Problem 100 - Chemistry: An Atoms-Focused Approach

Question

Titanium dioxide and zinc oxide are common names of two of the active ingredients approved by the U.S. FDA for use in sunscreens. a. What are the chemical formulas of these compounds? b. What are the proper names of the compounds based on the rules for naming described in Chapter \(4 ?\) c. Which of the two compounds contains the higher percentage of oxygen by mass?

Step-by-Step Solution

Answer

Answer: Titanium dioxide (TiO\(_2\)) has a higher percentage of oxygen by mass (approximately 40.03%) compared to zinc oxide (ZnO) (approximately 19.66%).

Step 1: Write down the chemical formulas of titanium dioxide and zinc oxide

Titanium dioxide is a compound formed by titanium (Ti) and oxygen (O). Its chemical formula is TiO\(_2\). Zinc oxide is a compound formed by zinc (Zn) and oxygen (O). Its chemical formula is ZnO.

Step 2: Apply the rules for naming from Chapter 4 to find the proper names of the compounds

Based on the rules for naming described in Chapter 4, the proper names of these compounds are as follows: - Titanium dioxide: The proper name is Titanium(IV) oxide since the charge on the titanium ion is +4. - Zinc oxide: The proper name is Zinc(II) oxide since the charge on the zinc ion is +2.

Step 3: Calculate the percentage of oxygen by mass in both compounds and compare them

To calculate the percentage of oxygen by mass in both compounds, let's first find the molar mass of each compound and the molar mass of oxygen. For titanium dioxide (TiO\(_2\)): - Molar mass of Ti = 47.87 g/mol - Molar mass of O = 16.00 g/mol - Molar mass of TiO\(_2\) = Molar mass of Ti + 2(Molar mass of O) = 47.87 + 2(16.00) = 79.87 g/mol - Percentage of oxygen by mass in TiO\(_2\) = \(\frac{2 \times Molar \,mass \,of \,O}{Molar \,mass \,of\, TiO_2} \times 100\%\) = \(\frac{2 \times 16.00}{79.87} \times 100\% \approx 40.03\%\) For zinc oxide (ZnO): - Molar mass of Zn = 65.38 g/mol - Molar mass of ZnO = Molar mass of Zn + Molar mass of O = 65.38 + 16.00 = 81.38 g/mol - Percentage of oxygen by mass in ZnO = \(\frac{Molar \,mass \,of \,O}{Molar\, mass\, of \,ZnO} \times 100\%\) = \(\frac{16.00}{81.38} \times 100\% \approx 19.66\%\) Comparing the percentages of oxygen by mass in both compounds, we find that the titanium dioxide (TiO\(_2\)) contains a higher percentage of oxygen by mass (approximately 40.03%) than zinc oxide (ZnO) (approximately 19.66%).

Key Concepts

Molar Mass Calculation

Molar mass calculation is a crucial concept in chemistry that helps us determine the mass of a chemical compound based on its constituent elements. Molar mass is the sum of the relative atomic masses of the atoms in a compound's chemical formula. For example, in the case of titanium dioxide (TiO\(_2\)), we need to find the molar mass by adding the atomic masses of one titanium atom and two oxygen atoms.

• Molar mass of titanium (Ti) is 47.87 g/mol.
• Molar mass of oxygen (O) is 16.00 g/mol.

To find the total molar mass of TiO\(_2\), we add the molar mass of one titanium atom and double the molar mass of oxygen, making a total of 79.87 g/mol.
Similarly, for zinc oxide (ZnO), we calculate the molar mass by summing up the atomic masses of zinc and oxygen. The molar mass of zinc is 65.38 g/mol, while the molar mass of oxygen remains 16.00 g/mol, resulting in 81.38 g/mol for ZnO.
Through this method, you can calculate the molar mass of any compound by adding up the atomic masses of its elements according to their proportions in the chemical formula.

Chemical Nomenclature

Chemical nomenclature involves the systematic naming of chemical compounds in accordance with predefined rules. This helps clearly identify the composition and structure of a compound. The naming rules can differ based on the type of compound, such as ionic, covalent, or acid.For ionic compounds like titanium dioxide (TiO\(_2\)), the name is derived from the cation and anion present in the compound. In TiO\(_2\), titanium combines with oxygen, forming titanium(IV) oxide. The roman numeral IV indicates that titanium has a +4 charge.Zinc oxide (ZnO) follows the same rule, where zinc (Zn) combines with oxygen (O). In this case, zinc typically forms a +2 charge, leading to the systematic name zinc(II) oxide. Remember, the numeral II reflects the specific charge on the zinc ion, ensuring correct interpretation of the compound's structure.
Understanding these naming conventions is key to clearly communicating and understanding chemical formulas in scientific discussions and documents.

Percentage Composition

Percentage composition is a way to express the relative quantities of elements in a compound. It shows the percentage by mass of each element in the overall compound. To calculate it, divide the mass of each element by the total molar mass of the compound, then multiply by 100%.In titanium dioxide (TiO\(_2\)), the percentage composition of oxygen is calculated as follows:

• Mass of oxygen in TiO\(_2\) = 2 \(\times\) 16.00 g/mol = 32.00 g/mol.
• Total molar mass of TiO\(_2\) = 79.87 g/mol.
• Percentage of oxygen = \(\left( \frac{32.00}{79.87} \right) \times 100\% \approx 40.03\%\).

For zinc oxide (ZnO), the calculation would be:

• Mass of oxygen in ZnO = 16.00 g/mol.
• Total molar mass of ZnO = 81.38 g/mol.
• Percentage of oxygen = \(\left( \frac{16.00}{81.38} \right) \times 100\% \approx 19.66\%\).

These calculations highlight how each element contributes to the mass of the compound and allows for comparison. In our example, titanium dioxide has a higher percentage of oxygen compared to zinc oxide. Knowing percentage compositions is vital for many applications, including material science and formulation chemistry.