The Gabriel phthalimide synthesis is used to prepare primary amines (R-NH2). Since the question asks for aromatic amines with the formula C8H11N, we need to consider isomeric primary aromatic amines.
The degree of unsaturation (DU) for C8H11N is:
\( DU = C + 1 - \frac{H - N}{2} = 8 + 1 - \frac{11 - 1}{2} = 9 - 5 = 4 \)
A DU of 4 suggests the presence of a benzene ring (DU = 4). This leaves us with C2H5 to account for. Since the Gabriel synthesis produces primary amines, the nitrogen must be attached to one of these carbons.
The possible isomers are:

Other dimethylanilines (like 3,4-dimethylaniline) are identical to the ones listed above. 2,6-dimethylaniline is the same as 2,3-dimethylaniline.
Therefore, there are 6 possible isomeric aromatic amines that can be synthesized by Gabriel phthalimide synthesis.
Which one of the following graphs accurately represents the plot of partial pressure of CS₂ vs its mole fraction in a mixture of acetone and CS₂ at constant temperature?

Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.