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Chapter 3: Problem 13

Tooth enamel is \(\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3}(\mathrm{OH}) .\) Calculate the percent composition of the elements present.

Short Answer

Expert verified
Calcium: 41.21%, Phosphorus: 19.10%, Oxygen: 39.49%, Hydrogen: 0.21%.

Step by step solution

01

Identify the Molar Mass

Identify the molar mass of each element in the chemical formula \( \mathrm{Ca}_{5}(\mathrm{PO}_{4})_{3}(\mathrm{OH}) \). The atomic masses are approximately: \( \mathrm{Ca}: 40.08 \, \mathrm{g/mol} \), \( \mathrm{P}: 30.97 \, \mathrm{g/mol} \), \( \mathrm{O}: 16.00 \, \mathrm{g/mol} \), and \( \mathrm{H}: 1.01 \, \mathrm{g/mol} \).
02

Calculate the Molar Mass of Each Element in the Compound

Calculate the total molar mass of each element in the compound:- \(5 \times 40.08 = 200.40 \, \mathrm{g/mol} \) for calcium- \(3 \times 30.97 = 92.91 \, \mathrm{g/mol} \) for phosphorus- \( (3 \times 4 + 1) \times 16.00 = 192.00 \, \mathrm{g/mol} \) for oxygen- \(1.01 \, \mathrm{g/mol} \) for hydrogen.
03

Calculate the Total Molar Mass of the Compound

Sum the molar masses of all elements to obtain the total molar mass:\[200.40 + 92.91 + 192.00 + 1.01 = 486.32 \, \mathrm{g/mol}.\]
04

Determine the Percent Composition of Each Element

Calculate the percent composition of each element:- Calcium: \((200.40 / 486.32) \times 100 \approx 41.21\%\)- Phosphorus: \((92.91 / 486.32) \times 100 \approx 19.10\%\)- Oxygen: \((192.00 / 486.32) \times 100 \approx 39.49\%\)- Hydrogen: \((1.01 / 486.32) \times 100 \approx 0.21\%\).

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Key Concepts

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

Molar Mass Calculation
When working with chemical formulas, understanding molar mass is crucial. Molar mass is essentially the mass of one mole of a substance and is expressed in grams per mole (g/mol). To calculate the molar mass of a compound, you need to know the atomic masses of the individual elements present.
  • The atomic mass for calcium (\( \mathrm{Ca} \)) is 40.08 g/mol.
  • For phosphorus (\( \mathrm{P} \)), it's 30.97 g/mol.
  • Oxygen (\( \mathrm{O} \)) has an atomic mass of 16.00 g/mol.
  • While hydrogen (\( \mathrm{H} \)) is 1.01 g/mol.
To find the compound's molar mass, multiply the atomic masses by their respective counts in the molecule, and sum them up. For example, in tooth enamel, we're dealing with the formula \(\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3}(\mathrm{OH})\.\)
Here, you multiply the molar mass of each element by its corresponding number of atoms, and add these to get the total molar mass of 486.32 g/mol.
Tooth Enamel Chemistry
The chemistry of tooth enamel is fascinating and integral to understanding its composition. Tooth enamel is primarily made of a compound known as hydroxyapatite, represented by the chemical formula \( \mathrm{Ca}_{5}(\mathrm{PO}_{4})_{3}(\mathrm{OH})\)\. This compound is a form of calcium phosphate and is responsible for the hardness of tooth enamel.
Enamel mainly consists of calcium, phosphorous, oxygen, and hydrogen. These elements come together to form a strong and resilient outer layer for our teeth.
  • Calcium contributes to the structural integrity of enamel.
  • Phosphorus helps in building strength and resistance against decay.
  • Oxygen and hydrogen bond within the hydroxide ions (\( \mathrm{OH}^{-} \)) in the compound, playing significant roles in the stability of the compound network.
Recognizing these elements and their contributions offers insights into oral health and dental care.
Elemental Composition Calculation
Elemental composition calculation tells us the proportion of each element in a compound. This is done by determining the percentage of each element with respect to the total molar mass of the compound. The step-by-step approach involves calculating the mass of individual elements in the compound and dividing it by the total molar mass.
For instance:
  • The percent composition for calcium is found by taking its total mass in the compound (\(200.40\ g/mol\)) and dividing it by the total molar mass (\(486.32\ g/mol\)), then multiplying by 100. This gives roughly 41.21\%.
  • Similarly, for phosphorus, oxygen, and hydrogen, the calculations yield 19.10\%, 39.49\%, and 0.21\% respectively.
Calculating the percent composition is a valuable tool in chemistry as it helps us understand the makeup of compounds and points towards their potential characteristics and functionality. It's especially useful in fields like material science and biochemistry where the elemental makeup is directly related to the substance's properties and applications.

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Most popular questions from this chapter

Silicon tetrachloride \(\left(\mathrm{SiCl}_{4}\right)\) can be prepared by heating Si in chlorine gas: $$ \mathrm{Si}(s)+2 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SiCl}_{4}(l) $$ In one reaction, \(0.507 \mathrm{~mol}\) of \(\mathrm{SiCl}_{4}\) is produced. How many moles of molecular chlorine were used in the reaction?

The following is a crude but effective method for estimating the order of magnitude of Avogadro's number using stearic acid \(\left(\mathrm{C}_{18} \mathrm{H}_{36} \mathrm{O}_{2}\right)\). When stearic acid is added to water, its molecules collect at the surface and form a monolayer; that is, the layer is only one molecule thick. The cross-sectional area of each stearic acid molecule has been measured to be \(0.21 \mathrm{nm}^{2}\). In one experiment, it is found that \(1.4 \times 10^{-4} \mathrm{~g}\) of stearic acid is needed to form a monolayer over water in a dish of diameter \(20 \mathrm{~cm}\). Based on these measurements, what is Avogadro's number? (The area of a circle of radius \(r\) is \(\pi r^{2}\).)

One of the reactions that occurs in a blast furnace, where iron ore is converted to cast iron, is $$ \mathrm{Fe}_{2} \mathrm{O}_{3}+3 \mathrm{CO} \longrightarrow 2 \mathrm{Fe}+3 \mathrm{CO}_{2} $$ Suppose that \(1.64 \times 10^{3} \mathrm{~kg}\) of Fe is obtained from a \(2.62 \times 10^{3}-\mathrm{kg}\) sample of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\). Assuming that the reaction goes to completion, what is the percent purity of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) in the original sample?

A common laboratory preparation of oxygen gas is the thermal decomposition of potassium chlorate \(\left(\mathrm{KClO}_{3}\right)\). Assuming complete decomposition, calculate the number of grams of \(\mathrm{O}_{2}\) gas that can be obtained from \(46.0 \mathrm{~g}\) of \(\mathrm{KClO}_{3}\). (The products are \(\mathrm{KCl}\) and \(\mathrm{O}_{2}\).)

What mole ratio of molecular chlorine \(\left(\mathrm{Cl}_{2}\right)\) to molecular oxygen \(\left(\mathrm{O}_{2}\right)\) would result from the breakup of the compound \(\mathrm{Cl}_{2} \mathrm{O}_{7}\) into its constituent elements?
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