Problem 77 - Chemistry The Molecular Nature of Matter

Question

How many atoms of each element are represented in each of the following formulas? For each, name the elements prescnt. (a) \(\mathrm{K}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) (b) \(\mathrm{H}_{2} \mathrm{SO}_{3}\) (c) \(\mathrm{C}_{12} \mathrm{H}_{26}\) (d) \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\), (e) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4}\)

Step-by-Step Solution

Answer

(a) 2 K, 2 C, 4 O; (b) 2 H, 1 S, 3 O; (c) 12 C, 26 H; (d) 2 C, 4 H, 2 O; (e) 2 N, 9 H, 1 P, 4 O

Step 1: Analyze Formula (a) \(\mathrm{K}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\)

To determine the number of atoms for each element in the given compound, count the subscript numbers for each element. For \(\mathrm{K}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\), there are 2 potassium (K) atoms, 2 carbon (C) atoms, and 4 oxygen (O) atoms.

Step 2: Analyze Formula (b) \(\mathrm{H}_{2} \mathrm{SO}_{3}\)

In the compound \(\mathrm{H}_{2} \mathrm{SO}_{3}\), there are 2 hydrogen (H) atoms, 1 sulfur (S) atom, and 3 oxygen (O) atoms.

Step 3: Analyze Formula (c) \(\mathrm{C}_{12} \mathrm{H}_{26}\)

The formula \(\mathrm{C}_{12} \mathrm{H}_{26}\) indicates there are 12 carbon (C) atoms and 26 hydrogen (H) atoms.

Step 4: Analyze Formula (d) \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\)

In the compound \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\), there are 2 carbon (C) atoms, 4 hydrogen (H) atoms (do not forget the first H at the beginning), and 2 oxygen (O) atoms.

Step 5: Analyze Formula (e) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4}\)

In the compound \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4}\), for the \mathrm{NH}_{4}\ group, we have 2 groups of ammonium \(\mathrm{NH}_{4}\) which gives us a total of 2 nitrogen (N) atoms and 8 hydrogen (H) atoms (as there are 2 \(\mathrm{NH}_{4}\) groups). Additionally, there is 1 phosphorus (P) atom and 4 oxygen (O) atoms present.

Key Concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships of the elements in chemical reactions. It is a fundamental concept that requires an understanding of the law of conservation of mass, which states that matter is neither created nor destroyed in a chemical reaction. Therefore, atoms are simply rearranged, and stoichiometry helps us determine how these atoms are rearranged and in what ratios.

For instance, if you're given the chemical formula \( \mathrm{K}_{2}\mathrm{C}_{2}\mathrm{O}_{4} \), stoichiometry allows you to quantify the atoms within the compound. By evaluating the subscripts (the small numbers that follow an element's symbol), we can calculate the molar ratios of elements which opens the door to various calculations. In practical scenarios, stoichiometry is applied whenever you need to calculate the amount of reactants required or products formed in a given reaction.

Molecular Composition

Understanding molecular composition is key to mastering chemistry. It's the identification of the elements and the number of each atom that make up a molecule. This also falls under quantitative properties - where the mass can be derived from the molecular composition.

Counting Atoms

Take, for example, the formula \( \mathrm{C}_{12}\mathrm{H}_{26} \). Here, the subscript '12' next to carbon (C) tells us there are twelve carbon atoms present in the molecule. The '26' next to hydrogen (H) informs us that there are twenty-six hydrogen atoms. This molecular composition, specifically the atomic ratio, speaks volumes about the structure and properties of the substance. For molecules like \( \mathrm{H}_{2}\mathrm{SO}_{3} \), not only do we see two atoms of hydrogen and three atoms of oxygen, but we also identify the central atom as sulfur, which holds significance in defining the molecule's geometry and reactivity.

Chemical Nomenclature

Chemical nomenclature is the systematic naming of chemical compounds based on their composition and structure. It provides a uniform way to refer to substances and is pivotal for communication within the scientific community. Taking our previous example \( \mathrm{HC}_{2}\mathrm{H}_{3}\mathrm{O}_{2} \), this compound is acetic acid, a name derived following specific rules of chemistry.

Each part of the name gives insight into the compound's structure and components. For example, the 'acet-' hints at the presence of a methyl group attached to a carboxylic acid function. The '-ic acid' indicates the compound is an acid with a certain group (carboxyl group in this case) at the highest oxidation state. The knowledge of chemical nomenclature is invaluable when interpreting chemical formulas and understanding the substances they represent.