The dipole moment (μ) of HBr (a polar covalent molecule) is 0.838D (debye), and its percent ionic character is 12.4 %. Estimate the bond length of the H-Br bond in picometers.

Note that

1 D=3.34*10-30 C⋅m and

in a bond with 100% ionic character, Q=1.6*10-19 C.

When two electrical charges, of opposite sign and equal magnitude, are separated by a distance, a dipole is established. The size of a dipole is measured by its dipole moment (μμ). Dipole moment is measured in Debye units, which is equal to the distance between the charges multiplied by the charge (1 Debye equals 3.34*10-30Cm3.34*10-30Cm). The dipole moment of a molecule can be calculated by Equation 1.11.1:

μ = qr

where

μ⃗ μ→ is the dipole moment vector qiqi is the magnitude of the ithith charge, and r⃗ ir→i is the vector representing the position of ithith charge.

r = μ/q

r = [0.838D (3.34*10-30 C⋅m / 1D) ] / (1.6*10-19 C) * 0.124

r = 1.41 x10^-10 m