Question

The experimental $\mathrm{Bi}-\mathrm{I}$ bond length in bismuth triiodide, ${\mathrm{BiI}}_3$, is $2.81\text{AA}$. Based on this value and data in Figure $7.7$, predict the atomic radius of $B$ i.

Short answer

The atomic radius of Bismuth (Bi) can be predicted using the given bond length of $\mathrm{Bi}-\mathrm{I}$ in ${\mathrm{BiI}}_3$ and the atomic radius of Iodine (I) from Figure 7.7. Using the bond length formula, we find that the predicted atomic radius of Bi is approximately $1.41\text{AA}$.

Step-by-step solution

Bond Length Formula

The bond length between two atoms in a compound can be estimated as the sum of their atomic radii. The bond length for $\mathrm{Bi}-\mathrm{I}$ in ${\mathrm{BiI}}_3$ can be represented as follows: Bond length = Atomic radius of Bi + Atomic radius of I Now, let's isolate the atomic radius of Bi in the formula: Atomic radius of Bi = Bond length - Atomic radius of I Since we know the bond length and will find the atomic radius of I, we can then compute the atomic radius of Bi.

Determine the Atomic Radius of Iodine

For this step, refer to the data provided in Figure 7.7. From the data, we find that the atomic radius of Iodine (I) is approximately $1.40\text{AA}$.

Calculate the Atomic Radius of Bismuth

Now that we have all the necessary data, we can calculate the atomic radius of Bismuth using the formula from Step 1: Atomic radius of Bi = Bond length - Atomic radius of I Plug in the given values: Atomic radius of Bi = $2.81\text{AA}-1.40\text{AA}$ Atomic radius of Bi = $1.41\text{AA}$ So, the predicted atomic radius of Bismuth (Bi) is approximately $1.41\text{AA}$.

Key concepts

Understanding Chemical Bond Length

Chemical bond length is a measure of the distance between the nuclei of two bonded atoms in a molecule. It's an essential aspect of understanding molecular geometry and plays a critical role in determining the physical and chemical properties of a compound.

When atoms connect to form molecules, they do so through bonds that have characteristic lengths, depending on the atoms and the type of bond formed. These bond lengths are usually tabulated based on experimental data or calculated using quantum chemical methods. In simple terms, the bond length can be seen as the sum of the atomic radii of the bonding atoms when the bond is a single covalent one.

Relevance in Predicting Atomic Radius

Knowing the bond length enables chemists to predict the atomic radius of an unknown atom in a compound if the radius of the other is known. It is a significant concept for students to grasp because it lays the foundation for predicting the shapes of molecules and understanding how molecules will interact with each other.

The Atomic Radius of Bismuth

The atomic radius of an element, like bismuth, is the distance from the center of its nucleus to the outer boundary of its electrons. Bismuth, with the chemical symbol Bi, is a heavy, brittle metal that is part of the p-block elements.

The atomic radius of bismuth can be influenced by several factors, including the number of electron shells, effective nuclear charge, and the presence of nearby atoms or ions. In metallic crystals like bismouth, atoms are arranged in a very compact and orderly pattern. As you encounter bismuth in chemical compounds, the atomic radius is used to assess the size of its atoms, which further helps in comprehending the structure of the compound and the interactions that may occur within it.

Atomic Radius in Predictions

Accurately predicting the atomic radius of bismuth is vital in understanding its reactivity and the nature of its bonds with other elements. It's this characteristic that enables us to use bismuth in various applications and to predict how it will behave in complex chemical reactions.

Examining the Atomic Radius of Iodine

Iodine is a halogen with the chemical symbol I, known for its significant role in the human thyroid gland. Its atomic radius plays a central role when it comes to forming compounds like bismuth triiodide.

To determine the atomic radius of iodine, scientists often employ x-ray crystallography or spectroscopic methods to gather data about the electron cloud's extension as it pertains to the iodine atoms in a molecule. In the case of iodine, atomic radius provides valuable insight into how the atom will form bonds and interact with other elements, influencing properties of the resulting molecules.

Importance in Molecular Formation

The knowledge of iodine's atomic radius is crucial for predicting and modeling molecular structures, polarizability, and how it participates in van der Waals interactions that underpin the physical basis for molecular recognition in chemical and biological systems.

The Structure of Bismuth Triiodide

Bismuth triiodide, or BiI3, is a compound composed of one bismuth and three iodine atoms. This compound crystallizes in a trigonal structure where each bismuth atom is surrounded by iodine atoms in a slightly distorted octahedral arrangement.

The structural composition of BiI3 is fascinating because it helps us understand the interaction between large atoms with a considerable number of electrons, such as bismuth and iodine. The bond lengths and angles within this compound can tell us a lot about the nature of the chemical bonds and how the compound will behave under different conditions.

Understanding Compound Characteristics

Studying the structure of bismuth triiodide offers insights into its properties, such as its color, solubility, and stability. The layout of atoms within its structure provides a basis for discussions on ionic vs. covalent character and introduces a deeper understanding of complex bonding in materials.