Problem 139 - A Complete Resource Book in Chemistry for JEE Main

Question

The halogen form compound among themselves with the formula \(\mathrm{AA}, \mathrm{AA}_{3}, \mathrm{AA}_{5}\) and \(\mathrm{AA}_{5}\), where \(\mathrm{A}\) is the heavier halogen. Which of the following pairs representing their structures and being polar and non-polar are correct? 1\. AA, linear, polar 2\. \(\mathrm{AA}_{3}\), T-shaped, polar 3\. \(\mathrm{AA}_{5}\), square pyramidal, polar 4\. AA \(_{7}\), pentagonal bipyramidal, non-polar (a) 1 and 3 are correct (b) 1,2 and 3 are correct (c) 2,3 and 4 are correct (d) \(1,2,3\) and 4 are correct

Step-by-Step Solution

Answer

The correct pairs are 2, 3, and 4; choice (c) is correct.

Step 1: Analyze the Compound Structures

For each compound, identify the molecular geometry based on the number of atoms and the electron pairs. Use VSEPR (Valence Shell Electron Pair Repulsion) theory to predict the shapes. - **AA**: This diatomic molecule contains two atoms and is linear by default. - **AA3**: For a molecule like AA3 where one central atom is bonded to three other atoms and has two lone pairs, the shape is T-shaped. - **AA5**: In this compound, the central atom bonded to five others and one lone pair results in a square pyramidal structure. - **AA7**: With seven bonded atoms around a central atom and no lone pairs, the structure is pentagonal bipyramidal.

Step 2: Determine Polarity of Each Structure

Assess the polarity of each structure by examining the arrangement of bonds and lone pairs: - **AA (linear)**: The molecule is linear and would not be polar as the dipoles cancel out. - **AA3 (T-shaped)**: The shape is T-shaped and with dipoles not cancelling out makes it polar. - **AA5 (square pyramidal)**: This shape has an asymmetrical arrangement causing it to be polar due to lone pair influence. - **AA7 (pentagonal bipyramidal)**: Since the shape is symmetric with dipoles cancelling out, it is non-polar.

Step 3: Match Structures to Descriptions

The problem statement provides potential characteristics of the compounds to match: 1. AA, linear, polar 2. AA3, T-shaped, polar 3. AA5, square pyramidal, polar 4. AA7, pentagonal bipyramidal, non-polar According to our analysis from Steps 1 and 2: - AA is non-polar, thus statement 1 is incorrect. - AA3 is indeed T-shaped and polar. - AA5 is square pyramidal and polar. - AA7 is pentagonal bipyramidal and non-polar.

Step 4: Verify Correctness of Each Statement Pair

Evaluate which pairs of the statements (1, 2, 3, 4) conform to our analysis: - Statement 1 is incorrect; AA is non-polar. - Statement 2 is correct as AA3 is T-shaped and polar. - Statement 3 is correct; AA5 is square pyramidal and polar. - Statement 4 is correct; AA7 is pentagonal bipyramidal and non-polar. Thus, the correct pairs are 2, 3, and 4.

Key Concepts

Understanding VSEPR Theory

VSEPR theory, or Valence Shell Electron Pair Repulsion theory, is a model used to predict the geometry of molecules. This theory is based on the idea that electron pairs around a central atom will arrange themselves as far apart as possible to minimize repulsion.

• The number of electron pairs, including both bonding pairs and lone pairs, influences the shape of the molecule.
• For example, a molecule with two electron pairs, like in a diatomic molecule (0symbol{AA}), adopts a linear shape.
• When a central atom has three bonded pairs and two lone pairs, as in 0symbol{AA}_{3}, a T-shaped geometry forms.
• Molecules like 0symbol{AA}_{5}, with five bonded atoms and one lone pair, typically display a square pyramidal shape.
• A structure like 0symbol{AA}_{7}, involving seven atoms around a central atom and no lone pairs, results in a pentagonal bipyramidal configuration.

VSEPR theory is crucial for understanding molecular geometry, which directly influences the properties, including polarity, of a molecule.

The Role of Molecular Geometry

Molecular geometry concerns the three-dimensional arrangement of atoms in a molecule, which determines its shape. This arrangement affects how the molecule behaves and interacts with other molecules.

• Molecular geometry impacts the molecule's polarity, its boiling and melting points, and its general reactivity.
• Linear molecular geometry, as seen in diatomic molecules like 0symbol{AA}, typically results in a non-polar molecule.
• T-shaped geometry, like in 0symbol{AA}_{3}, contributes to a polar molecule due to the asymmetrical arrangement of polar bonds.
• For square pyramidal (0symbol{AA}_{5}) and pentagonal bipyramidal (0symbol{AA}_{7}) structures, the molecular shape dictates whether the molecule is polar or non-polar.

Understanding molecular geometry is essential for predicting molecular behavior and properties, particularly when analyzing complex structures.

Exploring Bond Dipoles

Bond dipoles occur in molecules where there is an unequal sharing of electrons between atoms with different electronegativities. This leads to a separation of charge, with one end of the bond being slightly negative and the other slightly positive.

• The magnitude and direction of each dipole can determine the overall polarity of a molecule.
• In a molecule like 0symbol{AA}_{3}, individual bond dipoles do not cancel out, leading to a polar molecule as the net dipole is non-zero.
• For 0symbol{AA}_{5}, asymmetry in the molecular geometry due to lone pairs results in a polar molecule.
• However, in 0symbol{AA}_{7}, the symmetrical pentagonal bipyramidal arrangement allows bond dipoles to cancel, making it non-polar.

Considering bond dipoles is crucial when assessing the polarity of molecular structures and their intermolecular interactions.

Lone Pairs Impact on Molecular Polarity

Lone pairs of electrons affect the shape and, consequently, the polarity of a molecule. They occupy more space than bonding pairs because their electron cloud is less constrained, leading to distortions in molecular geometry.

• Lone pairs on a central atom can cause bond angles to decrease, altering the molecular geometry from expected symmetrical shapes.
• In 0symbol{AA}_{3}, the presence of two lone pairs results in a T-shaped geometry, creating a polar molecule.
• With 0symbol{AA}_{5}, one lone pair leads to a square pyramidal shape; this asymmetry makes the molecule polar.
• Lone pairs influence molecular polarity significantly, as seen in molecules with asymmetric shapes where dipoles don't cancel.

Understanding the effect of lone pairs is key when analyzing molecules, as they can be the determining factor in molecular polarity and reactivity.