Question

Identify the incorrect statement among the following (b) The dipole moment of \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\) is greater than that of \(\mathrm{CH}_{3} \mathrm{Cl}\). (c) The cis isomers become increasingly less stable as the size of the \(\mathrm{R}\) groups increase. (d) Alkenes with two identical groups on the same doubly bonded carbon have no geometrical isomers.

Short answer

a) The exercise does not provide an incorrect statement. b) The dipole moment of CH₂Cl₂ is greater than that of CH₃Cl. c) As the size of R groups increases in cis isomers, the stability decreases. d) Alkenes with two identical groups on a doubly bonded carbon have no geometrical isomers. Answer: a) The exercise does not provide an incorrect statement.

Step-by-step solution

Statement (b)

Firstly, let's analyze the statement (b) about the dipole moment of \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\) and \(\mathrm{CH}_{3} \mathrm{Cl}\). Dipole moment is a measure of the polarity of a molecule, which is related to the electronegativity difference between the bonded atoms and their bond angles. \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\) is a tetrahedral molecule with two chlorine atoms and two hydrogen atoms bonded to a central carbon atom, whereas \(\mathrm{CH}_{3} \mathrm{Cl}\) is also a tetrahedral molecule with one chlorine atom and three hydrogen atoms bonded to a central carbon atom. Since chlorine is more electronegative than carbon and hydrogen, the polarities of \(\mathrm{C-Cl}\) bonds in both molecules are higher and cause a dipole moment. In the case of \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\), the dipole moments caused by two \(\mathrm{C-Cl}\) bonds are not exactly opposite, resulting in a net nonzero dipole moment. In the case of \(\mathrm{CH}_{3} \mathrm{Cl}\), the dipole moment is caused by the single \(\mathrm{C-Cl}\) bond. Comparing the two molecules, the net dipole moment of \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\) is indeed greater than that of \(\mathrm{CH}_{3} \mathrm{Cl}\). So this statement is correct.

Statement (c)

Now, let's examine statement (c) about the stability of cis isomers as the size of the \(\mathrm{R}\) groups increase. Cis isomers are geometrical isomers, where two identical functional groups are located on the same side of a double bond, while their trans counterparts have these groups on opposite sides of the double bond. It is well-known that as the size of the \(\mathrm{R}\) groups attached to the double bond increases, cis isomers tend to experience more steric hindrance, which in turn makes them less stable compared to their corresponding trans isomers. Therefore, this statement is also correct.

Statement (d)

Finally, let's analyze statement (d) which states that alkenes with two identical groups on the same doubly bonded carbon have no geometrical isomers. To clarify, a molecule has geometrical (cis/trans) isomers only if there is a possibility of varying the orientation of the functional groups on the double bond. In a molecule with two identical groups attached to the same doubly bonded carbon atom, there are no alternative orientations for the functional groups. Such a molecule does not have any geometrical isomers as a result. Therefore, this statement is also correct. Since statements (b), (c), and (d) are all correct, the incorrect statement is not provided. However, the given exercise states only to analyze the provided statements, so this conclusion is adequate.

Key concepts

Dipole Moment

The dipole moment is a vector quantity that measures the overall polarity of a molecule. It arises from differences in electronegativity between bonded atoms, which create positive and negative poles within the molecule. Interestingly, the geometry of a molecule greatly influences the net dipole moment. For example, let's consider molecules such as \(\mathrm{CH}_2\mathrm{Cl}_2\) versus \(\mathrm{CH}_3\mathrm{Cl}\). In \(\mathrm{CH}_2\mathrm{Cl}_2\), the molecule is tetrahedral with two \(\mathrm{C-Cl}\) bonds that add their dipole moments vectorially to result in a higher net dipole moment.

Conversely, \(\mathrm{CH}_3\mathrm{Cl}\) also has a tetrahedral shape but only one \(\mathrm{C-Cl}\) bond. The geometry and the vector addition of the bond dipole moments in \(\mathrm{CH}_2\mathrm{Cl}_2\) lead to a greater net dipole moment than that in \(\mathrm{CH}_3\mathrm{Cl}\), confirming our initial understanding. When imagining molecular polarity and dipole moments, visualizing molecular shapes and considering the vectors of each bond's polarity helps students grasp the concept more easily.

Steric Hindrance

Steric hindrance occurs when atoms or groups within a molecule are so close to each other that their electron clouds experience repulsion. This phenomenon becomes evident when discussing the stability of cis-trans isomers. In \(\mathrm{cis}\) isomers, the similar groups are on the same side, which can lead to increased steric hindrance, especially as the size of these groups grows. For students struggling with this concept, it might be helpful to think of steric hindrance as a 'crowding' effect that creates repulsion within a molecule. Larger groups take up more space, leading to greater repulsion and less stability in \(\mathrm{cis}\) isomers compared to their \(\mathrm{trans}\) counterparts that distribute the bulky groups more evenly on opposite sides of the double bond.

Cis-Trans Isomerism

Cis-trans isomerism is a type of geometrical isomerism that arises from the restricted rotation around a double bond. For a compound to exhibit cis-trans isomerism, each carbon in the double bond must have two different substituents. When both groups are on the same side, it is the \(\mathrm{cis}\) form; when on opposite sides, it is the \(\mathrm{trans}\) form. A crucial point for students to consider is that in order for geometrical isomers to exist, the groups attached to the carbons in the double bond must be different. This ties in with the given exercise, where statement (d) affirms that alkenes with two identical groups on the same doubly bonded carbon cannot have geometrical isomers. This statement holds true, simplifying the concept: if there's no difference in attached groups, there's no alternative spatial arrangement, and hence, no isomerism.