Question

The iodine monobromide molecule, IBr, has a bond length of \(2.49 \AA\) and a dipole moment of \(1.21\) D. (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, \(e\).

Short answer

The more electronegative atom in the IBr molecule is Bromine (Br), which is expected to have a negative charge. The effective charges on the Iodine (I) and Bromine (Br) atoms in IBr are +0.1018 e and -0.1018 e, respectively.

Step-by-step solution

1. Identify the more electronegative atom

Since electronegativity increases from left to right and from bottom to top in the periodic table, bromine (Br) is expected to be more electronegative than iodine (I). Thus, Br will have a partial negative charge, while I will have a partial positive charge. Answer to part (a): Bromine (Br) is expected to have a negative charge.

2. Calculate the bond dipole vector

The bond dipole vector (µ) can be calculated using the formula: \( µ = \frac{q \times r}{D} \) where q is the effective charge, r is the bond length, and D is the dipole moment. Given the dipole moment µ = 1.21 D and bond length r = 2.49 Å, we just need to convert the bond length to meters and the dipole moment to Coulomb meters: \( r = 2.49 × 10^{-10} m \) \( µ = 1.21 × 3.336 \times 10^{-30} C m \) Now we can calculate q: \( q = \frac{µ \times D}{r} = \frac{1.21 × 3.336 \times 10^{-30}}{2.49 × 10^{-10}} = 1.63 × 10^{-20} C \)

3. Express charges in terms of electronic charge e

The electronic charge is \( e = 1.602 \times 10^{-19} C \). To express the charges of I and Br in terms of e, we simply divide the effective charge q by e: \( q_{eff} = \frac{q}{e} = \frac{1.63 \times 10^{-20}}{1.602 \times 10^{-19}} = 0.1018 e \) Since Br has a partial negative charge, the effective charge on Br will be -0.1018 e, and the effective charge on I will be +0.1018 e. Answer to part (b): The effective charges on the I and Br atoms are +0.1018 e and -0.1018 e, respectively.

Key concepts

Electronegativity

Electronegativity is a measure of an atom's ability to attract and hold onto electrons when it forms a chemical bond. Picture it like a tug of war between atoms over a pair of electrons. The stronger player, or in our case the atom with higher electronegativity, will pull harder, gaining a bit of negative charge.

When two atoms in a molecule have different electronegativities, the shared electrons are pulled closer to the atom with the higher electronegativity. This uneven distribution of electrons leads to the creation of a dipole moment, with a partial negative charge at the more electronegative atom and a partial positive charge at the less electronegative one. In the case of iodine monobromide (IBr), bromine is the 'stronger player', so it carries a partial negative charge.

Bond Length

Bond length is the distance between the nuclei of two bonded atoms. It is determined by the size of the atoms involved and the type of bond they share. Think of it as the 'arm's length' at which two atoms are comfortable holding onto each other.

The distance not only defines the size of the molecule but also influences the strength of the bond and the magnitude of the dipole moment. The longer the bond, usually the weaker the bond is, and the dipole moment can change depending on how unevenly the electrons are shared across this distance. In our textbook problem, the bond length between iodine and bromine in IBr is given to be 2.49 Å, which is crucial information for calculating the dipole moment.

Electronic Charge

The electronic charge, often symbolized as 'e', is the basic unit of electric charge in an atom. It is carried by a single proton or a single electron, though the charge carried by an electron is considered negative.

In our problem, we equate different kinds of electric charge – from the macroscopic ones like Coulombs to the atomic-level ones, quantified in terms of the elementary charge. We deal with tiny effective charges on the atoms in a molecule, which are fractions of the electronic charge. Understanding how to switch between these scales is crucial for accurately calculating the charge distribution in a molecule.

Bond Dipole Vector

The bond dipole vector is a vector quantity that represents both the magnitude and the direction of the partial charges in a polar bond. Its direction points from the positive to the negative end of the dipole, and its magnitude is proportional to the product of the bond length and the amount of charge separation.

In the context of IBr, we calculate the bond dipole vector to understand the distribution of charges and the polarity of the molecule. The calculation done in the solution involves using the known bond length and electronic charge to figure out the effective charge on the atoms. Knowing how to visualize and quantify the bond dipole vector is essential for a deeper understanding of molecular polarity.