Step 1: Analyze Statement (I).
As established previously, the C-Cl bond is more polar than the C-Br bond due to the higher electronegativity of chlorine. In the \( \textit{cis } \) isomers, the bond dipoles have a net vector sum, resulting in a polar molecule. Since the C-Cl bond is more polar, \( \textit{cis}-1,2-dichloroethene \) will have a larger net dipole moment and thus be more polar than \( \textit{cis}-1,2-dibromoethene \). Statement I is correct.
Step 2: Analyze Statement (II).
The first part of Statement II is correct: \( \textit{trans}-1,2-dibromoethene \) is nonpolar (due to the cancellation of bond dipoles), and \( \textit{cis}-1,2-dibromoethene \) is polar. Polar molecules generally have stronger intermolecular forces (dipole-dipole interactions) compared to nonpolar molecules (van der Waals forces of similar magnitude), leading to higher boiling points. Thus, the boiling point of \( \textit{trans}-1,2-dibromoethene \) is lower than that of \( \textit{cis}-1,2-dibromoethene \).
The second part of Statement II claims that \( \textit{cis}-1,2-dibromoethene \) is more polar than \( \textit{trans}-1,2-dibromoethene \). \( \textit{cis}-1,2-dibromoethene \) has a net dipole moment (it is polar), while \( \textit{trans}-1,2-dibromoethene \) has a zero net dipole moment (it is nonpolar). Therefore, \( \textit{cis}-1,2-dibromoethene \) is more polar than \( \textit{trans}-1,2-dibromoethene \).
However, the structure provided in Statement II has a typo. It shows \( \textit{trans}-1,2-dibromoethene \) being compared to another molecule that is also \( \textit{trans}-1,2-dibromoethene \), making the comparison meaningless. Assuming the second molecule in the polarity comparison was intended to be \( \textit{cis}-1,2-dibromoethene \), then the statement "it is more polar than \( \textit{trans}-1,2-dibromoethene \)" would be correct.
Given the figure as presented, Statement II makes an incorrect comparison for polarity. Therefore, Statement II is incorrect as written.
Step 3: Determine the correctness of both statements.
Statement I is correct, but Statement II is incorrect as presented in the figure.
Step 4: Choose the appropriate option.
The option that states Statement I is correct but Statement II is incorrect is (1).