Question

The compound \(\mathrm{Cr}\left(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\right)_{3}\) is used in the tanning of leather. How many atoms of each element are given in this formula?

Short answer

There is 1 atom of Cr, 6 atoms of C, 9 atoms of H, and 6 atoms of O.

Step-by-step solution

Identifying the Elements

First, identify the elements present in the compound: chromium (Cr), carbon (C), hydrogen (H), and oxygen (O).

Determining the Number of Each Atom

Next, look at the formula and find the subscript numbers after each element to determine the number of atoms present. For the chromium atom (Cr), there is no subscript, indicating there is one atom of chromium. For the acetate ion \(\mathrm{C}_{2} \mathrm{H}_{3}\mathrm{O}_{2}\), the subscript '2' indicates two carbon atoms, the subscript '3' indicates three hydrogen atoms, and the subscript '2' indicates two oxygen atoms per acetate ion.

Multiplying for the Entire Compound

Since there are three acetate ions as indicated by the subscript outside the parentheses, multiply the number of each atom (C, H, and O) in one acetate ion by 3 to get the total number of each in the compound.

Key concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships of the elements and compounds involved in chemical reactions. It is essentially the math behind chemistry, allowing us to understand and predict how different substances will react together. By applying the principles of stoichiometry, students can ascertain how much of a reactant is needed to produce a desired amount of product, or how much product can be expected from a given amount of reactant. In the context of the provided exercise, stoichiometry helps us understand the proportions of different elements in the compound used for tanning leather.

In practical terms, stoichiometry involves calculations based on the chemical formula, which tells us the ratio of elements in a compound. As shown in the solution, by analyzing the subscripts and coefficients in the formula \(\mathrm{Cr}(\mathrm{C}_{2} \mathrm{H}_{3}\mathrm{O}_{2})_{3}\), students can determine the exact number of atoms of each element present. In this case, stoichiometric principles allow us to conclude that the compound contains a total of one chromium atom, six carbon atoms, nine hydrogen atoms, and six oxygen atoms.

Molecular Composition

Understanding molecular composition is crucial for grasping the fundamental concepts of chemistry. It refers to the types and numbers of atoms that constitute a molecule. For every compound, its molecular composition is defined by its chemical formula. This formula provides invaluable information such as the exact number of atoms of each element within a single molecule.

For instance, the exercise uses the compound \(\mathrm{Cr}(\mathrm{C}_{2} \mathrm{H}_{3}\mathrm{O}_{2})_{3}\), which showcases the molecular composition clearly. Each element’s subscript in the formula represents the number of atoms in one of its molecules. However, when elements are within parentheses with a subscript outside, as with the acetate ion in the example, the subscript applies to everything within the parentheses. Hence, each acetate ion \(\mathrm{C}_{2} \mathrm{H}_{3}\mathrm{O}_{2}\) needs to be multiplied by the number three, since the subscript '3' indicates the presence of three such ions bonded with the chromium atom. This step is vital for accurately determining the total count of each type of atom within the whole compound.

Chemical Nomenclature

Chemical nomenclature is the system used for naming chemical substances. It is developed so that a chemical formula reflects not only the types of atoms present in a compound but also their relationships, such as the number of atoms of each element and the method used to bond them. Chemical nomenclature involves rules that allow chemists to derive a compound's name from its formula or vice versa. For students, mastering chemical nomenclature is a key step in understanding and communicating about different chemicals effectively.

In relation to the given exercise, the compound \(\mathrm{Cr}(\mathrm{C}_{2} \mathrm{H}_{3}\mathrm{O}_{2})_{3}\) is referred to as chromium(III) acetate. 'Chromium(III)' denotes the presence of chromium with a valency of three, and 'acetate' is the common name for the \(\mathrm{C}_{2} \mathrm{H}_{3}\mathrm{O}_{2}\) ion. The number '3' after the parenthesis indicates that there are three acetate ions bonded to the chromium atom. The nomenclature provides not only the composition but also hints at its three-dimensional structure, as the valency usually indicates the number of bonds an atom can make.