A hypothetical covalent molecule, X–Y, has a dipole moment of 1.62 D and a bond length of 179 pm. Calculate the partial charge on a pole of this molecule in terms of e (where e is the charge on an electron).
To calculate the partial charge on a pole of a molecule, you need to use the equation:
μ = q × d
Where:
μ is the dipole moment of the molecule (in Debye, D)
q is the magnitude of the partial charge (in e)
d is the bond length (in meters)
First, we need to convert the dipole moment from Debye (D) to Coulomb meters (C·m) using the conversion factor: 1 D = 3.336 × 10^-30 C·m.
Given:
μ = 1.62 D
d = 179 pm = 179 × 10^-12 m
Converting μ from D to C·m:
μ = 1.62 D × 3.336 × 10^-30 C·m/D ≈ 5.401 × 10^-30 C·m
Now we can rearrange the equation to solve for q:
q = μ / d
Substituting the values we have:
q = 5.401 × 10^-30 C·m / (179 × 10^-12 m) ≈ 3.02 × 10^-19 C
To express the charge in terms of e (charge on an electron), we need to divide by the elementary charge (e ≈ 1.602 × 10^-19 C):
q = (3.02 × 10^-19 C) / (1.602 × 10^-19 C/e) ≈ 1.885 e
Therefore, the partial charge on a pole of this molecule is approximately 1.885 times the charge on an electron (e).