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Question: If the H-X bond length is 2.00\(\mathop A\limits^0 \) and H-X bond has dipole moment \(5.12 \times {...

If the H-X bond length is 2.00A0\mathop A\limits^0 and H-X bond has dipole moment 5.12×10−30Cm5.12 \times {10^{ - 30}}Cm , the percentage of ionic character in the molecule will be:
(A) 10%
(B) 16%
(C) 18%
(D) 20%

Explanation

Solution

The formula to find the % ionic character of the bond is
% Ionic character = Observed dipole momentTheoretical dipole moment×100\% {\text{ Ionic character = }}\dfrac{{{\text{Observed dipole moment}}}}{{{\text{Theoretical dipole moment}}}} \times 100

Complete step by step solution:
We need to find the % ionic character in a bond where the actual dipole moment and its bond length is given.
- There is a formula which relates the charge on the dipoles of a bond, its dipole moment and the bond length. The formula can be given as
Dipole moment = Charge×Bond length{\text{Dipole moment = Charge}} \times {\text{Bond length}}
We are given that the bond length of the H-X bond is 2.00A0\mathop A\limits^0 which is equal to 2.00×10−10m2.00 \times {10^{ - 10}}m as 1A0=10−10m1\mathop A\limits^0 = {10^{ - 10}}m .
We know that H-X bond is an ionic bond and H atom is positive charge and X atom has negative charge. The charge on them is +1 and -1 respectively.
- That means the charge on them is of one electron only and we know that the charge of one electrons is 1.6×10−19C1.6 \times {10^{ - 19}}C
So, we can say that the dipole moment of H-X bond will be 1.6×10−19×2×10−10=32×10−30Cm1.6 \times {10^{ - 19}} \times 2 \times {10^{ - 10}} = 32 \times {10^{ - 30}}Cm
So, we obtained that the theoretical dipole moment of the compound is 32×10−30Cm32 \times {10^{ - 30}}Cm. We are given that the observed dipole moment is 5.12×10−30Cm5.12 \times {10^{ - 30}}Cm. From this, we can find the % ionic character of the molecule by the formula below.
% Ionic character = Observed dipole momentTheoretical dipole moment×100\% {\text{ Ionic character = }}\dfrac{{{\text{Observed dipole moment}}}}{{{\text{Theoretical dipole moment}}}} \times 100
So, we can write that
% Ionic character = 5.12×10−3032×10−30×100=0.16×100=16%\% {\text{ Ionic character = }}\dfrac{{5.12 \times {{10}^{ - 30}}}}{{32 \times {{10}^{ - 30}}}} \times 100 = 0.16 \times 100 = 16\%
Thus, we can say that the ionic character of this H-X bond will be 16%.

So, the correct answer is (B).

Note: Do not get confused between the observed and the theoretic dipole moment of a bond. Theoretical dipole moment is the value we obtain from the equation by calculation. Observed or actual dipole moment is the dipole moment measured practically.