Problem 85 - Chemistry The Central Science

Question

The As\(-\)As bond length in elemental arsenic is 2.48 A. The \(\mathrm{Cl}-\mathrm{Cl}\) bond length in \(\mathrm{Cl}_{2}\) is 1.99 A. (a) Based on these data, what is the predicted \(\mathrm{As}-\mathrm{Cl}\) bond length in arsenic trichloride, \(A s C l_{3},\) in which each of the three Cl atoms is bonded to the As atom? (b) What bond length is predicted for \(A s C l_{3},\) , using the atomic radii in Figure 7.7?

Step-by-Step Solution

Answer

(a) The predicted As-Cl bond length in AsCl3 using the given bond lengths for As-As and Cl-Cl is \(2.235 \, \textup{Å}\). (b) The bond length for AsCl3 using the atomic radii from Figure 7.7 will be the sum of the atomic radii of As and Cl as provided in the Figure.

Step 1: Determine the atomic radii for As and Cl

To find the predicted bond length for As-Cl in AsCl3, we need to first determine the atomic radii for As and Cl. We can do this using the given bond lengths for As-As and Cl-Cl. Since the bond length is the sum of the atomic radii of the two bonded atoms, we can calculate the atomic radii as follows: - Atomic radius of As = As-As bond length / 2 = 2.48 Å / 2 = 1.24 Å - Atomic radius of Cl = Cl-Cl bond length / 2 = 1.99 Å / 2 = 0.995 Å

Step 2: Determine the predicted bond length for As-Cl in AsCl3

Now that we have the atomic radii for As and Cl, we can determine the predicted bond length for As-Cl in AsCl3 by simply adding the atomic radii together: - Predicted bond length for As-Cl = Atomic radius of As + Atomic radius of Cl = 1.24 Å + 0.995 Å = 2.235 Å

Step 3: Determine the bond length for AsCl3 using the atomic radii from Figure 7.7

Now, we will determine the bond length for AsCl3 using the atomic radii provided in Figure 7.7. Use the given atomic radii for As and Cl from Figure 7.7 (not provided in the problem, but assuming you have access to it) to find the predicted bond length for AsCl3: - Predicted bond length for As-Cl using Figure 7.7 atomic radii = Atomic radius of As + Atomic radius of Cl (from Figure 7.7)

Step 4: Final Answers:

(a) The predicted As-Cl bond length in AsCl3 using the given bond lengths for As-As and Cl-Cl is 2.235 Å. (b) The bond length for AsCl3 using the atomic radii from Figure 7.7 will be the sum of the atomic radii of As and Cl as provided in the Figure.

Key Concepts

Atomic Radii

Atomic radii are crucial for predicting bond lengths in molecules. The atomic radius is essentially the size of an atom from its nucleus to the outer boundary of its electron cloud. It helps us quantify the space an atom occupies within a molecule.

Determining atomic radii can be tricky since atoms do not have a firm border like a ball, but by examining the bond length between two identical atoms, we can deduce their individual radii. For arsenic (As) and chlorine (Cl), the bond lengths in molecules like elemental arsenic and chlorine gas give us a starting point.

For example, by investigating the As-As bond length of 2.48 Å in elemental arsenic, we can calculate the atomic radius of As as half of that length, that is 1.24 Å. Similarly, the Cl-Cl bond length of 1.99 Å in chlorine gas suggests an atomic radius for Cl of 0.995 Å.

Understanding atomic radii allows chemists to predict how different atoms will interact in a compound, which is a foundation for understanding molecular structures.

As-Cl Bond

The As-Cl bond in arsenic trichloride ( AsCl_3 ) can be predicted using atomic radii. This bond is the connection between arsenic and chlorine atoms, which is fundamental in molecular chemistry.

To predict the bond length of an As-Cl bond , we sum the atomic radii of As and Cl. We calculated these from their respective homonuclear bond lengths, which results in a predicted length of 2.235 Å for the As-Cl bond . This approach assumes the two radii add linearly to form the complete bond length because each atom contributes half of its measured diameter.

The calculation follows a straightforward method of adding 1.24 Å (atomic radius of As) with 0.995 Å (atomic radius of Cl). While simple, this is a powerful method for estimating the size of a bond, especially when direct measurement is not possible. By grasping the concept of As-Cl bonding, students gain insight into how molecular structures are assembled from smaller, calculable properties like atomic radii.

AsCl3

Arsenic trichloride ( AsCl_3 ) is a compound featuring a central As atom bonded to three Cl atoms. Its geometric and chemical characteristics are directly influenced by the atomic properties of its constituent elements.

In AsCl_3 , understanding the bond lengths is crucial since these affect the shape and reactivity of the molecule. The geometry is typically trigonal pyramidal due to AsCl_3 being a type of molecular geometry where arsenic forms three bonds at approximately 109.5° angles, resembling a pyramid.

The calculation of the theoretical As-Cl bond length, utilizing the radii of arsenic and chlorine, offers a basis for constructing molecular models. These models assist scientists and chemists in predicting how AsCl_3 might behave in different chemical reactions or environments.

This understanding contributes to broader insights about how asbestos applications, such as synthesis in labs and industrial uses, might interact at a molecular level.