Problem 20 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following are arranged in the decreasing order of dipole moment? (a) \(\mathrm{CH}_{3} \mathrm{Cl}, \mathrm{CH}_{3} \mathrm{Br}, \mathrm{CH}_{3} \mathrm{~F}\) (b) \(\mathrm{CH}_{3} \mathrm{Cl}, \mathrm{CH}_{3} \mathrm{~F}, \mathrm{CH}_{3} \mathrm{Br}\) (c) \(\mathrm{CH}_{3} \mathrm{Br}, \mathrm{CH}_{3} \mathrm{Cl}, \mathrm{CH}_{3} \mathrm{~F}\) (d) \(\mathrm{CH}_{3} \mathrm{Br}, \mathrm{CH}_{3} \mathrm{~F}, \mathrm{CH}_{3} \mathrm{Cl}\)

Step-by-Step Solution

Answer

Option (b): \(\mathrm{CH}_{3}\mathrm{Cl}, \mathrm{CH}_{3}\mathrm{F}, \mathrm{CH}_{3}\mathrm{Br}\) is correct.

Step 1: Understand Dipole Moment

The dipole moment (\( ext{\boldsymbol{\vec{\mu}}}\)) is a vector quantity that measures the separation of positive and negative charges in a molecule. It depends on the difference in electronegativity between atoms and the distance of separation between them. Larger electronegativity differences and longer bond distances increase the dipole moment.

Step 2: Comparative Sizes and Electronegativity

The compounds given are \(\mathrm{CH}_{3}\mathrm{Cl}, \mathrm{CH}_{3}\mathrm{Br}, \mathrm{CH}_{3}\mathrm{F}\). Here, fluorine (F) has the highest electronegativity, followed by chlorine (Cl), and finally bromine (Br). However, the dipole moment is also influenced by bond length. F is smaller, resulting in shorter bond lengths compared to Cl and Br.

Step 3: Assess Bond Polarity and Dipole Impact

In \(\mathrm{CH}_{3}\mathrm{F}\), the bond polarity is the strongest due to F's high electronegativity, but the bond length is shortest. For \(\mathrm{CH}_{3}\mathrm{Cl}\), Cl is less electronegative than F but more than Br, and has a medium bond length. \(\mathrm{CH}_{3}\mathrm{Br}\), with the lowest electronegativity and largest bond length, has a smaller dipole moment compared to \(\mathrm{CH}_{3}\mathrm{F}\) and \(\mathrm{CH}_{3}\mathrm{Cl}\).

Step 4: Rank According to Decreasing Dipole Moment

Based on the combined effect of electronegativity and bond length, the decrease in dipole moment is: \(\mathrm{CH}_{3}\mathrm{Cl}, \mathrm{CH}_{3}\mathrm{F}, \mathrm{CH}_{3}\mathrm{Br}\), where \(\mathrm{CH}_{3}\mathrm{Cl}\) has the highest dipole moment due to a balance between bond length and electronegativity, followed by \(\mathrm{CH}_{3}\mathrm{F}\) and then \(\mathrm{CH}_{3}\mathrm{Br}\).

Step 5: Identify Matching Option

Review the options: (a) \(\mathrm{CH}_{3}\mathrm{Cl}, \mathrm{CH}_{3}\mathrm{Br}, \mathrm{CH}_{3}\mathrm{F}\); (b) \(\mathrm{CH}_{3}\mathrm{Cl}, \mathrm{CH}_{3}\mathrm{F}, \mathrm{CH}_{3}\mathrm{Br}\); (c) \(\mathrm{CH}_{3}\mathrm{Br}, \mathrm{CH}_{3}\mathrm{Cl}, \mathrm{CH}_{3}\mathrm{F}\); (d) \(\mathrm{CH}_{3}\mathrm{Br}, \mathrm{CH}_{3}\mathrm{F}, \mathrm{CH}_{3}\mathrm{Cl}\). The option \(\mathrm{(b)}\) has the correct order according to the explanation: \(\mathrm{CH}_{3}\mathrm{Cl}, \mathrm{CH}_{3}\mathrm{F}, \mathrm{CH}_{3}\mathrm{Br}\).

Key Concepts

Electronegativity

Electronegativity is a crucial concept in understanding molecular interactions. It is the property of an atom that indicates how strongly it attracts shared electrons in a chemical bond. The higher the electronegativity, the more an atom pulls the bonding electrons towards itself.
In the periodic table, as you move across a row from left to right, electronegativity generally increases. As you move down a group, it tends to decrease, though there are exceptions.

• Fluorine (F) is the most electronegative element, which makes its compounds notably polar.
• Chlorine (Cl) has a lower electronegativity than fluorine but is still higher than bromine (Br).
• Bromine (Br) has the least electronegativity amongst these three, making it the weakest in attracting bond electrons.

Understanding these trends helps predict the behavior of molecules. For instance, in the given molecules, CH₃F, CH₃Cl, and CH₃Br, the dipole moments are influenced by the differences in electronegativity between carbon and the halogen atoms involved.

Bond Length

Bond length is a fundamental factor that affects the dipole moment of a molecule. It is the average distance between the nuclei of two bonded atoms. This distance is influenced by the size of the atoms involved and the nature of the bond.
The size of the atom increases as you move down a group in the periodic table, leading to longer bond lengths. For example:

• Fluorine, being the smallest, forms the shortest bond.
• Chlorine, being larger than fluorine, forms moderately longer bonds.
• Bromine, the largest of the three, forms the longest bond.

The dipole moment of a molecule is directly proportional to both the difference in electronegativity and the bond length. Therefore, a balance between these two factors determines the dipole moment value for molecules like CH₃F, CH₃Cl, and CH₃Br. While CH₃F has a strong bond polarity due to fluorine's electronegativity, its short bond length can limit the dipole moment compared to CH₃Cl.

Molecular Polarity

Molecular polarity arises from the uneven distribution of electrons across a molecule, leading to the formation of partial positive and negative charges. Polarity is a key determinant in the physical properties and reactivity of a molecule.
Each CH bond in a molecule like CH₃F, CH₃Cl, or CH₃Br contributes to the overall dipole moment. However, the most significant contribution comes from the bond between carbon and the halogen atom (F, Cl, or Br).
In simple terms:

• When differences in electronegativity between the bonded atoms are significant, molecular polarity is strong.
• CH₃F shows strong bond polarity but shorter bond length, so its impact on the dipole may be less dominant in comparison to other molecules.
• CH₃Cl, with a moderate bond length and significant electronegativity difference, exhibits the highest dipole moment among the three.
• CH₃Br, with the least electronegativity difference and longest bond length, displays the lowest dipole moment.

Understanding molecular polarity not only helps in predicting molecular interactions but also assists in determining the order of dipole moments among related compounds.