Question #44546

An unknown aromatic amine $X$ (molecular formula \ce{C7H9N}) is dissolved in water to form a $0.10 \text{ M}$ solution at $300 \text{ K}$. The osmotic pressure of this solution is measured to be $2.46 \text{ atm}$ (Use $R = 0.082 \text{ L atm K}^{-1} \text{mol}^{-1}$). When $X$ is treated with \ce{NaNO2 / HCl} at $0-5^\circ\text{C}$ followed by alkaline $\beta$-naphthol, an intense orange-red dye is formed.

A student incorrectly assumes that the nitrogen lone pair in $X$ is fully localized (ignoring its resonance with the aromatic ring) and assigns it a hypothetical base dissociation constant $K_b = \frac{1}{900}$.

Based on this flawed assumption, what is the student's calculated osmotic pressure ($\pi_{\text{calc}}$), and what is the true identity of $X$?