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Chapter 3: Problem 148

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

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

Step by step solution

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01

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: \[ \text{Total Molar Mass} = 120.24 + 61.94 + 128.00 = 310.18 \text{ g/mol} \]
02

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: \( \frac{128.00}{310.18} \times 100\% \approx 41.27\% \).
03

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

These are the key concepts you need to understand to accurately answer the question.

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.

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Most popular questions from this chapter

Limestone \(\left(\mathrm{CaCO}_{3}\right)\) is decomposed by heating to quicklime \((\mathrm{CaO})\) and carbon dioxide. Calculate how many grams of quicklime can be produced from \(1.0 \mathrm{~kg}\) of limestone.

Potash is any potassium mineral that is used for its potassium content. Most of the potash produced in the United States goes into fertilizer. The major sources of potash are potassium chloride \((\mathrm{KCl})\) and potassium sulfate \(\left(\mathrm{K}_{2} \mathrm{SO}_{4}\right) .\) Potash production is often reported as the potassium oxide \(\left(\mathrm{K}_{2} \mathrm{O}\right)\) equivalent or the amount of \(\mathrm{K}_{2} \mathrm{O}\) that could be made from a given mineral. (a) If \(\mathrm{KCl}\) costs \(\$ 0.55\) per \(\mathrm{kg},\) for what price (dollar per kg) must \(\mathrm{K}_{2} \mathrm{SO}_{4}\) be sold to supply the same amount of potassium on a per dollar basis? (b) What mass (in kg) of \(\mathrm{K}_{2} \mathrm{O}\) contains the same number of moles of \(\mathrm{K}\) atoms as \(1.00 \mathrm{~kg}\) of \(\mathrm{KCl}\) ?

The annual production of sulfur dioxide from burning coal and fossil fuels, auto exhaust, and other sources is about 26 million tons. The equation for the reaction is $$ \mathrm{S}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g) $$ How much sulfur (in tons), present in the original materials. would result in that quantity of \(\mathrm{SO}_{2}\) ?

Titanium(IV) oxide \(\left(\mathrm{TiO}_{2}\right)\) is a white substance produced by the action of sulfuric acid on the mineral ilmenite \(\left(\mathrm{FeTiO}_{3}\right):\) $$ \mathrm{FeTiO}_{3}+\mathrm{H}_{2} \mathrm{SO}_{4} \longrightarrow \mathrm{TiO}_{2}+\mathrm{FeSO}_{4}+\mathrm{H}_{2} \mathrm{O} $$ Its opaque and nontoxic properties make it suitable as a pigment in plastics and paints. In one process, \(8.00 \times\) \(10^{3} \mathrm{~kg}\) of \(\mathrm{FeTiO}_{3}\) yielded \(3.67 \times 10^{3} \mathrm{~kg}\) of \(\mathrm{TiO}_{2}\). What is the percent yield of the reaction?

Myoglobin stores oxygen for metabolic processes in muscle. Chemical analysis shows that it contains 0.34 percent Fe by mass. What is the molar mass of myoglobin? (There is one Fe atom per molecule.)
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