Question

Artificial Sweetener Some diet sodas contain the artificial sweetener aspartame, a compound containing carbon, nitrogen, oxygen, and other atoms. Create a table showing the atomic and ionic radii of carbon, nitrogen, and oxygen. (Assume the ionization states shown in Figure $6.14.$ ) Use the table to predict whether the sizes of carbon, nitrogen, and oxygen atoms increase or decrease in size when they form bonds in aspartame.

Short answer

In aspartame, the sizes of carbon, nitrogen, and oxygen atoms are predicted to increase when they form bonds. This is based on the ionic radii data for these elements, which are larger than their respective atomic radii, indicating electron gain and formation of ionic bonds.

Step-by-step solution

Find atomic and ionic radii of carbon, nitrogen, and oxygen

Using a periodic table or another resource, we'll look up the atomic and ionic radii of carbon, nitrogen, and oxygen. Keep in mind that the ionic radii of a non-metal element will be in its anionic state (the ionization state shown in Figure 6.14) * Carbon: Atomic radius = 77 pm, Ionic radius (C${}^{4-}$) = 260 pm * Nitrogen: Atomic radius = 75 pm, Ionic radius (N${}^{3-}$) = 171 pm * Oxygen: Atomic radius = 73 pm, Ionic radius (O${}^{2-}$) = 140 pm

Create a table with atomic and ionic radii

Now we'll create a table to display the atomic and ionic radii of carbon, nitrogen, and oxygen. | Element | Atomic Radius (pm) | Ionic Radius (pm) | |---------|--------------------|-------------------| | Carbon | 77 | 260 | | Nitrogen| 75 | 171 | | Oxygen | 73 | 140 |

Analyze radii values to predict atom size changes in aspartame

By observing the table, we can see that the ionic radii of carbon, nitrogen, and oxygen are larger than their respective atomic radii. When these atoms form bonds in aspartame, they will most likely form ionic bonds, as that is the most common type of bond formed by non-metallic elements. When forming ionic bonds, electrons are gained, which results in larger ionic radii compared to atomic radii. Therefore, based on the ionic radii data for carbon, nitrogen, and oxygen in the table, we can predict that the sizes of these atoms will increase when they form bonds in aspartame.

Key concepts

Understanding the Periodic Table

The periodic table is a systematic arrangement of elements according to their atomic numbers, which dictate the number of protons in an element's nucleus. This table is instrumental in understanding the properties of elements, including atomic and ionic radii. The atomic radius is a measure of the size of an atom, from the nucleus to the outermost electron shell. As we move from left to right across a period, the atomic radius generally decreases because, although the number of protons and electrons increases, the electrons are added to the same energy level while the increased nuclear charge pulls them closer to the nucleus.

Conversely, as we descend a group, the atomic radius increases. This is due to each element in the group having an additional electron shell compared to the one above it, making their overall size larger. Understanding these trends on the periodic table is crucial when comparing the atomic radii of carbon (C), nitrogen (N), and oxygen (O) as discussed in the exercise concerning aspartame's structure.

Chemical Bonds and Electron Configuration

Chemical bonds are the physical forces holding atoms together to form molecules. The major types of chemical bonds include ionic, covalent, and metallic bonds. Ionic bonds form between atoms that transfer electrons from one to another, resulting in positively and negatively charged ions. Covalent bonds, on the other hand, arise from the sharing of electron pairs between atoms.

In the context of aspartame's structure, knowing how ionic and covalent bonds affect atomic and ionic radii is key. Ions form when atoms gain or lose electrons, changing the balance between protons and electrons. For nonmetals, gaining electrons to form anions (negatively charged ions) typically results in a larger ionic radius compared to the atom's neutral state. This is due to the increased electron-electron repulsion in the anion, which allows the electron cloud to expand slightly.

The Structure of Aspartame

Aspartame is an artificial sweetener composed of amino acids, primarily aspartic acid and phenylalanine, which are linked together. Each of these amino acids features atoms of carbon, nitrogen, and oxygen, which are key to its structure. The exercise references these atoms' atomic and ionic radii because their size changes as they form chemical bonds within the aspartame molecule.

For instance, aspartame's molecular structure includes both ionic and covalent bonds. In the ionic states, as shown in the exercise, carbon would form a $C^{4-}$ ion, nitrogen a $N^{3-}$ ion, and oxygen an $O^{2-}$ ion when they gain electrons. These anionic forms are larger than their atomic radii because of increased electron repulsion, which pushes the electrons farther apart. This is an important consideration when predicting the behavior of these atoms within aspartame's molecular structure, as the ionization states influence the overall shape and function of the molecule.