Problem 44 - Chemistry: The Central Science in SI Units, Global Edition

Question

The iodine monobromide molecule, IBr, has a bond length of \(249 \mathrm{pm}\) and a dipole moment of \(1.21 \mathrm{D} .(\mathbf{a})\) Which atom of the molecule is expected to have a negative charge? (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 atom is expected to have a negative charge. (b) The effective charges on the I and Br atoms in IBr are approximately 10.1e and -10.1e, respectively.

Step 1: (Step 1: Identifying Electronegativity of Atoms in IBr)

Determine the electronegativity of both Iodine (I) and Bromine (Br) atoms. From the periodic table, we have the following approximate electronegativity values: Iodine (I): 2.66 Bromine (Br): 2.96 Since Bromine is more electronegative than Iodine, the electrons in the I-Br bond will be closer to Bromine, making it slightly negatively charged.

Step 2: (Step 2: Finding the Direction of the Dipole Moment)

As we established in the previous step, Bromine is more electronegative than Iodine, and thus has a partial negative charge. This means that the dipole moment vector points towards the Bromine atom. Answer to part (a): Bromine atom is expected to have a negative charge.

Step 3: (Step 3: Converting Dipole Moment to SI Units)

The given dipole moment is in Debye (D), and we need to convert it to SI units (Coulomb meter, C m) before proceeding to the next step. The conversion factor is 1 D = \(3.336 \times 10^{-30}\) C m. Dipole moment in SI units: \(1.21 \, \mathrm{D} \times \frac{3.336 \times 10^{-30} C m}{1 \, \mathrm{D}} \approx 4.03 \times 10^{-30}\) C m

Step 4: (Step 4: Calculating Effective Charges in IBr)

To calculate the effective charges on Iodine and Bromine atoms in IBr, we will use the following equation for the dipole moment: \( \mathrm{Dipole\, moment} = \mathrm{Effective\, charge\, difference} \times \mathrm{Bond\, length} \) Let the effective charge on Iodine be \(q_I\) and on Bromine be \(q_{Br}\). Since the total charge of the molecule is neutral, we have: \(q_I + q_{Br} = 0 \) \( q_{Br} = -q_I \) Now, we plug the values for the dipole moment and bond length into the equation: \(4.03 \times 10^{-30}\, \mathrm{C\, m} = (q_{Br} - q_I) \times 249 \times 10^{-12}\, \mathrm{m} \) Rearrange and solve for \(q_I\): \(q_I = \frac{4.03 \times 10^{-30}\, \mathrm{C\, m}}{249 \times 10^{-12}\, \mathrm{m}} = 1.62 \times 10^{-18}\) C With \(q_{Br} = -q_I\), we have: \(q_{Br} = -1.62 \times 10^{-18}\) C Now, divide the effective charges by the electronic charge \(e (1.6 \times 10^{-19}\, \mathrm{C})\) to get the effective charges in units of e: \(q_I (e) = \frac{1.62 \times 10^{-18}}{1.6 \times 10^{-19}} \approx 10.1\, e \) \(q_{Br} (e) = \frac{-1.62 \times 10^{-18}}{1.6 \times 10^{-19}} \approx -10.1\, e \) Answer to part (b): The effective charges on the I and Br atoms in IBr are approximately 10.1e and -10.1e, respectively.

Key Concepts

Iodine Monobromide

Iodine monobromide, abbreviated as IBr, is a diatomic molecule comprising one iodine atom and one bromine atom bonded together. It is noteworthy due to its intermediate properties between iodine and bromine elements.

• Appearance: It appears as a red-brown solid under normal conditions.
• Bond Characteristics: The bond between iodine and bromine results from the attraction between their nuclei and shared electrons.

The molecular structure of IBr plays a significant role in determining its chemical behavior. It is characterized by a polar bond due to differences in electronegativity between iodine and bromine, affecting its physical properties such as its dipole moment.

Electronegativity

Electronegativity is an essential concept for understanding why atoms attract shared electrons differently in a chemical bond. It refers to the tendency of an atom to attract electrons towards itself when chemically bonded to another atom.

• Bromine Electronegativity: 2.96
• Iodine Electronegativity: 2.66

Because bromine has a higher electronegativity compared to iodine, it means that in the IBr molecule, electrons are more strongly attracted to the bromine atom. This results in bromine obtaining a partial negative charge while iodine gains a partial positive charge. The difference in electronegativity is what creates the molecule's dipole moment, pointing from iodine to bromine.

Bond Length

Bond length is a measure of the distance between the nuclei of two bonded atoms. For iodine monobromide, this length is critical in understanding the molecule's dipole moment.

• IBr Bond Length: 249 picometers (pm)

The bond length is influenced by the sizes of the iodine and bromine atoms. In general, longer bond lengths are weaker and typically found in molecules with larger atoms. In IBr, the bond length also plays a role in determining the dipole moment. The dipole moment is directly proportional to both the effective charge and the bond length. This means, for a given dipole moment, larger bond lengths may indicate smaller effective charges.

Effective Charge

Effective charge quantifies the net charge resulting from the imbalance of electron distribution in a molecule. In the context of the iodine monobromide molecule, this concept helps in determining the charge each atom appears to carry as a result of their differing electronegativities.Using the dipole moment equation:\[\text{Dipole Moment} = \text{Effective Charge Difference} \times \text{Bond Length} \]we calculated the effective charges:

• Effective Charge on Iodine: 10.1e
• Effective Charge on Bromine: -10.1e

These values are noted in terms of electronic charge units, where one electronic charge (e) equals \(1.6 \times 10^{-19}\) coulombs. The opposite signs indicate that the charges are balanced out in the molecule, with electrons being drawn more towards bromine, leaving iodine with an effective positive charge.