Identify the geometrical isomers of $2$-butene

Structure of $2$-butene is: $\mathrm{CH_3-CH=CH-CH_3}$

Since each carbon of the double bond has two different groups attached, it shows geometrical isomerism:

• cis-2-butene: both $\mathrm{CH_3}$ groups on the same side
• trans-2-butene: both $\mathrm{CH_3}$ groups on opposite sides

Check each statement

Option A:

"cis-2-butene and trans-2-butene are not interconvertible at room temperature."

Interconversion of cis and trans forms would require rotation about the $\mathrm{C=C}$ double bond, but rotation is restricted because of the $\pi$ bond.

Therefore, under normal conditions at room temperature, they are not interconvertible.

So, A is correct.

Option B:

"trans-2-butene is more stable than cis-2-butene."

In trans-2-butene, the two bulky $\mathrm{CH_3}$ groups are on opposite sides, so steric repulsion is less.

Hence, trans-2-butene is more stable than cis-2-butene.

So, B is correct.

Option C:

"cis-2-butene has less dipole moment than trans-2-butene."

In cis-2-butene, the bond dipoles do not cancel completely, so it has a non-zero dipole moment.

In trans-2-butene, due to symmetry, bond dipoles largely cancel out, so its dipole moment is very small (approximately zero).

Therefore: $\mu(\text{cis-2-butene}) > \mu(\text{trans-2-butene})$

The statement says cis has less dipole moment than trans, which is wrong.

So, C is incorrect.

Option D:

"cis-2-butene and trans-2-butene are stereoisomers."

Geometrical isomers are a type of stereoisomers because they differ in spatial arrangement of atoms.

So, D is correct.

Conclusion

The incorrect statement is: $\boxed{\text{C}}$