Problem 126 - Chemistry

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.

Step-by-Step Solution

Answer

The percent composition by mass of calcium in calcium phosphate is 38.77\%, the percent composition by mass of phosphorus is 19.97\%, and the percent composition by mass of oxygen is 41.26\%.

Step 1: Calculate the molar mass of \(Ca_3(PO_4)_2\)

The molar mass of \(Ca_3(PO_4)_2\) is the sum of the molar masses of its atoms. There are 3 calcium atoms (\(Ca\)), each with a molar mass of 40.08 g/mol, 2 phosphorus atoms (\(P\)), each with a molar mass of 30.97 g/mol, and 8 oxygen atoms (\(O\)), each with a molar mass of 16.00 g/mol. Therefore, the total molar mass is \(3(40.08) + 2(30.97) + 8(16.00) = 310.18\) g/mol.

Step 2: Calculate the mass percent of each element

The percent composition (mass %) of an element in a compound is the mass of the element divided by the total molecular mass, multiplied by 100. For calcium, the calculation is \((3 * 40.08 / 310.18) * 100 = 38.77\%\). For phosphorus, it is \((2 * 30.97 / 310.18) * 100 = 19.97\%\). For oxygen, it is \((8 * 16.00 / 310.18) * 100 = 41.26\%\).

Step 3: Check your work

The mass percentages of all elements in a compound should add up to 100\%. In this case, 38.77\% + 19.97\% + 41.26\% = 100\%. It checks out, thus fulfilling the requirement.

Key Concepts

Molar Mass Calculation

Understanding the molar mass of a compound is essential for a plethora of chemical calculations. The molar mass, expressed in grams per mole (g/mol), corresponds to the mass of one mole of a substance. One mole is defined as Avogadro's number, which is approximately 6.022 x 10²³units of that substance, whether they're atoms, molecules, ions, or other particles.

To calculate the molar mass of a compound, like calcium phosphate \(Ca_3(PO_4)_2\), each atom's individual molar mass (found on the periodic table) is multiplied by its respective number of atoms within the compound and then summed up.

• For \(Ca_3(PO_4)_2\), each calcium (Ca) atom has a molar mass of 40.08 g/mol, so for three calcium atoms, the total is 3 x 40.08 g/mol.
• Each phosphorus (P) atom has a molar mass of 30.97 g/mol, and with two of them, the contribution to the total molar mass is 2 x 30.97 g/mol.
• Oxygen (O) has a molar mass of 16.00 g/mol, and in the compound, there are eight oxygen atoms, totaling 8 x 16.00 g/mol.

Adding these contributions together gives the total molar mass of the compound. This calculation forms the foundation for other quantitative analysis in chemistry such as stoichiometry, which is crucial for understanding chemical reactions and the relationships between reactants and products.

Chemical Composition

Chemical composition reveals the identity and quantity of the elements that make up a chemical compound. It’s like a recipe that indicates what and how much of each ingredient is needed to create the substance. Knowing the chemical composition is essential for understanding the properties and behavior of the compound.When studying compounds like calcium phosphate \(Ca_3(PO_4)_2\), it's important to recognize that the compound is made up of calcium, phosphorus, and oxygen atoms in a 3:2:8 ratio. This ratio can help you determine many characteristics of the compound, such as its reactivity and nutritional value in the case of calcium phosphate being a part of bone composition.Moreover, the percent composition by mass of each element in a compound provides insights into the relative amounts of each element. It tells us, for example, how much of the compound's mass is due to calcium versus phosphorus or oxygen. This is crucial for applications in medicine, geology, nutrition, and many other scientific domains.

Stoichiometry

Stoichiometry, at its core, is the study of the quantitative relationships or ratios between the reactants and products in a chemical reaction guided by the balanced chemical equation. It allows chemists to predict the amount of products that will form during a reaction, and the amounts of reactants required to create a desired amount of product.
By knowing the molar mass of a substance, such as calcium phosphate \(Ca_3(PO_4)_2\), we can use stoichiometry to determine how these masses interact in a chemical reaction. For instance, if a biologist wants to produce a certain amount of bone tissue, they need to know how much of each element is needed. Stoichiometry would be used to calculate the precise quantities of calcium, phosphorus, and oxygen needed, based on their percent composition by mass and the molar ratios indicated in the chemical equation.

In a balanced equation, the proportions of reactants and products are expressed in moles, which can then be converted to grams through molar mass. This interplay between molar mass, chemical composition, and stoichiometry is key to formulating and predicting outcomes in the lab, industrial processes, and even within biological systems.