Question

Give the formula for calcium phosphate and then answer the following questions: a. Calculate the percent composition of each of the elements in this compound. b. If you knew that there was \(50.0 \mathrm{g}\) of phosphorus in your sample, how many grams of calcium phosphate would you have? How many moles of calcium phosphate would this be? How many formula units of calcium phosphate?

Short answer

The formula for calcium phosphate is \(\mathrm{Ca_3(PO_4)_2}\), with a molar mass of 310.18 g/mol. The percent composition of each element is approximately 38.76% Calcium, 19.97% Phosphorus, and 41.27% Oxygen. With 50.0 g of Phosphorus in the sample, there are 250.38 g of calcium phosphate, equivalent to 0.807 moles or approximately \(4.85 \times 10^{23}\) formula units of calcium phosphate.

Step-by-step solution

Determine the formula for calcium phosphate

Calcium phosphate has the chemical formula \(\mathrm{Ca_3(PO_4)_2}\).

Calculate the molar mass of calcium phosphate

To calculate the percent composition of each element, we need to first find the molar mass of calcium phosphate. The molar mass of an element is the sum of the atomic masses of all the atoms in the compound. So, the molar mass of \(\mathrm{Ca_3(PO_4)_2}\) is: \(3 ×(40.08\,\mathrm{g/mol \, Ca}) + 2 ×(3 ×(1.01\,\mathrm{g/mol\, H}) + 15.99\,\mathrm{g/mol\, O} + 30.97\,\mathrm{g/mol\, P}) =\) \((3 \times 40.08)\, \mathrm{g/mol} + 2 \times (3 \times 1.01 + 15.99 + 30.97)\, \mathrm{g/mol}\) Calculating the molar mass: \(120.24\, \mathrm{g/mol} + 2 × (3.03 + 15.99 + 30.97)\, \mathrm{g/mol} = 310.18\, \mathrm{g/mol}\)

Calculate the percent composition of each element

Now we'll calculate the percent composition of each element in calcium phosphate: Percent composition of Calcium (\(\mathrm{Ca}\)): \(\frac{3 \times 40.08}{310.18} \times 100\% \approx 38.76\%\) Percent composition of Phosphorus (\(\mathrm{P}\)): \(\frac{2 \times 30.97}{310.18} \times 100\% \approx 19.97\%\) Percent composition of Oxygen (\(\mathrm{O}\)): \(\frac{8 \times 15.99}{310.18} \times 100\% \approx 41.27\%\)

Calculate the mass of calcium phosphate and moles of calcium phosphate

We are given that there are 50.0 g of Phosphorus (\(\mathrm{P}\)) in the sample. Using the percent composition of Phosphorus obtained in step 3, we can calculate the mass of calcium phosphate: \(\frac{50.0\,\mathrm{g\,P}}{(0.1997)\frac{\mathrm{g\,P}}{\mathrm{g\,Ca_3(PO_4)_2}}}\)= \(= 250.38\,\mathrm{g\,Ca_3(PO_4)_2}\) Now, we'll determine the moles of calcium phosphate in the 250.38 g sample: Moles of calcium phosphate = \(\frac{250.38\,\mathrm{g\,Ca_3(PO_4)_2}}{310.18\,\mathrm{g/mol\,Ca_3(PO_4)_2}} = 0.807\,\mathrm{moles\,Ca_3(PO_4)_2}\)

Calculate the number of formula units of calcium phosphate

Finally, we will determine the number of formula units of calcium phosphate using Avogadro's number (\(6.022 \times 10^{23}\, \mathrm{formula \, units/mol}\)): Number of formula units of calcium phosphate = \(0.807\,\mathrm{moles\,Ca_3(PO_4)_2} \times 6.022 \times 10^{23}\, \mathrm{formula \, units/mol} = 4.85 \times 10^{23}\, \mathrm{formula \, units\,Ca_3(PO_4)_2}\) So, based on the given information, we have 250.38 g of calcium phosphate, which is equivalent to 0.807 moles or approximately \(4.85 \times 10^{23}\) formula units of calcium phosphate.

Key concepts

Percent Composition

Understanding the percent composition of a compound is crucial for students of chemistry. It tells us the percentage, by mass, of each element in the compound. For calcium phosphate, with the formula \(\text{Ca}_3(PO_4)_2\), we'd first need to calculate the molar mass of the compound. This value represents the sum of the atomic masses of all the atoms in one mole of the compound.

After calculating the molar mass, the percent composition is found by dividing the total mass of each element in one mole of the compound by the molar mass of the compound, and then multiplying by 100% to get the percentage. For example, calcium (\(\text{Ca}\)) has a mass of about 40.08 g/mol, and since there are three calcium atoms in the compound, you would multiply this atomic mass by three. This calculation is then put over the total molar mass of calcium phosphate and multiplied by 100% to find calcium's percent composition. Similar calculations are performed for phosphorus (\(\text{P}\)) and oxygen (\(\text{O}\)), with the results showing us how much of the total mass of the compound is taken up by each element.

Molar Mass Calculation

Molar mass calculation is a fundamental skill that enables you to convert between mass and moles, a common need in stoichiometry problems. To calculate the molar mass of a compound, you'll look at the periodic table to find the atomic mass of each element. Multiply the atomic mass by the number of atoms of that element in the compound and sum all the values together.

For instance, calcium phosphate, \(\text{Ca}_3(PO_4)_2\), consists of three calcium atoms, two phosphorus atoms, and eight oxygen atoms. By adding the mass contributions of each atom, you arrive at the compound's molar mass. Having the molar mass allows us to transition between the mass of a substance and the number of moles present, an essential step in many chemical calculations such as determining how much of a compound can be produced in a reaction, or in this exercise, how to move from a known quantity of one element to the mass of the compound.

Stoichiometry

Stoichiometry is the mathematical relationship between the amounts of reactants and products in a chemical reaction. It's anchored in the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. Therefore, every atom of the reactants must be accounted for in the products.

Using stoichiometry in the context of the calcium phosphate exercise, once the percent composition by mass of phosphorus is determined and the molar mass is calculated, we can figure out the total mass of the sample if we know the mass of just the phosphorus present. By converting mass to moles, we can use stoichiometry to determine how many formula units are present. In essence, stoichiometry allows us to scale reactions up or down and work with quantitative data to predict how much of each substance is involved in a chemical reaction, making it a powerful tool in both theoretical and applied chemistry.