Aniline forms diazonium salt with  $NaN{O}_2$/HCl, which gives orange-red dye with $\beta$-naphthol. What is the degree of unsaturation (DU) of the product (orange-dye)

The degree of unsaturation (DU) can be calculated as:

DU = C - (H/2) + (N/2) + 1, 
where C is the number of carbon atoms, H is the number of hydrogen atoms, and N is the number of nitrogen atoms in the compound.

The orange-red dye formed in this reaction is generally an azo compound, which has the structure:

Ar-N=N-Ar'

where Ar is the aromatic ring from aniline and Ar' is the aromatic ring from β-naphthol.

This structure involves two benzene rings (each contributing four degrees of unsaturation due to one ring and three double bonds each) and an azo group (-N=N-), which contributes one additional degree of unsaturation.

Thus, the total degree of unsaturation is: 
4 (benzene ring from aniline) + 4 (benzene ring from β-naphthol) + 1 (azo group) = 9 DU.