Problem 52 - Chemistry The Central Science In Si Units

Question

How many of the indicated atoms are represented by each chemical formula: (a) carbon atoms in \(\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{COOCH}_{3}\), (b) oxygen atoms in \(\mathrm{Ca}\left(\mathrm{ClO}_{3}\right)_{2},(\mathbf{c})\) hydrogen atoms in \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4} ?\)

Step-by-Step Solution

Answer

(a) 5 carbon atoms; (b) 6 oxygen atoms; (c) 9 hydrogen atoms.

Step 1: Analyzing the Formula for Carbon Atoms

Identify the number of carbon atoms in the compound \( \mathrm{C}_{4} \mathrm{H}_{9} \mathrm{COOCH}_{3} \). The formula shows \( \mathrm{C}_{4} \) indicating 4 carbon atoms from the first section of the formula, and the "COOCH\(_3\)" segment adds 1 more carbon. Therefore, the total number of carbon atoms is \( 4 + 1 = 5 \).

Step 2: Determining Oxygen Atoms in the Compound

Examine \( \mathrm{Ca}\left(\mathrm{ClO}_{3}\right)_{2} \). The group \( \mathrm{ClO}_{3} \) contains 3 oxygen atoms. Since this group is inside the parentheses followed by a \(2\), multiply the oxygen count by 2: \( 3 \times 2 = 6 \) oxygen atoms are present.

Step 3: Calculating Hydrogen Atoms

Look at \( \left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4} \). Each \( \mathrm{NH}_{4} \) contains 4 hydrogen atoms, and the parentheses indicate there are 2 such groups, giving \( 4 \times 2 = 8 \) hydrogen atoms. Additionally, there is 1 more hydrogen atom from \( \mathrm{HPO}_{4} \), leading to a total of \( 8 + 1 = 9 \) hydrogen atoms.

Key Concepts

Carbon Atoms

Carbon atoms are fundamental to the structure of organic compounds. They are tetravalent, which means that each carbon atom can form four covalent bonds with other atoms. This makes carbon one of the most versatile elements, capable of forming long chains and complex rings. In the chemical formula \( \mathrm{C}_{4} \mathrm{H}_{9} \mathrm{COOCH}_{3} \), the indicated carbon atoms are found in two parts: the \( \mathrm{C}_{4} \) section and the "COOCH\(_3\)" part. The \( \mathrm{C}_{4} \) part directly tells us there are 4 carbon atoms. The additional carbon comes from the "COOCH\(_3\)" group, which contains 1 more carbon atom. Thus, we have a total of 5 carbon atoms in this molecule. Understanding the placement and count of carbon atoms helps in determining the molecular structure of a compound, influencing properties like volatility, solubility, and reactivity.

• \( \mathrm{C}_{4} \): 4 carbon atoms
• "COOCH\(_3\)": 1 additional carbon atom
• Total carbon atoms: 5

Oxygen Atoms

Oxygen atoms, with their ability to form two covalent bonds, are abundant in many compounds, especially those that are involved in biological and chemical processes. In the compound \( \mathrm{Ca}\left(\mathrm{ClO}_{3}\right)_{2} \), oxygen atoms are part of the \( \mathrm{ClO}_{3} \) group. Each \( \mathrm{ClO}_{3} \) contains 3 oxygen atoms. Since the formula indicates \( \left(\mathrm{ClO}_{3}\right)_{2} \), you multiply the number of oxygen atoms by 2, giving you \( 3 \times 2 = 6 \) oxygen atoms in total.
Understanding how to count oxygen atoms in chemical formulas is crucial in determining the oxygen content, and thereby the potential reactivity and interaction with other substances.

• Each \( \mathrm{ClO}_{3} \): 3 oxygen atoms
• Total groups: 2
• Total oxygen atoms: 6

Hydrogen Atoms

Hydrogen atoms are the simplest and most abundant chemical elements. Their presence in a molecule influences factors like acidity and basicity, as well as molecular shape and stability. In the formula \( \left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4} \), hydrogen atoms can be found in two places. The \( \mathrm{NH}_{4} \) part, known as the ammonium ion, provides 4 hydrogen atoms per group. Since there are 2 ammonium groups (as shown by the parentheses and the subscript \(2\)), this contributes \( 4 \times 2 = 8 \) hydrogen atoms. The \( \mathrm{HPO}_{4} \) component adds 1 more hydrogen atom, for a total of 9 hydrogen atoms. Counting hydrogen atoms is important for predicting chemical behavior, such as reaction pathways and energy content.

• \( \mathrm{NH}_{4} \) groups: 4 hydrogen atoms each
• Total \( \mathrm{NH}_{4} \) groups: 2
• Additional hydrogen from \( \mathrm{HPO}_{4} \): 1
• Total hydrogen atoms: 9