Question

How many of the indicated atoms are represented by each chemical formula: (a) carbon atoms in \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{COOCH}_{3}\), (b) oxygen atoms in \(\mathrm{Ca}\left(\mathrm{ClO}_{4}\right)_{2}\), (c) hydrogen atoms in \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4} ?\)

Short answer

(a) There are 4 carbon atoms in \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{COOCH}_{3}\). (b) There are 8 oxygen atoms in \(\mathrm{Ca}\left(\mathrm{ClO}_{4}\right)_{2}\). (c) There are 9 hydrogen atoms in \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4}\).

Step-by-step solution

(a) Counting carbon atoms in \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{COOCH}_{3}\)

To find the number of carbon atoms in this chemical formula, look for all the instances of "C" and note their subscripts. If no subscript is present, it defaults to 1. There are three instances of carbon: 1. \(\mathrm{C}_{2}\) has a subscript of 2, 2. \(\mathrm{C}\) (in \(\mathrm{COO}\)) has no subscript, so it defaults to 1, 3. \(\mathrm{C}\) (in \(\mathrm{CH}_{3}\)) has no subscript, so it defaults to 1. Sum up all of these subscripts: \(2 + 1 + 1 = 4\). So, there are 4 carbon atoms in this compound.

(b) Counting oxygen atoms in \(\mathrm{Ca}\left(\mathrm{ClO}_{4}\right)_{2}\)

To find the number of oxygen atoms in this chemical formula, look for all instances of "O" and note their subscripts, along with considering the number of times that section of the compound exists. The \(\mathrm{O}_{4}\) is within parenthesis which means we have \(\mathrm{ClO}_{4}\) present twice in the compound. Multiply the subscript of "O" (4) by the number of times the portion of the compound exists (2): \(4 \times 2 = 8\). So, there are 8 oxygen atoms in this compound.

(c) Counting hydrogen atoms in \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4}\)

To find the number of hydrogen atoms in this chemical formula, we need to identify all the instances of "H" and note their subscripts, along with considering the number of times that section of the compound exists. There are two instances of hydrogen: 1. \(\mathrm{H}_{4}\) (in \(\left(\mathrm{NH}_{4}\right)_{2}\)), which has a subscript of 4 and occurs twice, 2. \(\mathrm{H}\) (in \(\mathrm{HPO}_{4}\)) has no subscript, so the default is 1. Combine these instances of hydrogen: 1. \(\mathrm{H}_{4}\) occurs twice: \(4 \times 2 = 8\) 2. \(\mathrm{H}\) (in \(\mathrm{HPO}_{4}\)) occurs once: \(1 \times 1 = 1\) Sum up all of these instances: \(8 + 1 = 9\). So, there are 9 hydrogen atoms in this compound.

Key concepts

Chemical Subscript

Chemical subscripts are small numbers written to the bottom right of a chemical symbol in a molecular formula. They play a crucial role in interpreting the amount of atoms present in a compound. For instance, in the formula \(\mathrm{CO}_{2}\), the subscript '2' indicates the presence of two oxygen atoms.

When no subscript is mentioned, it's implied to be 1, as seen with the carbon atom in the compound \(\mathrm{CH}_{4}\), where carbon does not have a subscript and thus is present in a single quantity. It's worthwhile noting that when a chemical formula includes a group of atoms enclosed in parentheses with a subscript, the subscript applies to every atom within the parentheses. This is evident in \(\mathrm{Ca}\left(\mathrm{ClO}_{4}\right)_{2}\), where the subscript outside the parentheses determines that there are two groups of \(\mathrm{ClO}_{4}\), affecting the count of oxygen atoms.

Molecular Composition

Molecular composition describes the types and numbers of atoms that make up a molecule. To determine this, one examines the chemical formula and uses the information about chemical subscripts. The formula \(\mathrm{H}_{2}\mathrm{O}\) illustrates that water is composed of two hydrogen atoms and one oxygen atom.

The understanding of molecular composition is essential in chemistry because it lays the foundation for understanding properties, behaviors, and reactions between different substances. When chemicals react, they do so in fixed ratios determined by their molecular composition, which is why having a precise understanding is critical for predicting the outcomes of chemical reactions.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships of the reactants and products in a chemical reaction. It operates on the principle of the conservation of mass, where the total mass of the reactants equals the total mass of products.

The stoichiometric coefficients in a balanced chemical equation provide the ratio in which substances react and are formed. For example, the equation \(2 \mathrm{H}_{2} + \mathrm{O}_{2} \rightarrow 2 \mathrm{H}_{2}\mathrm{O}\) indicates that two molecules of hydrogen gas react with one molecule of oxygen gas to produce two molecules of water. Understanding stoichiometry is vital for calculating how much of each reactant is needed to produce a desired amount of product.

Atom Counting

Atom counting is a fundamental skill for understanding the composition of a molecule, particularly in complex structures. This process involves recognizing each atom and its corresponding subscript in the molecular formula.

For instance, in the compound \(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{COOCH}_{3}\), we tally carbon atoms by noting the subscript '2' next to the first 'C,' and then the single carbons without subscripts in the 'COO' and 'CH3' parts. As a result, we find four carbon atoms in total.

Mastering atom counting is essential for progressing into more advanced topics in chemistry, such as reaction stoichiometry and molecular geometry, where knowing the number of each type of atom is fundamental.