Question

Which has maximum dipole moment?
A.

B.

C.

D.

Answer 1

Hint: Dipole moment describes the charge separation of the compound and it is denoted by symbol $\mu $. When the bond angle is given then we can use the formula:
$\mu =\sqrt{{{x}^{2}}+{{y}^{2}}+2xy\cos \theta }$

Complete step-by-step answer:
When a bond is formed between two atoms having a difference in electronegativity, then the electrons of the bond are slightly towards the atom having higher electronegativity. This is described by the dipole moment, which tells the charge separation between the atoms of the bond and it is denoted by the symbol $\mu $. It is shown by an arrow in which the head part is towards the more electronegative atom and the tail part is towards the less electronegative atom.
Now, in the options given in the question, there is the direction of the dipole moment and there is an angle between the atoms. So, we can use the formula:
$\mu =\sqrt{{{x}^{2}}+{{y}^{2}}+2xy\cos \theta }$
We can clearly see that the $\cos \theta $ decides the magnitude of the dipole moment.
In option (a), the angle between the dipole moments is ${{40}^{\circ }}$.
In option (b), the angle between the dipole moments is ${{90}^{\circ }}$.
In option (c), the angle between the dipole moments is ${{120}^{\circ }}$.
In option (d), the angle between the dipole moments is ${{180}^{\circ }}$.
The maximum value of $\cos \theta $ will be at ${{0}^{\circ }}$ because the its value is 1, and at ${{90}^{\circ }}$, the value of $\cos \theta $ is 0. Thereafter, on increasing the bond angle, the value will become negative.
Therefore, the lower the bond angle, the higher will be the dipole moment.

Hence the correct answer is an option (a).

Note: When the angle is ${{180}^{\circ }}$, which means one dipole moment is in the opposite direction of the other, then the dipole moment will cancel out each other, and the value will be zero.