Problem 42 - Chemistry: The Central Science

Question

The iodine monobromide molecule, IBr, has a bond length of \(2.49 \AA\) and a dipole moment of \(1.21 \mathrm{D}\). (a) Which atom of the molecule is expected to have a negative charge? Explain. (b) Calculate the effective charges on the I and Br atoms in IBr, in units of the electronic charge \(e\).

Step-by-Step Solution

Answer

(a) The Bromine (Br) atom is expected to have a negative charge due to its higher electronegativity value (2.96) compared to Iodine (2.66). (b) The effective charges on the Iodine and Bromine atoms in IBr in units of the electronic charge (e) are approximately ±0.102e. The Iodine atom has a +0.102e (partial positive charge) and the Bromine atom has a -0.102e (partial negative charge).

Step 1: Determine Electronegativity of Iodine and Bromine Atoms

To find out which atom carries a negative charge, we need to compare the electronegativity values of the Iodine and Bromine atoms. Electronegativity is the ability of an atom to attract bond electrons towards itself. The atom with higher electronegativity will carry a partial negative charge due to its stronger attraction to the shared electrons in the bond. The electronegativity values for Iodine and Bromine are (according to Pauling Scale): - Iodine (I) = \(2.66\) - Bromine (Br) = \(2.96\) Since Bromine has a higher electronegativity value, it will have a partial negative charge, while Iodine will have a partial positive charge.

Step 2: Convert the bond length from Angstroms to meters

We are given the bond length between Iodine and Bromine atoms as \(2.49 \AA\). We need to convert this value to meters to use it in further calculations: \(1 \AA = 1\times 10^{-10}\) meters So, \(2.49 \AA = 2.49 \times 10^{-10}\) meters

Step 3: Convert the dipole moment from Debye to Coulomb meters

The dipole moment is given in Debye, and we need to convert it to Coulomb meters to use it in our calculations. The conversion factor is: \(1 D = 3.336\times 10^{-30} Cm\) So, \(1.21 D = 1.21\times 3.336\times 10^{-30} Cm\)

Step 4: Use the dipole moment formula to find the effective charges

The formula for the dipole moment (\(\mu\)) is: \(\mu = Q \times d\) Where: - \(\mu\) is the dipole moment (in Coulomb meters) - Q is the effective charge (in Coulombs) - d is the bond length (in meters) Now, we can solve for Q (effective charges): \(Q = \dfrac{\mu}{d}\) \(Q = \dfrac{1.21 \times 3.336 \times 10^{-30} Cm}{2.49 \times 10^{-10} m}\) Calculating the value of Q: \(Q = 1.628 \times 10^{-20} C\) Now, let's convert the charge into units of electronic charge (e): \(1e = 1.602\times10^{-19} C\) So, \(Q = \dfrac{1.628 \times 10^{-20} C}{1.602\times10^{-19} C/e}\) \(Q = 0.102e\) Thus, the effective charges on the Iodine and Bromine atoms in IBr in units of the electronic charge (e) are approximately ±0.102e. The Iodine atom has a +0.102e (partial positive charge) and the Bromine atom has a -0.102e (partial negative charge).

Key Concepts

Electronegativity

In chemistry, electronegativity is a fundamental concept when discussing how atoms interact within a molecule. Electronegativity refers to the ability of an atom to attract electrons towards itself in a chemical bond. This property is pivotal in determining which atom in a bond holds a partial negative charge.
A higher electronegativity means stronger attraction of electrons. Electronegativity values are assigned based on the Pauling scale, where larger numbers indicate higher electronegativities. For instance:

• Bromine (Br) has an electronegativity of 2.96.
• Iodine (I) has an electronegativity of 2.66.

In the case of iodine monobromide (IBr), bromine's greater electronegativity implies that it attracts electrons more strongly than iodine. Consequently, bromine acquires a partial negative charge, whereas iodine assumes a partial positive charge. This principle helps us understand the electron distribution in molecules and can predict molecular behavior.

Bond Length

Bond length is another key concept in understanding molecular structure. It is defined as the average distance between the centers of two covalently bonded atoms. Bond length is inherently connected to a molecule's geometry and can influence its dipole moment.
The bond length is typically measured in angstroms (\(\AA\)), where \(1 \AA = 1\times 10^{-10}\) meters. In the iodine monobromide (IBr) molecule, the bond length is \(2.49 \AA\). This means the I and Br atoms are \(2.49 \times 10^{-10}\) meters apart.
How the bond length interacts with other factors like molecular size and electron distribution impacts the physical and chemical properties of a compound. Shorter bond lengths often indicate stronger bonds, while longer bond lengths might be associated with weaker interactions.

Effective Charge

The concept of effective charge deals with the separation of electric charge within a molecule, which can be created due to differences in electronegativity. The effective charge reflects the represented charge on each atom of a molecule due to dipole formation.
For IBr, we use the formula for the dipole moment (\(\mu\)), defined as \(\mu = Q \times d\) (where \(Q\) represents the effective charge and \(d\) is the bond length). By calculating, \(Q = \dfrac{\mu}{d}\), we find the effective charge of IBr to be approximately \(\pm 0.102e\).
This result indicates iodine holds a +0.102e effective charge while bromine holds -0.102e, revealing the charge distribution in the molecule. This effective charge contributes to the dipole moment, showing how distinct amounts of charge influence molecular behavior.

Iodine Monobromide

Iodine monobromide is an interesting diatomic molecule often abbreviated as IBr. It involves a combination of iodine and bromine, forming a covalent bond. Each element contributes different properties, leading to unique molecular characteristics.
In IBr, bromine's higher electronegativity compared to iodine means bromine will attract more of the shared electrons, influencing the molecule's polarity. The dipole moment observed for IBr, calculated using its bond length and effective charges, is indicative of this polarity.
Understanding molecules like iodine monobromide sheds light on molecular chemistry concepts, such as how differences in atomic properties dictate the overall change in a molecule and its interactions with other substances.