Chemical BondinghardNUMERICAL

A hypothetical molecule exhibits a bent molecular geometry with a bond angle of exactly . If the indChemical Bonding Chemistry Question

Question

A hypothetical molecule $AB_2$ exhibits a bent molecular geometry with a bond angle of exactly $120^\circ$. If the individual bond dipole moment of each $A-B$ bond is $2.0 \text{ D}$, what is the magnitude of the resultant dipole moment of the entire molecule in Debye (D)?

Answer: 2

💡 Solution & Explanation

Dipole moment is a vector quantity. The resultant dipole moment $\mu_R = \sqrt{\mu_1^2 + \mu_2^2 + 2\mu_1\mu_2\cos\theta}$. Given $\mu_1 = \mu_2 = 2.0 \text{ D}$ and $\theta = 120^\circ$ ($\cos 120^\circ = -0.5$). Thus, $\mu_R = \sqrt{2^2 + 2^2 + 2(2)(2)(-0.5)} = \sqrt{4 + 4 - 4} = \sqrt{4} = 2.0 \text{ D}$.

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