), there are: \( 8 \times 16.00 \text{ g/mol} = 128.00 \text{ g/mol} \).

By adding these together, we find the total molar mass of the compound:
\[ 120.24 + 61.94 + 128.00 = 310.18 \text{ g/mol} \]
This calculation allows us to move forward in determining the percent composition of the compound.

Calcium Phosphate

Calcium phosphate, a critical component in bone structure, is represented by the formula \( \text{Ca}_3(\text{PO}_4)_2 \). This compound is significant not only in biology but also in chemistry due to its complex structure.

The structure involves repeating units containing calcium, phosphorus, and oxygen. Calcium atoms bond ionically with the phosphate groups, forming a stable solid. The presence of these elements in specific proportions makes calcium phosphate an essential mineral in bone health, providing mechanical strength and rigidity.

In analytical chemistry, calculating the percent composition of each element in calcium phosphate helps in understanding its precise elemental makeup, which in turn aids in various applications, including nutritional assessments and material science. Knowing the molar mass of such compounds is the first step in calculating these percentages accurately, ensuring proper balance and uniformity in applications involving calcium phosphate.

Elemental Analysis

Elemental analysis involves determining the relative abundance of each element within a compound. For calcium phosphate \( \text{Ca}_3(\text{PO}_4)_2 \), this involves using its molar mass to find how much of each element it contains by mass.

By dividing the mass contributions of each element by the total molar mass, and then multiplying by 100, we find the percent composition:

• Calcium's contribution: \( \frac{120.24}{310.18} \times 100\% \approx 38.76\% \)
• Phosphorus's contribution: \( \frac{61.94}{310.18} \times 100\% \approx 19.97\% \)
• Oxygen's contribution: \( \frac{128.00}{310.18} \times 100\% \approx 41.27\% \)

These calculations are important for verifying the integrity of the compound and ensuring its consistent quality. When all these percentages are summed, they equate to 100% if the calculations are accurate. Thus, verifying the sum is a crucial final step in any elemental analysis to ensure that all measurements were executed correctly.