To identify the erroneous statements concerning geometrical isomerism, we shall examine each option:
- Statement (A): Propene exhibits geometrical isomerism.
Geometrical isomerism necessitates restricted rotation about a double bond and distinct substituents on the double-bonded carbons. Propene's structure is CH3-CH=CH2. One carbon of the double bond has a hydrogen and a methyl group, while the other has two hydrogen atoms. The presence of two identical hydrogen atoms on one double-bonded carbon precludes geometrical isomerism. Consequently, statement (A) is false. - Statement (B): A trans isomer features identical atoms or groups positioned on opposite sides of the double bond.
This assertion is accurate. In trans isomers, identical groups are located on opposing sides of the double bond, distinguishing them from cis isomers, where they are on the same side. - Statement (C): Cis-but-2-ene possesses a higher dipole moment than trans-but-2-ene.
Cis isomers typically exhibit larger dipole moments than their trans counterparts, owing to the additive effect of substituent polarities on the same side of the double bond. Thus, statement (C) is true for cis-but-2-ene and trans-but-2-ene. - Statement (D): 2-methylbut-2-ene displays two geometrical isomers.
The structure of 2-methylbut-2-ene is (CH3)2C=CH-CH3. Since one carbon of the double bond bears two identical methyl groups, geometrical isomerism is not possible. Therefore, statement (D) is false. - Statement (E): The trans isomer has a lower melting point than the cis isomer.
This statement is generally false. For most compounds, trans isomers exhibit higher melting points than cis isomers due to their more symmetrical structure, allowing for more efficient packing in the solid state. Statement (E) asserts the contrary, making it false.
Therefore, the false statements are (A), (D), and (E). The correct selection is:
(A), (D) and (E) only