Question

Which bond angle θ would result in the maximum dipole moment for the triatomic molecule $X{{Y}_{2}}$ ?
(A) $\theta ={{90}^{o}}$
(B) $\theta ={{120}^{o}}$
(C) $\theta ={{150}^{o}}$
(D) $\theta ={{180}^{o}}$

Answer 1

Hint: A dipole moment arises due to the electronegativity difference between the two elements of a bond. This means one of the atoms pulls the electron pair more toward itself than the other. Thus, it measures the polarity of a bond. It is a vector quantity. The greater the electronegativity difference between the two atoms, the greater the dipole moment of their bond.

Formula Used: The dipole moment is calculated as
$\mu =\sqrt{{{X}^{2}}+{{Y}^{2}}+2XY\operatorname{Cos}\theta }$; where $\theta $is the angle between the two dipoles.

Complete Step by Step Answer:
When we calculate the dipole moment from the above formula using$\theta ={{90}^{o}}$, the value of the dipole moment comes out to be $\mu =\sqrt{{{X}^{2}}+{{Y}^{2}}}$ as $\operatorname{Cos}{{90}^{o}}=0$. As the angle $\theta $ increases from${{90}^{o}}$, the value of cos $\theta $becomes negative, and hence the value of the dipole moment will decrease.

Hence, the bond angle $\theta ={{90}^{o}}$ would result in the maximum dipole moment for the triatomic molecule$X{{Y}_{2}}$.
Correct Option: (A) $\theta ={{90}^{o}}$.

Additional Information: For a diatomic molecule (example-$HCl,HF$ etc.), the dipole moment is calculated as the product of the magnitude of charge and the distance between the two atoms. For a polyatomic molecule (example-$N{{H}_{3}},C{{H}_{4}}$etc.), the net dipole moment is the vector sum of all the dipoles in a molecule.

Note: The unit of dipole moment is D (Debye). The values of the cosine of each of the angles should be known to answer the question. The cosine of ${{120}^{o}},{{150}^{o}}$ and ${{180}^{o}}$ are negative values.