(c) The measured dipole moment of BrCl is 0.57 D. If you assume the bond length in BrCl is the sum of the atomic radii, what are the partial charges on the atoms in BrCl using the experimental dipole moment?

Verified step by step guidance

1. Identify the formula for dipole moment: \( \mu = q \times d \), where \( \mu \) is the dipole moment, \( q \) is the partial charge, and \( d \) is the bond length.
2. Convert the dipole moment from Debye to Coulomb-meters if necessary. Note that 1 D = 3.33564 \times 10^{-30} \text{ C}\cdot\text{m}.
3. Estimate the bond length \( d \) by adding the atomic radii of Br and Cl. Use a periodic table or a reliable source to find these values.
4. Rearrange the dipole moment formula to solve for the partial charge \( q \): \( q = \frac{\mu}{d} \).
5. Substitute the values of \( \mu \) and \( d \) into the equation to calculate the partial charge \( q \).

Key Concepts

Dipole Moment

The dipole moment is a vector quantity that measures the separation of positive and negative charges in a molecule. It is calculated as the product of the charge and the distance between the charges. In the case of BrCl, the dipole moment indicates the polarity of the bond, with a value of 0.57 D suggesting a significant difference in electronegativity between bromine and chlorine.

Partial Charges

Partial charges arise in polar covalent bonds when electrons are not shared equally between atoms due to differences in electronegativity. In BrCl, the chlorine atom, being more electronegative, will attract the shared electrons more strongly, resulting in a partial negative charge (δ-) on Cl and a partial positive charge (δ+) on Br. These charges can be calculated using the dipole moment and the bond length.

Bond Length and Atomic Radii

The bond length in a diatomic molecule like BrCl can be estimated by summing the atomic radii of the two atoms involved. The atomic radius is a measure of the size of an atom, typically defined as the distance from the nucleus to the outermost electron shell. For BrCl, using the atomic radii allows for an approximation of the distance over which the dipole moment acts, facilitating the calculation of partial charges.