Problem 51 - Chemistry: The Central Science in SI Units, Global Edition

Question

How many hydrogen atoms are in each of the following: (a) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH},\) (b) \(\mathrm{Ca}\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{COO}\right)_{2}\), (c) \(\left(\mathrm{NH}_{4}\right)_{3} \mathrm{PO}_{4} ?\)

Step-by-Step Solution

Answer

In \(\mathrm{C}_{2}\mathrm{H}_{5} \mathrm{OH}\), there are 6 hydrogen atoms, in \(\mathrm{Ca}\left(\mathrm{C}_{2}\mathrm{H}_{5} \mathrm{COO}\right)_{2}\), there are 14 hydrogen atoms, and in \(\left(\mathrm{NH}_{4}\right)_{3}\mathrm{PO}_{4}\), there are 12 hydrogen atoms.

Step 1: Understanding chemical formulas

Chemical formulas represent the number of atoms of each element in a chemical compound. The subscript number next to the element symbol indicates the number of atoms for that element in the compound. If there is no subscript, it means there is only one atom of that element.

Step 2: Finding the number of hydrogen atoms in \(\mathrm{C}_{2}\mathrm{H}_{5} \mathrm{OH}\)

In \(\mathrm{C}_{2}\mathrm{H}_{5} \mathrm{OH}\), the subscript 5 after \(\mathrm{H}\) indicates that there are 5 hydrogen atoms in the ethyl group \((\mathrm{C}_{2}\mathrm{H}_{5})\). In addition, there is one hydrogen atom in the hydroxyl group \((\mathrm{OH})\). Thus, the total number of hydrogen atoms in the compound is: \[5 + 1 = 6\]

Step 3: Finding the number of hydrogen atoms in \(\mathrm{Ca}\left(\mathrm{C}_{2}\mathrm{H}_{5} \mathrm{COO}\right)_{2}\)

In this compound, the ethyl group \(\left(\mathrm{C}_{2}\mathrm{H}_{5} \mathrm{COO}\right)\) is within parentheses with subscript 2, meaning that there are two of this group in the compound. The ethyl group contains 5 hydrogen atoms, as indicated by the subscript 5 after \(\mathrm{H}\). There are also 2 hydrogen atoms in the carboxylate group \( (\mathrm{COO})\). Since there are two such groups in the compound, we multiply the number of hydrogen atoms in the ethyl group and carboxylate group by 2. The total number of hydrogen atoms in the compound is: \[(5 + 2) \times 2 = 14\]

Step 4: Finding the number of hydrogen atoms in \(\left(\mathrm{NH}_{4}\right)_{3}\mathrm{PO}_{4}\)

In this compound, the ammonium group \((\mathrm{NH}_{4})\) is within parentheses with subscript 3, indicating that there are three of these groups in the compound. There are 4 hydrogen atoms in the ammonium group, as indicated by the subscript 4 after \(\mathrm{H}\). Since there are three such groups in the compound, we multiply the number of hydrogen atoms in the ammonium group by 3. The total number of hydrogen atoms in the compound is: \[4 \times 3 = 12\] So, there are 6 hydrogen atoms in compound (a), 14 hydrogen atoms in compound (b), and 12 hydrogen atoms in compound (c).

Key Concepts

Hydrogen Atoms

Hydrogen atoms are often represented by the letter "H" in chemical formulas. They are the simplest and most abundant element in the universe. Each hydrogen atom consists of a single proton and electron, making it unique and essential in chemical compounds. Hydrogen is highly reactive and bonds easily with other elements. It forms various compounds, such as water (H₂O) and organic molecules like alcohols. In chemical formulas, knowing the number of hydrogen atoms helps in understanding the compound's composition and reactivity. For example, assessing the number of hydrogen atoms in substances like C₂H₅OH or NH₄, we get insights into their molecular structure and behavior.

Chemical Compounds

Chemical compounds are substances formed by the combination of two or more elements. These compounds can exhibit very different properties from the individual elements that compose them. In chemical compounds, elements are held together by chemical bonds, forming a unique chemical formula.

• Covalent bonds result from the sharing of electrons between atoms, as seen in water (H₂O).
• Ionic bonds occur from the transfer of electrons between a metal and a non-metal, such as in sodium chloride (NaCl).

Chemical compounds are identified and distinguished by their chemical formulas, which show not only the elements present but also their proportions. Chemical formulas like C₂H₅OH provide a blueprint of the molecules, indicating the number and types of atoms each consists of.

Subscripts in Formulas

The subscript in a chemical formula is crucial as it specifies the number of atoms of the element directly preceding it. For instance, in the formula C₂H₅OH, the subscript '5' tells us there are five hydrogen atoms as part of the ethyl group. When there's no subscript shown, it implies a single atom of that element.
Subscripts apply not just to individual elements but can also affect entire groups of atoms. In compounds like Ca(C₂H₅COO)₂, the subscript outside the parenthesis indicates that everything inside should be considered twice in terms of atom count.
Understanding subscripts is essential because they help define the precise makeup of a chemical formula, revealing the molecule's complexity and stoichiometry. Through subscripts, chemists can determine the exact number of each type of atom involved in a compound, aiding in calculations necessary for reactions and equations.