The dipole moment (mu) of HBr (a polar covalent molecule) is 0.851 D (debye), and its percent ionic character is 12.6 %. Estimate the bond length of the H-Br bond in picometers.
151 pm
To estimate the bond length of the H-Br bond in picometers, we can use the relationship between the dipole moment and percent ionic character.
The dipole moment (μ) of a molecule is given by the formula:
μ = Q × d
where Q represents the charge and d represents the bond length. The dipole moment (μ) is a measure of the polarity of a molecule.
The percent ionic character is related to the dipole moment by the formula:
Percent Ionic Character = (μ/μionic) × 100
Here, μionic is the dipole moment of an ionic compound with the same atoms.
Given that the dipole moment (μ) of HBr is 0.851 D, and the percent ionic character is 12.6%, we can rearrange the formula to solve for the bond length (d) in picometers.
Step 1: Convert the percent ionic character from a percentage to a decimal:
Percent Ionic Character = 12.6% = 0.126
Step 2: Rearrange the formula to solve for the bond length (d):
d = μ / (Q × 0.126)
Since we don't have the charge (Q) or the dipole moment of an ionic compound (μionic) in this problem, we can't obtain an exact value for the bond length. However, we can estimate it using typical values.
For H-Br, the bond length is approximately 141 picometers (pm).
To estimate the bond length of the H-Br bond in picometers, we can use the relationship between dipole moment and percent ionic character.
The equation for percent ionic character (IC) is given by:
IC = ((mu^2) / (4.8 x δ^2)) x 100
Where:
mu is the dipole moment in Debye (D)
δ is the bond length in angstroms (Å)
Since we need to estimate the bond length in picometers (pm), we will convert it from angstroms later.
First, let's rearrange the equation to solve for the bond length (δ):
δ = sqrt((mu^2) / ((IC / 100) x 4.8))
Plugging in the given values:
mu = 0.851 D
IC = 12.6 %
Converting the percent to a decimal:
IC = 12.6 / 100 = 0.126
Substituting the values into the equation:
δ = sqrt((0.851^2) / ((0.126 / 100) x 4.8))
= sqrt(0.725601 / 0.0006048)
= sqrt(1200000)
= 1095.45 Å
Now, let's convert the bond length from angstroms to picometers:
1 Å = 100 pm
δ = 1095.45 Å x 100 pm/Å
= 109,545 pm
Therefore, the estimated bond length of the H-Br bond is approximately 109,545 picometers (pm).